inverse rendering: from concept to applications

EUROGRAPHICS 2006 Tutorial

Inverse Rendering: From Concept to Applications

Celine Loscos1 and Katrien Jacobs1 and Gustavo Patow2 and Xavier Pueyo2

1Virtual Environment and Computer Graphics lab, UCL2Girona Graphics Group, Universitat de Girona

AbstractInverse problems are usually of extreme complexity and are an important research topic for the graphics com-munity due to their wide applicability. Those problems are considered for which the input data is captured fromreality with a camera, so it is possible to extract information about the scene illumination, reflectance properties,or geometry. Unfortunately, sometimes standard techniques fail due to practical issues: uncertainty in acquisi-tion methods, dynamic behaviors, complexity of the scene and approximate geometrical or lighting model. Thiscourse not only aims at the presentation of the fundamental principles behind inverse rendering problems, but alsopresents some practical considerations that arise in some applications, explains the new problems introduced andshows adequate solutions. In the introduction, a review is given of the course objectives, the context and some ofthe prerequisites, e.g. a general definition of global illumination. The first part of the course gives a definition ofinverse rendering, and presents a selection of inverse rendering solutions present in the literature. The second partof the course, describes practical methods that can be used in specific applications of inverse rendering. Retrievingreflectance and illumination properties of an existing site is of interest in areas as post-production, architecturaland urban planning, and interior lighting design. Modeling geometric properties of an object based on illumina-tion output can be used in the design of reflectors in the car industry or urban lighting design. The course is givenas a lecture and is supported by slides and videos. Material created by the course organizers and coming fromother sources is used to illustrate the ideas presented in the course. At the end of the course, attendees will have agood understanding of inverse rendering problems, and be able to select a method from the literature to apply toa specific application.

1. Outline

1. Introduction2. Inverse Rendering Definition

2.a.Theoretical Background2.b.Problem Classification2.c.Characterization of existing techniques2.d.General solutions/approaches

i. State of the art in Inverse Lightingii. State of the art in Inverse Reflectometryiii. State of the art in Inverse Surface De-

sign

3. Applications to Inverse Lighting

3.a.General problems for complex scenes3.b.Postproduction: capturing HDRIs for out-

door scenes

3.c.Urban planning: simulating common illu-mination

3.d.Indoor Lighting Design

4. Applications to Inverse Geometry

4.a.Numerical Aspects of Inverse Surface De-sign

4.b.General design of reflectors4.c.User-guided design of reflectors

5. Conclusion and future work

2. Necessary background

The attendees of the course need to have a minimum levelof understanding in Mathematics (equations, integrals, andderivatives) and a general knowledge of computer graph-ics and some understanding of the global illumination meth-

c© The Eurographics Association 2006.

http://www.eg.org

http://diglib.eg.org

C. Loscos, K. Jacobs, G. Patow, X. Pueyo / Inverse Rendering: From Concept to Applications

ods. In the introduction of the course, these prerequisites arebriefly reviewed.

3. Resume of the presenters

Celine Loscos

University College London, Virtual Environment and Com-puter Graphics lab; contact: [email protected]

Celine Loscos joined the Department of Computer Sci-ence at UCL in 2000 as a post-doc, after completing herPhD on interactive relighting for augmented reality (1999,IMAG-INRIA, France). Since 2001, she has been a lecturerin department and teaches computer graphics to undergrad-

uate and postgraduate students. She is part of Virtual Envi-ronments and Computer Graphics (VECG) laboratory. Herresearch focuses on real-time rendering, animation and inter-action in complex environments for mixed reality on whichshe has co-authored papers published in IEEE, ACM and EGconferences/journals.

Katrien Jacobs

University College London, Virtual Environment and Com-puter Graphics lab; contact: [email protected]

Katrien Jacobs graduated as a Electrical Engineer at theKatholieke University of Leuven (ESAT-KUL), Belgium, in2002 and started her PhD in Computer Science at University


C. Loscos, K. Jacobs, G. Patow, X. Pueyo / Inverse Rendering: From Concept to Applications

College London (UCL) in 2003. Her work includes devel-oping common illumination and relighting solutions for dif-ficult to capture and model environments. Recent publishedwork includes a survey on illumination methods for mixedreality in Computer Graphics Forum. She is supervised byDr. Celine Loscos.

Gustavo Patow

Universitat de Girona, Girona Graphics Group; contact: [email protected]

Gustavo Patow got a degree in physics from the Universi-dad de La Plata, Argentina, and got his PhD at the Universi-tat Politècnica de Catalunya at Barcelona, Spain, under thesupervision of Xavier Pueyo and Àlvar Vinacua. His thesistopic was the inverse design of reflector surfaces for lumi-naire design, and his current research continues in the in-verse rendering set of problems. He currently holds an asso-ciate professor position at the Universitat de Girona, Spain.

Xavier Pueyo

Universitat de Girona, Girona Graphics Group; contact:[email protected]

Xavier Pueyo received a PhD in Engineering from Uni-versitat Politecnica de Catalunya (UPC), Spain, in 1986 andthe degree of Docteur Ingenieur in Computer Sciences fromUniversite de Rennes I, France, in 1984. He is a professorof Computer Sciences at the Universitat de Girona (UdG),Spain, since 1996 and he has been the dean of its Schoolof Technology. He taught Computer Sciences (Programmingand Computer Graphics) at UdG from 1993 to 1996 and atUPC from 1988 to 1993 as an associate professor. His re-search interest includes computer graphics, realistic com-puter rendering and visualization. Pueyo has chaired theEurographics Rendering Working Group and the SpanishChapter of Eurographics.


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1


Celine LoscosKatrien Jacobs

Virtual environments and Computer Graphics Lab, UCL

Xavier PueyoGustavo Patow

Grup de Gràfics de Girona

This course is presented by Celine Loscos and Katrien Jacobs from the VECG graphics lab at University College London and Xavier Pueyo and Gustavo Patow from the Graphics Group in Girona. The topic of this course is Inverse Rendering: from concepts to applications.

2


Introduction

3

Direct Rendering

CameraCamera

GeometryGeometry

Materials (BRDF)Materials (BRDF)

Light SourcesLight Sources

++

++

++

== ImageImage

When the camera position, the scene geometry, materials in the scene and the light source positions and intensities are given, an image can be create of that scene, under the current illumination properties and from the given camera viewpoint using the radiance equation. This is how rendering works.

4

Inverse Rendering• Goes the other way round:

– from Image + some extra info, infer the other missing parameters

• Depending on the available information, we face different problems:– one vs. many images of the scene – known vs. unknown real geometry– known vs. unknown lighting– known vs. unknown material properties– exact or approximate information

Inverse rendering goes the other way around, based on an image and some extra information, the missing information in the radiance equation can be calculated. Depending on the amount/type of information available, different strategies apply to calculate the missing information.

5

Information availability• Geometry information from:

– 3D Scanner– Photogrammetric techniques– Primitives

• BRDF information from:– Known light probe → pure specular (when building the HDR image)– Known materials for some surfaces

• Lighting information from:– Known, calibrated light sources– HDR image from a light probe (computed as a preprocessing step)

Various ways exist to calculate/retrieve geometric, BRDF and illumination information.

6

Inverse Rendering: Classification

• image + geometry → camera parameters– (camera calibration: Well known problem)

• image → geometry – (photogrammetry)

• image + geometry + BRDF → lighting – (inverse lighting)

• image + geometry + lighting → BRDF/textures – (inverse reflectometry)

• image + geometry → BRDF + lighting– (inverse combined problem)

• image + lighting + BRDF → geometry– (inverse surface design)

As mentioned earlier, based on the type/amount of missing information in the radiance equation, a certain strategy applies to retrieve the missing information. On this slide some of these different strategies are listed. For instance when an image and the geometry of a scene are given, the camera properties can be calculated, this type of problem is labelled “Camera calibration”.

7

Example Application: Relighting1. Insert new virtual elements2. Remove some real elements3. Change real/virtual object placement4. Change lighting conditions5. Change viewpoint6. …

Inverse rendering can be used to perform relighting. Relighting a scene, means that virtually new elements can be added to an existing scene, it can also mean that some existing objects are virtually removed. For each of these cases, relighting will calculate the illumination changes due to the addition or removal of these objects in the scene. An extreme example of relighting is that the scene is virtually ‘relit’ using a completely different illumination distribution than the one present in the real scene.

8

Example Application: Reflector Design

• Design of reflector shapes from prescribed optical properties and geometrical constraints.

• Constraints on the shape imposed by industry needs must be taken into account.

Another application of Inverse rendering is reflector design.

9

Problems with Real Inverse Rendering

Unfortunately, sometimes standard techniques fail:

1. Uncertainty in acquisition methods2. Dynamic behaviors3. Approximate geometrical model

• not completely modeled• coarsely modeled

4. Approximate lighting model• light sources known only approximately

There are some well-known problems with performing inverse rendering. These problems are mainly a result of the failure to capture/model accurately the scene parameters, such as geometry, radiance distribution and light sources.

10

Solutions ?• Dynamic Scenes:

– Automatic HDRI generation of dynamic Environments [Jacobs-Ward-Loscos-05]

• Approximate geometry and/or approximate light sources– Automatic generation of consistent shadows

[Jacobs-et al.-05]

• Unknown or approximate geometry– Reflector Design from Radiance Distributions

[Patow-Pueyo-Vinacua-04]– User-guided Inverse Reflector Design

[Patow-Pueyo-Vinacua-TR05]

• …

Some solutions are given in the literature to overcome these problems. Some of these solutions are listed on this slide; they will be discussed throughout this course.

11

Outline


The following slides detail the outline of this talk.

12


1. Inverse Rendering Definition1. General definition of inverse rendering & characterization of

existing techniques2. General solutions/approaches

First a definition is given of inverse rendering; this section consists of three subsections. First a general definition of inverse rendering is given Followed by a characterization of the existing techniques And finally some general solutions and approaches will be described After this section, the course attendee will have a good understanding of the concept ‘inverse rendering’ and know which solutions exist and can be applied based on the problem at hand.

13


1. Inverse Rendering Definition2. Applications to Inverse Lighting

1. General problems for outdoor scenes 2. Postproduction: capturing HDRI for outdoor scenes 3. Urban planning: simulating common illumination 4. Indoor Lighting Design

After the break, a first set of applications of inverse rendering are presented, more precisely those related to inverse lighting. This second session consists out of 4 different subsections. Each will be presented and illustrated with demos in the form of videos.

14


1. Inverse Rendering Definition2. Applications to Inverse Lighting3. Applications to Inverse Geometry

1. General design of reflectors2. User-guided design of reflectors

The third section discusses the applications related to inverse geometry. This section consists out of two subsections, and each will be presented in more detail, and illustrated with some demos/videos.

15


1. Inverse Rendering Definition2. Applications to Inverse Lighting3. Applications to Inverse Geometry4. Conclusion and Future Work

Finally a conclusion and an overview of the future work is given.

16

General definition of Inverse Rendering Problems

Gustavo PatowXavier Pueyo

Grup de Gràfics de GironaUniversitat de Girona

Image courtesy of Ravi Image courtesy of Ravi RamamoorthiRamamoorthi

In this part of the tutorial we will introduce a general definition and a classification of Inverse Rendering Problems.

17

Context: Inverse problems

• In general, they are of an extreme complexity

• Unfortunately, they are important – e.g.: for lighting engineering, lighting design,

animators and lighting for films• Research in graphics has focused mainly

on Direct/Forward Problems– Compute the radiance distribution from a

known environment

Inverse problems are usually of an extreme complexity and are emerging as an important research topic for the graphics community due to their interest in a wide range of fields including lighting engineering and lighting design. Even animators and lighting experts for the film industry would also highly benefit from them. Although progress in rendering to date has mainly focused on improving the accuracy of the physical simulation of light transport and developing algorithms with better performance, some attention has been paid to the problems related to inverse analysis, leading recently to very interesting results. Traditional forward problems in lighting involve the computation of the radiance distribution in an a priori, completely known environment (geometry and materials).

18

Inverse Rendering definition

• Inverse Rendering Problems refer to all the problems where – Some aspects of the scene are unknown– We know in advance the desired illumination

at some surfaces of the scene• The algorithm has to work backwards to

establish the missing parameters

Inverse Lighting Problems refer to all the problems where, as opposed to what happens with traditional direct lighting problems, some aspects of the scene are unknown. One common characteristic of this kind of problem is that, in general, we know in advance the desired illumination at some surfaces of the scene (their final appearance). Therefore, the algorithm has to work backwards to establish the missing parameters, which would produce the desired illumination.

19

Estimating BRDF and Lighting (I)

Photographs

Geometric model

ForwardForwardRenderingRenderingAlgorithmAlgorithm

Rendering

Lighting

BRDF

Courtesy of Ravi Courtesy of Ravi RamamoorthiRamamoorthi

To illustrate this, we can see a simple example. Given a known geometric model like this cat, with completely known material properties, (that is, with known BRDF), under controlled lighting conditions, it can be rendered to a picture like the one shown above (bottom-left side of the slide). Forward or direct rendering aims at making this photograph indistinguishable from the one above, taken with a real camera from a cat figurine.

20

Estimating BRDF and Lighting (II)

Photographs

Geometric model

InverseInverseRenderingRenderingAlgorithmAlgorithm

Lighting

BRDF


Instead, if we only know the geometric model and some photographs, we can work the other way round, and try to approximately infer the BRDF and/or the lighting conditions. This process is known as an inverse lighting, inverse reflectometry or a combined problem depending on what we want to find out. We can say that inverse problems infer parameters of a system from observed or desired data, which define their behavior, in contrast to direct problems which, given all the parameters, simulate the effects.

21

Estimating BRDF and Lighting (III)

Photographs

Geometric model

ForwardForwardRenderingRendering

(Relighting)(Relighting)

Rendering

Novel lighting

BRDF


Now, with the resulting information from the inverse problem, we can generate new images of the cat with different lighting and viewing conditions. Often, this process is called relighting.

22

From now on

• We have introduced the problem• Now, we will

– Explain the theoretical background• Introducing our main classification• Presenting the problems behind Inverse

Rendering– Explain alternative classifications to

enrich our view of the problems

23

Theoretical background

• Global Illumination• Most fundamental magnitude: radiance L(r,ω)• The boundary conditions of the integral form of

the transport equation are expressed as

iiiS re dLfLL ωθωωωωω cos),'(),(),(),( rrrr →+= ∫

θ

fr (r, ωi→ω)

L(r,ω)

rω

ωi

L(r',ωi)SS

Here we are in the context of the global illumination framework, where the most fundamental magnitude to work with is the radiance L. The equation that describes the boundary conditions of the integral form of the transport equation are expressed as that equation in the slide. Here, what we are saying is that the radiance leaving any point in the scene is the sum of the emittance of that point plus all the light that arrives at that point from the other surfaces in the scene, modulated by the material properties of the surface that contains the point, called the Bidirectional Reflectance Distribution Function, or BRDF for short. This equation is called “the rendering equation”. Now, we are going to introduce a couple of operators to write it in a clearer and shorter way for our purposes.

24

• Let's define it as [Marschner98]

• With dμ(ωi)=cosθ dωi

• maps incident light distribution onto the corresponding exiting light distribution resulting from one local reflection

Local reflection operator K)

)(),();(),)(( iiiS r dhfhK ωμωωωω rrr →≡ ∫)

K)

ω

rr

Firstly, let’s introduce the Local Reflection Operator K, which maps the incident light distribution onto the corresponding exiting light distribution resulting from one local reflection. As we can see, this operator takes the integral part of the Rendering Equation in the previous slide. [Marschner98]

25

Field radiance operator• Let's define it as

• Where ν(r,ω) is the visible surface functionν(r,ω) ≡ inf{x>0: r+xω ∈ Surfaces in the env.}

• And the ray casting functionp(r,ω) ≡ r + ν(r,ω) ω

G)

⎩⎨⎧ ∞<

≡otherwise

whenhhG

0),( )),,((

),)((ωνωω

ωrrp

r)

Now, let’s introduce the Field Radiance Operator G, which determines what is seen from a point in the scene in a given direction. Basically, it provides information on the nearest point in the scene, given a starting point and a desired direction. In order to do its job, it needs the definition of the Visible Surface Function, which, by the way, is not a continuous function. This Visible Surface Function, in turn, needs the definition of the ray casting function, which we see at the bottom of the slide

26

Final expression

• We can write the rendering equation as:

• Which leads us to our main classification

LGKLL e

))+=

So, we finally can write the rendering equation as this short expression. With this expression, and following Stephen Marschner’s work, we will be able to introduce our main classification.

27

Forward rendering

• Solve for L

Source

BRDF

Reflector

IlluminationDistribution

LGKLL e

))+=

LL

K)

G)

LLee

Direct problems are those which, given known values for Le, K and G, solve for L. But, if we only have some knowledge of L, and some of the other parameters, we can pose different kinds of inverse lighting problems.

28

Inverse lighting

• Solve for Le

Source

BRDF

Reflector


LGKLL e

))+=

LL

K)

G)

LLee

If Le is unknown, and K, G and L or part of it, are known, we have a problem of inverse lighting: given a photograph or any other information that covers part of L, and a complete model of the scene (K and G), find the emittances (Le) of the luminaries illuminating the scene.

29

Inverse reflectometry• Solve for K (BRDFs & textures)

Source

BRDF

Reflector


LGKLL e

))+=

LL

K)

G)

LLee

If K is unknown, and G, Le and part of L are known, we must solve for information about K. This problem can, in general, be called inverse reflectometry, and a particular case is the one called image-based reflectometry in [Marschner98], where images are used as input of the information about L. As described there, since K includes information about the variance of the reflectance both spatially and directionally, this can be a very difficult problem since it can be a complex function. Depending on the constraints imposed on the problem, we can subdivide it into the inverse texture measurement (constraints on the directional variation), or the inverse BRDF measurement (spatial uniformity is assumed).

30

Combined problems

• Solve for Le and K

Source

BRDF

Reflector


LGKLL e

))+=

LL

K)

G)

LLee

If we solve for both Le and K, we are talking about a combined problem, which are more difficult because of the relationships in the simulation process.

31

Inverse surfaces

Source

BRDF

Reflector


• Solve for G LGKLL e

))+=

LL

K)

G)

LLee

Finally, if G is unknown, we have an inverse geometry problem, where we want to find a shape from the effect it produces in the scene illumination. Quite often, this surface is called a reflector.

32

√??partialCombined Problems

Inverse Geometry

Inverse Reflectometry

Inverse Lighting

Direct Problems

?√√√

√?√partial

√√?partial

√√√?

GKLeL

Classification ofInverse Rendering Problems

LGKLL e

))+=

In general, we can build the following table, which shows what we have to know and what we want to find out for each kind of problem. As we can see, in Inverse Lighting, Inverse Reflectometry and combined problems we can have only partial information about the scene lighting, but Inverse Geometry problems are of such complexity that, we need to know the full illumination information.

33

Inverse Problems: Difficulties

Angular width of Light SourceAngular width of Light Source

Surf

ace

roug

hnes

sSu

rfac

e ro

ughn

ess

IllIll--posedposed(ambiguous)(ambiguous)


Now, let’s study the difficulties related to inverse rendering problems. As we can see from the slide, if we start with a highly specular surface and a point light source (bottom left figure), we see that we can perfectly identify the material and the shape of the source. The same happens when we increase the size of the source (bottom row, from left to right). On the other hand, if we start from the first situation, and we change the surface roughness, we get more and more blurred versions of the point light source. The problem is that, in general, we can not distinguish between the situations when the light source is larger with a specular BRDF, and the case when the BRDF is diffuse but the light is a point light. Even worse, as both the BRDF goes diffuse AND the light source gets bigger (softer lighting), we loose the capability of distinguishing which case we are facing. We see that the problem of recovering the information becomes more and more ambiguous, which in mathematical terms means that we have an ill-posed problem.

34

Inside the Rendering Equation (I)

• Let's peek at some details inside the equation

• Following [Ramamoorthi-Hanrahan01], we can absorb the cosθ into the BRDF, and if we assume the surfaces do not emit


iiiS r dLfL ωωωωω ),'(),('),( rrr →= ∫

To have a more precise understanding on the problems we face in Inverse Rendering problems, let's peek into the rendering equation. Following Ramamoorthi and Hanrahan's work, we can include the cos θ term into the BRDF, and if we assume the surfaces do not emit (that is, Le is zero for the surfaces we are studying), we get to a slightly simplified expression, the one shown in the bottom of the slide.

35

• From now on, let's work on a given vertex• And assume distant illumination• Let's write the lighting as

with Ylm aSpherical Harmonic

Inside the Rendering Equation (II)

)()(0

il

l

lmlmlmi YLL ωω ∑ ∑

∞

= −=

=

In order to continue our study, we can work on a vertex in isolation, so we don't need to worry about positional problems. Also, we will assume a distant illumination, which will make our formulation independent of the evaluation position on the surface. We always will be able to express all the quantities as an expansion in terms of basis functions. In this case, we will use spherical harmonics, which form an orthonormal basis in terms of which functions on the sphere can be expanded. The first few function of this basis is shown in the picture. We first expand the lighting in global coordinates, arriving at the expression in the slide.

36

• Do the same with the (isotropic) BRDF:

• And with the reflected light field

• With Λl = sqrt(4π / (2l + 1))• And Rlmq(n) the rotation coefficients

about the surface normal n.

Inside the Rendering Equation (III)

∑=→qpl

pqilqpqlqir YYff,,

*, )()(')(' ωωωω

)()(),(,,,

1opq

qpmllmqllmpqo YRBB ωω ∑ −Λ= nn

Isotropic

Anisotropic

We now represent the transfer function f' = f cosθi in terms of spherical harmonics. We note that f' is nonzero only over the upper hemisphere, i.e. when cos θ > 0 and cos θi > 0. We also use a complex conjugate for the first factor, to simplify the final results. If we assume we are dealing with isotropic BRDFs, which are those where rotating the local tangent frame makes no difference, we get the expression in the slide for f'. Proceeding similarly with the reflected light field, we arrive at the expression in the slide. We may observe that the Rlmq(n) are the rotation coefficients for the spherical harmonicas to accommodate the reference frame to local coordinates given by the local surface normal n.

37

• Putting it all together into the equation, we get

Blmpq= ΛlLlmf'lpq

• As we see, we have a "simple" system of algebraic equations

• (which, of course, is not "simple" at all)

Inside the Rendering Equation (IV)

Putting all together, comparing both expressions and equating coefficients, we arrive at this "simple" expression in the frequency-space domain, as the spherical harmonics we are using are the equivalent, for the sphere, to a Fourier analysis in 2D space. In frequency-space, the reflected light field is obtained simply by multiplying together coefficients of the lighting and BRDF, i.e. by convolving the incident illumination with the BRDF. Looking at this, we could think that this system of equations is easy to solve, but, as we hinted a few slides ago, it is not simple at all!

38

• Inverse BRDF:f'lpq= Λl

-1Blmpq/Llm

– We can see that BRDF recovery is well-posed unless the denominator vanishes

– But, if Llm vanishes, Blmpq has to vanish too to be physically accurate, and the RHS will be indeterminate

– It's ok, as long as, for all l, there is at least one value of m so that Llm ≠ 0

• Thus, BRDF recovery is well-conditioned when lighting contains high frequencies(e.g: directional sources)

• And is ill-conditioned for soft lighting

Inside the Rendering Equation (V)

Following [Ramamoorthi02] – Observing the expression resulting for f'lpq, we see that the BRDF estimation process will be well-posed (that is, unambiguous) as long as the denominator on the right-hand side does not vanish. But we must take into account that, in order to be physically accurate, the numerator will also be 0 if the denominator vanishes, as there won't be any reflected light field for that order of the expansion. In this case, the right-hand side will become indeterminate. From the equation in the slide, we see that if, for all l, there exists at least one value of m so that Llm = 0, then the problem of BRDF estimation is well posed. In other words, all orders in the spherical harmonic expansion of the lighting should have at least one coefficient with nonzero amplitude. If any order of the expansion completely vanishes, then we will find we won't be able to estimate the corresponding BRDF coefficients. In signal processing terms, if lighting, which is the input signal, has no amplitude along certain modes of the BRDF (our filter), those modes cannot be estimated. We can say that, when the spherical harmonic expansion of the lighting does not decay rapidly with increasing frequency, the BRDF recovery problem is well conditioned. This is telling us that, when the lighting contains high frequencies like directional sources or sharp edges it is well-conditioned. On the other hand, it is ill-conditioned for soft lighting. We can see that the equation in the slide gives a precise

mathematical characterization of the BRDF estimation problem, telling us when it is well-posed and when not.

39

• Inverse Lighting:Llm= Λl

-1Blmpq/f'lpq

• We can see lighting recovery is well-posedunless the denominator vanishes for all p,q for some l

• Thus, lighting recovery is well-conditioned when the BRDF contains high frequencies(e.g.: sharp specularities)

• And is ill-conditioned for diffuse surfaces

Inside the Rendering Equation (VI)

Continuing with the analysis presented in [Ramamoorthi02], now with respect to the Inverse Lighting problem. We can see that this problem will be well-posed when the denominator does not vanish for all p, q for some l. This means that the spherical harmonic expansion of the BRDF transfer function contains at least one non-zero value for all orders. If we resort again to the signal processing framework, we see that, when the BRDF filter truncates certain frequencies in the input lighting signal, we cannot determine those frequencies from the output signal (our reflected light field). This happens, for instance, if the BRDF acts as a low-pass filter. We can see that Inverse lighting is well-conditioned when the BRDF contains high-frequencies: when its frequency spectrum decays slowly. So, we conclude that inverse lighting is well-conditioned when the BRDF contains sharp specularities, like a mirror surface in the ideal case. On the other hand, inverse lighting from diffuse surfaces is ill-conditioned. We can explain that noting that highly specular surfaces act as high-pass filters, so the resulting images have most of the high frequency content in the lighting. In that case, the lighting can be estimated. On the contrary, diffuse surfaces blur the illumination, making it difficult or impossible to recover the high frequencies. We can say that they act as low-pass filters.

40

• Combined Inverse Problems:– The same way, we can see that, up to a global scale,

the reflected light field can be factored into the lighting and the BRDF

– (if the appropriate coefficients do not vanish)

• Inverse Surface Design:– Extrapolating the analysis, we can infer that, as the

BFDR goes more diffuse, surface recovery becomes harder, reducing convergence of any algorithm we could invent

Inside the Rendering Equation (VII)

Having analyzed estimation of the BRDF and lighting alone, we can extend the analysis to the problem of factorizing the light field, i.e., simultaneously recovering the lighting and BRDF when both are unknown. The main result is that the reflected light field can be factored into the lighting and the BRDF, provided the appropriate coefficients of the reflected light field do not vanish, i.e. the denominators above are nonzero. If the denominators do vanish, the inverse-lighting or inverse-BRDF problems become ill-posed and consequently, the factorization becomes ill-posed. We can also extrapolate the reasoning to the Inverse Surface Design problem, and we can infer that, as the BRDF goes more and more diffuse, the recovering of a surface becomes more difficult, obviously reducing the convergence of any algorithm we could invent.

41

Up to now

• Now, we have presented our main classification based on the compact version of the Rendering Equation

• And we have seen the problems involved in Inverse Rendering

LGKLL e

))+=

Up to now we have presented our main classification based on a compact form of the rendering equation, and we have presented the main problems involved in Inverse Rendering problems.

42

Alternative classifications

• But the one presented is not the only possible classification we can use, but is the main one

• Alternative classifications can be introduced to enrich our view of the problems and their solutions

Now, we are going to present some alternative ways of classification of the problems, as the one presented is not the only one we can use. Of course, it will be our main one, but other possible classifications will help us to enrich our view of the problems we are facing and their solutions.

43

Alternative Classification:Nature of the solving algorithm

• Direct-solving– Avoid solving the forward problem at any time– Mostly based on the construction of a linear system of

equations, and solving it– Others use a direct measuring approach– A few use Monte Carlo methods

• Indirect-solving– Based on an optimization procedure– Require the solution of a forward problem at least

once per iteration• Mixed

– A combination of both

We can present an alternative classification based on the nature of the solving algorithm used. Some of the algorithms are called "direct solving" methods, because they avoid solving the forward rendering problem at all. Most of these approaches build a linear system of equations, trying to solve them, while others take direct measurements of the available information and, finally, there are a few that are based on Monte Carlo methods. Other algorithms are "Indirect-solving" approaches, which need to compute, at least once per iteration, a forward solution to the problem. Those approaches are generally based on an optimization procedure. Finally, we can mention the "mixed" approaches, which are a mixture of the other two, estimating some parameters by direct computation, while leaving others for an optimization process.

44

Alternative Classification:Approximations to the equation

• Each approach needs to define how they treat the global illumination equation:

• General– General solution independent of any light propagation algorithm

• Radiosity– Diffuse surfaces, patches with constant radiance

• Monte Carlo– Firing rays from “known surfaces” towards “unknown surfaces”,

gathering information to integrate results• Local Illumination

– Only taking into account pathsemitter → surface → registration system (eye)


Another factor to take into account is whether the different papers treat the full rendering equation, or a simpler version based on a simplification of the illuminating equation. Basically, we can mention four main approaches: firstly, the general methods, which are independent of the lighting computation procedure chosen, being able to accommodate any rendering algorithm. The second group is the radiosity-based methods, which rely on the computation with diffuse surfaces, and considering patches with constant radiance. The third group is based on Monte Carlo algorithms, which in general are used to compute the unknown information by firing rays from the surfaces with known properties towards the surfaces with unknown properties,

gathering the information finally used. In general, this "gathering" process involves some sort of weighted averaging. The last group is the one based on local-illumination, considering only point light sources and without considering inter-reflections. Thus, they only consider the paths from the emitter to surface and from this surface to the registration system.

45

Alternative Classification:BRDF

• The Bidirectional Reflectance Distribution Function (BRDF) plays a key role

• General BRDF– Uses the BRDF information in a generic way

• Specific Model– Like the well known Phong, Torrance-Sparrow, …

• Diffuse– Just use a real number!

• Pure Specular– Provides the higher accuracy– Probably needs more computations: taking into

account many ray bounces

It is important to consider the sort of BRDF each approach uses, as the BRDF has a central role in the different inverse problems, as we mentioned before. For example, there are many approaches that try to use a general model for the BRDF, treating the information in a generic way. Others rely on a specific BRDF model, like a Phong or a Torrance-Sparrow BRDFs. Others, just use a lambertian BRDF, which is characterized just by a real number at each location! Finally, pure specular BRDFs are very commonly used, as are the ones who provide the maximum accuracy for inverse recovery problems, as we saw before. Unfortunately, as the BRDF is more specular, the computation of many light bounces becomes necessary, which could lead to larger computation times.

46

Alternative Classification:Visibility

• Remember:we need to compute the visible surface functionν(r,ω) ≡ inf{x>0: r+xω ∈ Surfaces in the env.}

• That means detecting blockers– between the sources and the surfaces– between the surfaces and the registration system (eye)

• Not computing this is much faster, but much more inaccurate– Could lead to solutions not applicable in real-life

It is also important to mention the treatment of visibility in the different approaches: when computing the radiance with the equations we explained before, the visibility problem consists of detecting if there are any blockers between the source and the surface being illuminated, so not adding their contribution in that case. The same is true for the paths from the surface to the eye or the region where the final radiance computations are needed. Most of the reviewed papers omit this treatment, arriving at solutions not applicable in real-life situations.

47

Alternative Classification:Specific aspects

• Each problem also allows to add specific, unique classifications that surely will help us understanding them

• Let’s look at each case in particular

Finally, we can present a classification with respect to the specific aspects each problem and of their solutions. These are specific, unique classifications that surely will help us understanding them. Let’s look at each case in particular.

48

Inverse lighting

• Light Simulation – General – Radiosity– Monte Carlo – Local Illumination

• Type– Emittances– Positioning

Source

BRDF

Reflector

Source

BRDF

Reflector


In the case of inverse lighting, we can find the four kinds of work: general approaches, radiosity-based, Monte Carlo-based and local illumination-based. But we also can classify them with respect to a specific classification that comes from the two possible sub-problems to solve: inverse emittances, where we only aim at finding the emittances of known light sources, or the problem of where to place a given source, known as "light positioning" problem.

49

Inverse Reflectometry

• Light Simulation – General – Radiosity– Local Illumination

• Points of view needed– One – Several.

Source

Reflector


(BRDFs & textures)

Source

Reflector


BRDF

BRDF

Here we find only three kinds of works: to the best of our knowledge, and although is theoretically possible to do it, there are no works that deal with an inverse reflectometry problem, using a Monte Carlo-based approach to solve it. On the other hand, the different approaches could be classified according to the number of images of the scene needed to solve the problem. Normally, this can be wither just one image, or several images, that could come from an animation or several calibrated pictures.

50

Combined problems

• Light Simulation– Radiosity– Local Illumination

Source

BRDF

Reflector


For the combined problems we only find radiosity or local illumination-based approaches, although we could think of the possibility of generating solutions with a general approach or with a Monte Carlo method.

51

Inverse Surfaces• Type

– Analytical– Numerical

• Light Simulation– “1-to-1”– Local illumination– Global illumination

• Shape Definition– Rotational Symmetric– Intersection of quadrics– Splines– Polygons



Source

BRDF

Source

BRDF


Source

BRDF

Source

BRDF

With respect to inverse surface problems, there are two main groups of works: those that are purely theoretical, showing and demonstrating some properties of the problem and their solutions, and those which try to get a numerical solution that could be implemented in a computer. So, each work treats the light propagation in different ways. Some of the proposed techniques introduce a new sort of lighting method, which we call "1-to-1", which a sever restriction on the local illumination setting. We are going to refer about a little bit later. Finally, it is important to mention that each work uses a different model for the surface, being the rotational symmetric surfaces and the intersection of volumes bounded by quadrics the most common in the theoretical works, while most of the numerical methods either use splines or polygons for the shape to be found.

52



1. State of the art in Inverse Lighting2. State of the art in Inverse Surface Design 3. State of the art in Reflectometry

2. Applications to Inverse Lighting3. Applications to Inverse Geometry4. Conclusion and Future Work


This first section gives an overview of the content of the following surveys and state of the art reports:

• A survey of inverse rendering problems, Gustavo Patow and Xavier Pueyo, Computer Graphics Forum, vol 22, num 4, pp. 663-687. 2003.

• A survey of inverse surface design from light transport behaviour specification, Patow, G. and Pueyo, X. Computer Graphics Forum. December 2005

• Classification of illumination methods for mixed reality, Katrien Jacobs and Celine Loscos, Computer Graphics Forum, vol 25, num 1, 2006.

Instead of a sample of slides, these three papers are included in this document, to give the reader an understanding of what will be presented. The discussion of these three surveys is followed by a break.

53

State of the art in Inverse Lighting



Keywords: Inverse Problems, Inverse Rendering, Inverse Geometry, Reflector Design, CAD for luminaries, Optimization

54

Inverse lighting

• Solve for Le• We can subdivide the work in

this area into– Inverse emittance: obtaining

the emittance– Inverse light positioning: find

the location of the sources

• Different approaches– General formulations– Monte Carlo– Radiosity– Local illumination

Source

BRDF

Reflector


LGKLL e

))+=

55

General Formulations (I)

• Find the luminaries intensities, positions and/or orientations

• Without depending on any particular rendering algorithm

56

General Formulations (II)

• If we consider n distant light sources• Each of them

– Characterized by a function Φi (its contr. to the env.) – Parameterized by some parameters uk

i

– In general, the uki will be

• its intensity u0i

• its position ri of the light source • its orientation ωi.

• Then, the illumination in a scene would be

)...( 10 kii

ni ii uuu∑ Φ=Φ

57

General Formulations (III)

• If we measure some intensity values αj at some evaluation points, that can be– On the surfaces – On the screen

• And, if we assume a linear relationship with the αj, we get

∑ Φℜ=Φℜ=n

i

kiiiij uuu ))...(()( 10α

58

General Formulations (IV)• It is very important to notice that

– As long as the rendering process ℜ(Φ) conserves this linearity, we can use any rendering algorithm

– The solutions posed this way are rendering-independent

– Just compare patch intensities or images– We don't care how the energy got there!

• In general– We are facing a non-linear problem– Probably with many minima– A global optimization procedure is needed

59

General Formulations (V)

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50 60

Target IlluminationTarget IlluminationRMS errorRMS error

[Patow06][Patow06]

Images courtesy of Àlex Méndez (GGG)

60

General Formulations (VI)• [Costa-Sousa-Cardoso99]

– Evaluated objectives defined on the surfaces• Intensity over certain surfaces• Avoid glares on operator’s faces (direct or by specular reflections)• Other: the objectives are specified by scripting

– Based on Simulated Annealing• [Shacked-Lischinski01]

– Perception-based image quality function as objective– Tries to effectively communicate information about shapes,

materials and spatial relationships– Steepest descent with “wisely chosen initial values”

• [Patow06]– Used images taken with a static camera– Objectives defined in image-space– Completely rendering-independent– Used Simulated Annealing

61

General Formulations (VII)Inverse Emittance:

• And, if we assume a linear relationship with the αj, we get

– We can try to find the ui as a typical least squares problem• [Schoeneman-Dorsey-Smits-Arvo-Greenberg93]

– “Painted” lighting requirements on the surfaces of the scene– Used a modified Gauss-Seidel iteration plus a regularization

process (remember: diffuse BRDF)• [Marschner-Greenberg97, Marschner98]

– From a 3D model and a photograph– Estimates the directional distribution of the incident light– Actually, used a basis Φi for each direction j– Least squares, but required regularization

∑ Φℜ=Φℜ=n

iiij u )()(α

62

Monte Carlo-Based Formulations (I)

• An Inverse Monte Carlo method is proposed:– Fire rays from the "known" surfaces towards

the "unknown" surfaces– Gather illumination information on some

"calculation points" on the "unknowns"– Average this info to get the final results

• Has never been used with light positioning problems…

63

Monte Carlo-Based Formulations (II)

• [Oguma-Howell95]"known" surface"known" surface

"Unknown" Surface"Unknown" SurfaceCalculation pointsCalculation points

AverageAverage

64

Radiosity-Based Formulations (I)

• The general problem is reduced to a radiosity one– Diffuse BRDF for the surfaces (patches)– Constant radiosity over each one

• To the best of our knowledge, never was applied to light positioning problems– Diffuse surfaces with sharp lighting… – probably very ill-conditioned– Unless stated at the full-patch level…

∑+=j

jijiei BFLBi

ρBBii the ithe i--thth patch patch radiosityradiosityLLeiei its its emittanceemittanceρρii its reflectivityits reflectivityFFijij the form factor between elements the form factor between elements ii and and jj

65

Radiosity-Based Formulations (II)• [Harutunian-Morales-Howell95]

– Context: Radiative heat transfer – Modified Truncated Singular Value Decomposition

• [França-Oguma-Howell98][Morales-Matsumura-Oguma-Howell97]– Same approach, but with participating media– Uses a FE approximation for the PDE for the medium

• [Fournier-Gunawan-Romanzin93]– Fitted emissions to observed values

• [Drettakis-Robert-Bougnoux97]– Improved by using a hierarchical radiosity system

• [Loscos-Frasson-Drettakis-Walter-Granier-Poulin99]– Photogrametry: Reconstructed scene geometry from photographs– Indirect lighting computed through a hierarchical radiosity system– Direct lighting computed separately with ray-casting

66

Local Illum.-Based Formulations (I)

• Basically, the consider only the direct illumination at a surface

• The rendering equation is actually never used

• Computations are much simpler and faster to do

• Depending on the application, results could be too unrealistic…

67

Local Illum.-Based Formulations (II)Inverse Emittance

• [Ramamoorthi-Hanrahan01]– First option: Solve a linear least squares system (like in the

general case)– Second option

• Subtract the diffuse component • use the resulting mirror-like distribution to recover a high resolution

angular space of the illumination• Two step process: estimate diffuse from illum, then illum frequency

parameters to get sharper results

• [Sato-Sato-Ikeuchi99a,b]– Use radiance inside shadows to estimate illum as a collection of

point sources • uniformly distributed in the scene• On a sphere of directions

– Solved a linear system

68

Local Illum.-Based Formulations (III)Light Positioning Problems

• [Poulin-Fournier92]– Use highlights and shadow for modeling directional

and point light sources• [Poulin-Ratib-Jacqes97]

– Used sketches of desired shadowsand highlights

• [Guillou00]– Creates many directional light sources from purely

diffuse regions in the scene– Groups them to estimate a point from the intersections– This point is used as starting point to an optimization

(Levenberg-Marquardt) of the least squares error

69



1. State of the art in Inverse Lighting 2. State of the art in Inverse Surface Design 3. State of the art in Reflectometry



70

State of the art in Inverse Surfaces




71

Inverse surfaces

Source

BRDF

Reflector


LGKLL e

))+=

• Type:– Analytical– Numerical

• Light Simulation:– “1-to-1”– Local illumination– Global illumination

• Shape Definition:– Rotational Symmetric– Intersection of quadrics– Spline– Polygons

Finally, if $\hat{G}$ is unknown, we have an \emph{inverse geometry} problem. For an in-depth survey on those problems, refer to \cite{PP00b}.

72

Far- vs. Near- vs. Near-Field• Far-Field

– Purely directional distribution– Ignores light origin– Sources are treated as anisotropic point lights

• Near-Field– Directional and spatial distributions– Equivalent to a Light-field or a Lumigraph

• Near-Field-RD (for reflector designers)– Often, in lighting engineering, they refer a Near-Field as

the illumination (irradiance) on plane near the source– This way, a Far-Field is a limiting case when the plane is

moved infinitely far away

73

Height

Reflector

Bulb

Target Optical Set

Firstly, we should define what an optical set is. The reflector shape to be found is just a piece of a set called in lighting engineering an optical set, which consists of a light bulb, the reflector and, possibly, the diffusor. The reflector has a border, contained in a plane, that limits its shape. In general, a reflector must fit inside a holding case, so its shape cannot be lower at any point than the plane defined by the border nor higher than a certain threshold defined by the case. We can say that the case defines a bounding box for the reflector.

74

Problem Statement• Given

– The radiance distribution of the light bulb– A reflector border– A desired outgoing radiance distribution for the

Optical Set

• Find a shape within a user-prescribed tolerance

We can state more precisely our problem as: Given the outgoing radiance distribution of a light bulb and a reflector border, and given a desired optical set-outgoing radiance distribution, find the corresponding shape for the reflector. Do this up to a user-defined tolerance.

75

Theoretical Works (I)

• Many of the earlier works were based on the "1-to-1" approximation

“1-to-1”

• It is a very restrictive approximation…• [Wescott-Norris75] [Wescott83]

76

• [Brickell-Wescott78]– Studied the Near-Field-RD problem– Got an equation of Monge-Ampère type

• [Oliker89, 02, 03]– Studied the Near-Field-RD problem– Worked with rotationally symmetric reflectors– Got a more general expression– Proved existence and uniqueness for the radially symmetric

case• [Wang96]

– Existence, uniqueness and smoothness for a far-field problem– Based on a differential geometry formulation– Showed that the regularity of the solution failed even with

simplest cases

Theoretical Works (II)

77

Numerical WorksGeneral Algorithm

ShapeShape00

ShapeShapeIteratorIterator

SimulationSimulation ErrorError OptimizatorOptimizator

Light Light DistrDistrii Light Light DistrDistrdesireddesired

bulbbulb

78

Numerical Methods:Local Illumination (I)

• [Kochengin-Oliker98, 03] [Caffarellli-Kochengin-Oliker99]• [Kochengin-Oliker-vonTempski98] (mostly theoretical)

(refractions → intersecting hyperboloids)

NearNear--FieldField--RDRD FarFar--FieldField

79

• [Neubauer94, 97]– Used a bicubic B-Spline for the surface– Minimized the mean square error between

• Obtained light distribution• User prescribed desired irradiances

– Light propagation by Gaussian quadrature• 4 x 4 nodes chosen on the reflector• Incoming and outgoing direction calculated• Outgoing energy distributed over neighbors in the registration region

(far-field)– Optimization

• Powell's method (projected conjugate gradients)• Line search via quadratic interpolation• Initialization must be quite accurate to avoid wrong minima !

Numerical Methods:Local Illumination (II)

80

• [Halstead-Barsky-Klein-Mandell95, 96]• [Halstead96]

Numerical Methods:Local Illumination (III)

Reprinted with permission of Brian A. Reprinted with permission of Brian A. BarskyBarsky, UC Berkeley, UC Berkeley

The The VideokeratographVideokeratograph

81

Numerical Methods:Local Illumination (IV)

• [Loos-Slusallek-Seidel98]– Designed progressive Lenses for defects in human visual

system– Lens represented as front surface

• Back surface is toroidal or spherical– Light Propagation

• Finds point the eye should focus on by tracing a single ray fromcenter of pupil to center of pixel

• Then, wavefront tracing is used for re-focusing the eye(get a sharp image)

• Distribution ray-tracing is used to get final pixel color– Accurate error functional for

• Desired properties (effective astigmatism)• Optical error across the lens

– Optimization• Variant of Newton iteration• Only two iterations needed !

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Numerical Methods:Global Illumination

• [Doyle-Corcoran-Connell99, 01]– Objective function

• Element-wise difference between desired and current light distribution• Penalty for rays outside this region• Difference between reflected and desired light power

– Light propagation: Flatland (2D)• Recursive ray tracing• Extended light sources defined as an array of lambertian-like points

on regular intervals on a circle– Surface

• Cubic Bézier curve – Optimization

• Evolution strategy (a variant of Genetic Algorithms)• Control points from the Bézier curve are the genes of the

chromosomes• [Patow-Pueyo-Vinacua04]

– Detailed description later

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1. State of the art in Inverse Lighting 2. State of the art in Inverse Surface Design 3. State of the art in Reflectometry



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State of the art in Reflectometry

Katrien JacobsCeline Loscos

University College LondonVirtual Environments and Computer Graphics

This talk will be about illumination methods for mixed-reality.

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Mixed Reality – definition

[Milgram91]

A definition of mixed-reality is given by Milgram et al. In their paper, it is stated that there exist 4 types of worlds.

86


Real Environment

(RE)

[Milgram91]

A first world consists of real elements only.

87


AugmentedReality(AR)

Real Environment

(RE)

© CREATE

[Milgram91]

In a second world some virtual objects are added to the real world, the resulting environment is called an augmented reality.

88



Augmented Virtuality

(AV)

Real Environment

(RE)

© PUREFORM

[Milgram91]

In the third world, real elements are added to an entirely virtual environment, the resulting environment is called an augmented virtuality.

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(AV)

Real Environment

(RE)

Virtual Environment

(VE)

© 1994 by Martin Moeck, Siemens Lighting

[Milgram91]

Finally the last world consists of virtual elements only, resulting in a virtual environment.

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(AV)

Real Environment

(RE)

Virtual Environment

(VE)

Mixed Reality

[Milgram91]

Mixed-reality is the combination of AR and AV.

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Mixed Reality – display methodssee-through display methods

Siconet-AR, Zentrum fur GraphischeDatenverarbeitung

computer augmented-reality

The CREATE project at UCL, model made by INRIA/CSTB using REALVIZ tools

A mixed-reality can be displayed using see-through glasses (left) or projected on a screen (right).

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Illumination methods• Illumination consistency between virtual and real object• 3 groups:

Common Illumination

Relighting Inverse Illumination

[Jacobs04] [Loscos00] [Boivin01]

When an effort is made to match the illumination of the virtual elements and real elements, three types of illumination methods can be distinguished: common illumination, relighting and inverse illumination. Common illumination: the real illumination is unchanged; the illumination effects induced by the virtual object are simulated (left). Relighting: the illumination of the real elements is changed and the virtual and real elements are re-lighted using the same illumination (middle) Inverse illumination: the BRDF of the real elements is calculated in order to achieve a physically correct relighting (right)

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Classification• Based on input required

– Geometry

– Scene radiance: • One image• Several images • Many images

In our state of the art report presented at EG04 and later published in CGF [Jacobs06], a classification is presented of existing illumination methods for MR. The classification is done based on the type of geometry and radiance information required by the method. The geometry is usually reconstructed using reconstruction software or using scanners. The scene radiance is extracted from input images.

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Classification1. No geometry, one input image2. Geometry, one input image3. Geometry, several input images4. Geometry, many input images

Based on this 4 different classes are identified: No geometry information is required, each scene point needs to be visible in one input image Geometry information is required, each scene point needs to be visible in one input image Geometry information is required, each scene point needs to be visible in several input images Geometry information is required, each scene point needs to be visible in many input images In what follows a short overview is given of these classes with only a SELECTION (not all) of the methods that exist in the literature that fall under this category.

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1. No geometry, one input image• Virtual object inserted inside real scene containing real objects• Anti-aliasing and distance taken into account• Shadow projection• Illumination virtual and real objects consistent• Fog generation

[Nakamae86]

A first method is from Nakamae et al. which uses a photograph and inserts virtual objects without knowing the scene geometry beforehand. They add shadows and fog.

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1. No geometry, one input image

4 steps: 1. Acquiring environment illumination (environment map)2. Pre-filtering environment illumination 3. Render using multiple passes (original texture preserved)4. shadow generation

[Agusanto03]

A second method is from Agusanto et al., this method uses pre-filtered environment maps to simulate the illumination on virtual objects.

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1. No geometry, one input image4 Steps:

1. low-level geometry reconstruction using pair of omni-directional images2. capturing illumination environment: environment map3. mapping of environment map onto the geometry 4. rendering VO using Ray Casting method

[Sato-Sato-Ikeuchi99b]

scaling factor [E2/E1]

Sato et al. present a common illumination method that makes use of environment maps to simulate virtual shadows. The shadow generation is non-real time.

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Geometry, one input image

[Haller03]

Modified shadow volume algorithm for AR environment:1. generating shadow volumes2. rendering algorithm for shadow volumes

Haller et al. present a local common illumination method that generates hard shadows using shadow volumes. The shadows are generated in real time, but problems arise when a virtual shadow overlaps with a real shadow (right). Shadows are generated from the real scene onto the virtual object and from the virtual object onto other virtual objects and onto the real scene.

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[Debevec03]

1. decompose scene into local and distant part2. calculate diffuse reflectance properties of real

objects in the real scene3. render scene using differential rendering

mechanism

Debevec et al. calculates the diffuse BRDF of the scene materials for the local scene using differential rendering. The result is a global common illumination solution, non-real-time.

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Geometry, one input image1. Capture scene2. Split scene into two parts: source

patches, receiver patches3. Construct shaft hierarchy between

source and receiver patches4. Render, assuming diffuse only

[Gibson 03]rendering reference

Gibson et al present a non-real time global common illumination method.

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Geometry, one input imageCommon illumination between real and computer generated scenes1. reconstruct the real scene: model the scene with few boxes: low-level geometry

reconstruction 2. divide scene in elements and estimate diffuse reflectance properties3. progressive radiosity is used to calculate global common illumination 4. render scene using ray casting

[Fournier-Gunawan-Romanzin93]

Fournier et al. present a non-real time common illumination solution. The diffuse material properties are estimated.

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Original photograph Without shadows Final rendering

[Loscos00]

B0Bi

display ratio

. Texture

relighting allowed

Bi

B0

B0Bi

This method is discussed in a following section in more detail.

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Geometry, one input imageImage-based rendering of diffuse, specular and glossy surface from one single image1. Reconstruct scene geometry, light source position 2. BRDF model according to Ward et al. : 3 or 5 parameters: diffuse, specular, roughness3. Iterative approximation based on one single image: 4. Use scene knowledge to fill in invisible parts of the scene

[Boivin01]

In this method from Boivin et al, the specular and diffuse material properties are estimated from one photograph. This method is discussed in more detail in a subsequent section.

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Geometry, several input images

x

x

avg.

reflectance confidence

merged reflectance

direct lighting: pixel per pixeldirect lighting: pixel per pixel

indirect lighting: optimised radiosity solutionindirect lighting: optimised radiosity solution

[Loscos-Frasson-Drettakis-Walter-Granier-Poulin99]

This method from Loscos et al. is explained in more detail in a subsequent section.

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Geometry, several input imagesImage based Photometric Reconstruction using Virtual Light Sources1. reconstruct scene 2. model direct illumination by a set of virtual light sources

spherical illumination surfaceset of virtual light sources must produce a similar illumination as real illumination

3. estimate reflectance of objects in real scene4. render using ray-tracing (not real-time)

original

augmented

[Gibson01]

synthetic light sources

In this method from Gibson et al. the scene illumination is reconstructed on a virtual illumination surface. This is used to calculate the BRDF properties. The result is a non-real time global relighting method.

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Geometry, many input images

Inverse global illumination:1. Reconstruct scene geometry and light source

positions2. Diffuse albedo estimated using inverse radiosity3. Roughness and specular albedo estimated using

non-linear optimisation4. Rendering with RADIANCE

input

relightedscene

[Yu99]

Yu et al.: calculate the diffuse and specular material properties using a non-linear optimisation. The result is a non-real time global illumination method.

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Geometry, many input imagesRecovering photometric properties from photographs1. Separate scene into four parts2. Radiance each point in the scene captured twice3. Two diffuse pseudo BRDF are calculated, specular component estimated (LSE)4. Rendering:

sky texture extracted and mapped on hemispheresky controlled by three parameters: sunset/sunrise, intensity, sun positionlocal scene rendered using pseudo-BRDF’s and radiance values

[Yu1998]

In this method from Yu et al. diffuse and specular effects are estimated using LSE by separating the scene into four parts (local model, sky, sun and surrounding environment). The radiance of a point needs to be captured once in shadow and once in sunlight, making this method very tedious. Then two BRDFs are calculated (material in sun, material not in sun) and combined.

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Discussions1. Pre-processing 2. Level of interactivity3. Quality obtained4. Applicability on indoor/outdoor scenes

The presented methods can be discussed and compared based on 4 different parameters: pre-processing time required Level of user interactivity The quality obtained of the simulated illumination The applicability of the method on indoor/outdoor environments

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Pre-processingPre-processing steps are those steps …

– that are carried out only once– before the actually rendering of the mixed-reality – e.g. geometry reconstruction / radiance capturing / reflectance calculation

1. Geometry reconstruction:– some require no geometric model of the real scene– most methods do require a geometric model– time consuming, unreliable

2. Radiance capturing:– from one / many viewpoint(s) – capturing HDR images: time-consuming, unreliable, subject to scene set-up,

…– methods requiring HDR images are error-prone

3. Reflectance calculation– diffuse BRDF relatively easy to calculate– specular BRDF estimation is error-prone and tedious but usually desired

A pre-processing step is a task that is carried out only once, before the actual rendering takes place. For instance geometry reconstruction, radiance capturing and reflectance calculation. Geometry: the more precise the geometry model needs to be the more time consuming the method will and also the more unreliable as it is not always possible to acquire a decent geometry model Radiance capture: the more input images needed, the more time-consuming the method and the less reliable, especially in a scene with changing illumination for instance, where it is is difficult to capture a scene point from many directions under the same illumination Reflectance calculation: the more high level the reflectance calculation, the better the quality of the final rendering, but the more tedious the method.

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Level of interactivityInteractivity:

– the possibility of navigating objects or viewpoints in the scene– the effort made to get an interactive rendering– the possibility to modify scene reflectance properties of real objects in the scene – the possibility to modify the illumination sources in the real scene

1. Few methods allow navigation of objects and/or viewpoints:– enough BRDF / geometry / illumination information available– or, they use different approach to fill in missing information

2. Final rendering of some methods are RT, some are near RT, most of them are not RT

– some did not spend enough effort on this– most methods can be altered such that navigation is made possible in RT–

3. in principle if geometry is calculated correctly, a new BRDF can be assigned to objects in the real scene

The level of interactivity depends on the possibility to navigate through the scene, to change/move the objects or to change the illumination of the scene.

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QualityQuality assessment:

– Compare rendering with photographic reference image [But how to assess the error ?]

– Estimate BRDF values and compare with real BRDF values (measured)– More complex BRDF model yields better quality of the MR (intuitively) – Subjective, using a test-audience

The quality of a method is very subjective, but can also be measured using more objective measures. For instance it is expected that with a high level BRDF model, the resulting rendering will be better. The quality of a method can also be measured by measuring the resulting rendering against a photographic reference, but in turn this poses the question: what to compare?.

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Applicability on indoor and outdoor scenes

• Outdoor scenes – more complicated than indoor scenes: – geometry more difficult to extract (too much detail, moving objects, less

controllable than indoor scenes)– radiance more difficult to capture (movement, intensity too high, less

controllable than indoor scenes)

• Methods using environment maps are usable for outdoor scene – if environment map is correct!!!

• Four methods explicitly tested their method on an outdoor scene – [Sato-Sato-Ikeuchi99a]– [Debevec98]– [Gibson03]– [Yu98]

Most methods are restricted in their applicability on complex scenes, like for instance outdoor scenes, where geometry reconstruction is often difficult, and where radiance capture is often hampered by weather conditions. Several methods presented can be applied on outdoor scenes, though it is a bit questionable if these methods are robust against fast weather changes and uncontrollable object movement.

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Conclusion• Mixed-Reality:

– Merging of real and virtual elements– Illumination consistency: virtual and real elements illuminated in the

same manner– Three methods to obtain illumination consistency:

• common illumination• relighting • inverse illumination methods

• Illumination methods: – The more information available, the better the quality of the final mixed-

reality– Therefore classification based on amount of input information available– Existing methods are not ideal

We’ve discussed mixed-reality illumination methods. Three types of illumination methods exist. The existing methods can be classified based on their input information required into four different groups.

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Bibliography• A survey of inverse rendering problems, Gustavo Patow

and Xavier Pueyo, Computer Graphics Forum, vol 22, num 4, pp. 663-687, 2003.

• A survey of inverse surface design from light transport behavior specification, Gustavo Patow and Xavier Pueyo. Computer Graphics Forum. December 2005

• Classification of illumination methods for mixed reality, Katrien Jacobs and Celine Loscos, Computer Graphics Forum, vol 25, num 1, January 2006.

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1. General problems with complex & uncontrollable scenes 2. Postproduction: capturing HDRI for outdoor scenes 3. Urban planning: simulating common illumination 4. Indoor Lighting Design

3. Applications to Inverse Geometry4. Conclusion and Future Work


Before actually discussing some applications of Inverse Rendering, some general problems with rendering methods are discussed first. The focus is on the efficiency of the existing methods in real-life situations. This is to highlight that most existing methods, though they often produce nice results, usually forget the practical applicability of the method.

116

General Problems with Complex, Uncontrollable scenes



117


Geometry:– Some (outdoor) scenes contain many (difficult to model)

details (e.g. buildings, trees, fauna, people, cars, …)– Some (outdoor) scenes are less easy to control: (e.g. people

passing, cars driving, objects moving because of wind)

Geometry extraction of outdoor scenes is complicated. The scene can contain lots of detail, which makes it difficult to model. The scene can be difficult to control, for instance the object might not be static, which makes it again difficult to model.

118


Illumination:– Complex illumination:

• Direct: Sun • Indirect: Sky & Objects

– Difficult to control:• Sun intensity too high to capture with camera• Clouds drifting in sky have significant effect on stability outdoor

illumination

And so is the extraction of the illumination. The illumination might not be static which makes the HDRI capturing error prone The intensity of the illumination can be too high to capture (e.g. Sun)

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Geometry Loss due to …

1. Reconstruction errors1. Shadows in texture show more detail than the reconstructed object 2. Outdoor scenes contain more detail than indoor scenes

As we can see, the shadow of the statue contains “rounded” edges, this indicates that the representation of the statue by a set of triangles/polygons is incorrect.

120

Geometry Loss due to …

1. Reconstruction errors2. HDR (high dynamic range) capturing of moving objects

1. Smeared out in final HDR image2. Outdoor scenes are less controllable than indoor scenes

Those persons that move during the HDRI capturing appear ‘blurred’ in the final HDRI. These ghost effects reduce the quality of the HDRI, and the radiance representation of the objects in the scene.

121

Incorrect Radiance information due to …

• Illumination changes during HDR capturing: set of LDR (low dynamic range) images with multiple exposures contain different illumination content, meaningless HDR image

• Illumination changes during radiance capturing entire scene: radiance images are required from different viewpoints.

• Sun intensity too high to capture using conventional ways

1/250 1/2000 HDRI

The radiance needs to be captured with HDRI images, these HDRI images are often generated from a set of multiple exposures. Problems arise when during the capturing of the multiple exposures, the scene objects move, or when the scene illumination changes. Also, when the intensity in the scene (sun) is too high to be captured with the fastest camera shutter speed.

122

• Using one environment map to illuminate the scene: this assumes that the illumination of the sun and the sky is diffuse,while it is not …

Incorrect Radiance information due to …

When one mirror ball is used to extract the entire illumination, it is implicitly assumed that the scene illumination is diffuse. However, this is not necessarily so.

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Solutions

Geometry– By using image processing techniques as shadow

detection/object recognition geometry loss can be compensated for

– Movements during HDRI capturing can be compensated for– …

Illumination– Detect illumination changes and compensate– Use homogenous filter to reduce sun intensity – Capture light probe at different positions in the scene– …

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1. General Problems with Complex & Uncontrollable scenes2. Postproduction: capturing HDRI for outdoor scenes 3. Urban planning: simulating common illumination 4. Indoor Lighting Design



A first application of inverse lighting can be found in post production in which HDRI images of the sky/scene are used to perform inverse illumination. When objects move in the scene, HDRI construction using multiple exposures is error prone. The following talk discusses a solution to minimize the influence of object movement and camera movement on the HDRI generation process.

125

Postproduction: Capturing HDRI for outdoor scenes



126

Postproduction: Capturing HDRI for outdoor scenes

1. Introduction2. What is the problem?3. Solutions:

1. Camera Alignment2. HCM removal3. LCM removal

4. Conclusion5. Limitations & Future work

127

• Images captured with ≠ shutter speed (called exposures or LDRIs)• Camera curve saturation effects: too bright – too dark • What if dynamic range of the scene is too large?

HDRI: High Dynamic Range Image?

dt1 dt2 dt3> >

Most cameras allow the user to change the exposure of an image by either changing the shutter speed or the aperture. When the shutter speed is long, the CCD of the camera has enough time to integrate the incoming light and sometimes the CCD might even saturate, like is visible in the image on the left, where the sky is plain white. On the other hand, when the shutter speed is short, the CCD of the camera might not have enough time to integrate the incoming light, especially in dark areas, and as a result some parts in the image can be too dark and not represent the actual light distribution in that area, as is visible in the images on the right. For a scene with a too high dynamic range, meaning that the scene contains both dark and bright areas, no shutter speed will capture both dark and bright areas without showing some saturation. This is all due to the characteristics of the CCD integration curve or the camera curve, which relates irradiance in the scene to intensity in the final image in function of exposure. This curve converges to a certain value Imax, and is nearly flat around 0.

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• HDRI from image sequence:– Camera curve maps intensities to irradiance– Final image is per-pixel weighted average of different exposures– No saturation effects

+

w1

w2

w3

f(x)

f(x)

f(x)


A High Dynamic Range Image, is a floating-point image that gives an accurate representation of the irradiance of the points in the scene, rather than the intensity of the pixels in an image. There are different ways of generating HDRIs, the method presented in this talk makes use of the multiple exposures. This kind of method is the cheapest way of generating HDRIs. It proceeds in the following manned: A sequence of exposures is captured of the same scene with different exposures The reconstructed camera curve is used to transform the intensities to irradiance. The final HDRI is a weighted average of these transformed exposures. The weights are defined per pixels and are based on the level of saturation a certain pixel has in a certain exposure. The task of the weights is basically to discard pixels that show saturation. The final HDRI will be free from saturation, and will actually represent the true irradiance distribution of the scene captured.

129

• What is it used for? – High quality images

Photosphere


Now what are these HDRIs used for? First of all, as they give an accurate representation of the true irradiance distribution in a real scene, they are of more quality than conventional images. After all, using post-processing techniques, any HDRI can be transformed into a conventional image, with all necessary saturation if that has to be. Professional software like Photosphere, HDRshop and photoshop are available to transform exposures into HDRIs. HDRIs are often used in movie-production and as a result we see companies emerge that design and build HDR cameras, like SpheronVR. And companies that build HDRI displays so that the user can actually see the floating point content of an HDRI.

130

• What is it used for? – High quality images– Illumination capturing/generation (environment/cube mapping)

© www.debevec.org


Secondly, since HDRIs represent irradiance, HDRIs are used to capture the illumination in a scene. For instance by using a light probe as can be seen in the image below. This light probe image can then in turn be used to illuminate virtual objects in a real scene.

131

Dynamic Scenes ?

• Camera movement:– Manual capturing without tripod– Translation and Rotation effects

• Object movements:– Controllable: people, cars, … – Uncontrollable: wind

The HDRI generation method presented here, allows the exposures to be captured in a dynamic environment, meaning: Firstly, that during the exposure capturing process, the camera does not need to be fixed on a tripod, but can be held manually. As a result, the camera position of the different exposures can be slightly different. Secondly, that the objects in the scene can move. Some objects in a scene move in a more or less controllable manner, like cars and people walking by. Other objects move due to uncontrollable powers: like for instance leaves or branches of tree in the wind. [Only visible in the slide when the slide is shown in presentation mode] Since the different exposures need to be captured sequentially, these movements will have an undesired effect on the HDRI generation.

132

+

w1

w2

w3

f(x)

f(x)

f(x)

What is the problem?• Conventional HDRI generation:

– Weighted average – 1-1 mapping between pixels in different exposure– Requirement: static scene

+

+

+

+

So, what is exactly the problem? Due to the weighted averaging of the pixels to generate the final HDRI the same pixel in the different exposure must correspond exactly to the same physical point in the scene. Or in other words, the scene has to be static, in order to calculate a correct representation of the irradiance in the scene.

133

What is the problem?• Dynamic Scene:

– Camera misalignment – Object movement

• Consequences:– Ghost effects– Blurring

When you allow camera misalignments, or object movement, the same pixels in the different exposures will not correspond to the same physical point in the scene. As a result, the final HDRI looks blurred or washed out; a ghost effect becomes visible. This can be seen in the example below, where the walking people appear multiple times in the final HDRI.

134

Postproduction: capturing HDRI for outdoor scenes

1. Introduction2. What is the problem?3. Solutions:

1. Camera Alignment2. HCM removal3. LCM removal

4. Conclusion5. Limitations & Future work

135

Solution! • Camera misalignment:

– Camera alignment

• Object movement:– High contrast movement removal (HCM)– Low contrast movement removal (LCM)

Basically there are two sources of error: the camera misalignment and the object movement. As a solution for the camera misalignments a camera alignment algorithm is proposed. The object movement is compensated for by two different algorithms: Low Contrast Movement (LCM) removal And High Contrast Movement (HCM) removal The choice of the algorithm depends on the type of movement the objects in the scene make.

136

Camera Alignment• Different exposures → different image features

2 ≠exposures

≠ features

Most camera alignment methods are feature-based: they align the images based on distinct features in an image, for instance the edges. Unfortunately, feature-based methods are unsuitable when aligning images captured with different exposure. An example is given here: The top two images are images captured at the same time, from approx. the same position, but with a different exposure time. When these images are processed with an edge detector, the two images at the bottom are generated. Different edges are detected and an alignment algorithm based on aligning the edges in the image would most likely fail or at least it will be very unreliable.

137

Camera Alignment• However:

– Between histograms: monotonic transformation– Same pixels smaller than median intensity value (approx.)

→ Median Threshold Bitmap Transformation

dt1 dt2

T1 T2

However, when the histograms of the two images are plot, the two histograms are related by a monotonic transformation. Or, the same group of pixels will have intensity values lower than the median intensity value in both exposures. This median intensity value can now be used as a threshold for a Median Threshold Bitmap Transformation.

138

Camera Alignment• Median Threshold Bitmap (MTB) Transformation:

2 ≠exposures

comparable features

As an example: For the same two images of the same scene captured with a different exposure speed the median intensity value is calculated and used as a threshold. The result is the two binary images at the bottom. This time, these binary images share the same features, and can therefore effectively be used in an alignment algorithm.

139

Camera Alignment• Results:

– Use MTB to find Translational and Rotational transformation matrix– Iterative procedure

Unaligned sequence

The final alignment algorithm works in the following manner:

• Take the different exposures • Calculate the median intensity value for each of

these exposures • Use this value as a threshold to generate the

binary images like the once shown in the previous slide

These are then used to calculate the rotational and translational misalignments between the images The rotation and translation is calculated in an iterative process. An example of an unaligned sequence of images is shown here, it is (should be) clear that there is a clear rotational and translational misalignment between the images. [Only visible when the slide is shown in presentation mode]

140

Camera Alignment

Aligned sequence

• Results: – Use MTB to find Translational and Rotational transformation matrix– Iterative procedure

This sequence shows the same exposures as in the previous slide but this time a rotational and translational transformation is applied to align the sequence. [Only visible when the slide is shown in presentation mode] This method is similar to the method used in Photosphere, but the alignment method is extended to deal with rotational misalignments as well.

141

• HCM: High Contrast Movement:– High contrast between moving object and background

– Can be identified by examining variance of pixel over the different exposures

HCM removal

HDRILDRI

As mentioned earlier, the movement present in the scene is compensated for by two different algorithms. Which algorithm should be used depends on the type of movement present in the scene. A first type of movement is called High Contrast Movement (HCM) and is displayed here: this type of movement occurs when moving object (walking people) and background are of high contrast. This type of movement can be identified by calculating the variance of a pixel across the different exposures.

142

HCM removal• Detection: creation of Variance Image (VI)

– Camera curve maps intensities to irradiance– VI is weighted variance image

Σwi(x – μ)2

w1

w2

w3

f(x)

f(x)

f(x) VI

The detection is done by constructing a Variance Image (VI) in the following manner: First the intensity values in the exposures are mapped to irradiance values using the camera curve. This is necessary in order to being able to actually compare the pixels. Then VI is constructed by calculating the weighted variance of one pixel across the different exposures. The weights used here are the same weights used for the HDRI generation: their task is to discard saturated pixels.

143

HCM removal• Removal:

– Threshold, dilation, erosion & segmentation– Substitute highlighted regions in original HDRI– Use best exposure available (not containing

saturation)• Result:

The removal of the movement is carried out by the following steps: First a threshold is applied to VI, the resulting binary image is dilated and eroded resulting in the second image on the right: the cluster of white pixels indicates HCM and needs to be removed. The actual removal consists of substituting those identified regions by pixel values by irradiance values coming from one exposure. That exposure is chosen, that shows the least saturation in the identified area. A result is given on the left hand side: the walking people are “de-blurred” and “de-ghosted”

144

LCM removal• LCM: Low Contrast Movement

– Low contrast between background and moving object

– Movement can be detected with entropic measurements

HDRILDRI

The second type of movement is called Low Contrast Movement. It occurs when moving object and background are similar or show low contrast. An example is shown on the right, the leaves and branches move due to the wind. The contrast between moving object and background is low, as they are essentially the same kind of objects. [Only visible when the slide is shown in presentation mode] The resulting HDRI is unclear and fails to represent the moving branches and leafs correctly. This type of movement is identified using entropy.

145

LCM removal• Detection: creation of Uncertaintly Image (UI)

– UI is weighted average of uncertainty measure:

ΣwiUI

w1

w2

w3

The detection of LCM proceeds in a similar fashion as the HCM detection. The detection is done through an Uncertainty Image (UI) and the following slide explains how UI is generated.

146

• Uncertainty measure:– Generate HDRI & split into cells 1’, 2’, …, I’, …, n’– Create empty uncertainty image UI– Split each exposure in cells 1, 2, …, I, …, n– For each cell in exposure calculate entropy H i– For corresponding cells calculate conditional entropy H i | i’– Add H i + H i | i’ to value stored in cell I in UI

LCM removal

HDRI

1’

i’

n’

Exposure 1

1

i

n

…

Exposure N

1

i

n

UI

1

i

n

First an HDRI is generated and split in a set of cells. Then an empty UI image is created, split into the same set of cells. Then for each exposure the following algorithm is applied:

• They are split into the cells • For each cell the entropy is calculated • Then the conditional entropy is calculated

between the cell in the exposure and in the HDRI • Finally the sum of the entropy and the conditional

entropy is added to the value stored in UI • This is repeated for all exposures

147

LCM removal• Removal:

– Threshold, dilation & erosion & segmentation – Substitute highlighted regions in original HDRI– Use best exposure available (not containing

saturation)• Result:

The removal of LCM proceeds in a similar fashion as the removal of the HCM: A threshold is applied to UI, the generated binary image is dilated and eroded. The resulting bright cluster of pixels is identified as pixels affected by LCM After HDRI generation this LCM region is substituted by pixel values from 1 exposure. An example is shown in the image on the right: all the leaves are clearly visible, all movement has been de-blurred.

148

Conclusion

• Automatic HDRI generation for Dynamic Scenes• Statistical decision process • Low cost HDRI generation using multiple exposures • Camera & object movement removal:

– Camera alignment– HCM & LCM removal

• Without user input

In this talk a method is presented that generates HDRIs in a low-cost manner, with low-cost equipment using multiple exposures. Limited camera and object movement is allowed. These movements are compensated for using a HCM & LCM removal and camera alignment procedures. All operations are executed automatically, without used input, the decisions made are based on statistical quantities.

149

Limitations & Future work• What if …

– too many/large objects would move– there is no suitable exposure for the substitution – the illumination changes during image capturing (cloud

movement)

Oblivious there are still limitations to the presented method and there is still some important future work: What if … Too many or large objects would move? Well, most likely the image alignment algorithm will fail. And if that fails, the image calibration, and HDRI generation will be incorrect as well. There is no suitable exposure, for instance, some light sources (for instance the sun) will always show saturation, and no matter what exposure speed is used? In that case, the HDRI will still show the saturation. The clouds change that fast, that during the capturing, the illumination has significantly changed as well? Well, in that case no correct HDRI image can be generated. It is essential that the different exposures are captured under the same illumination.

150


1. General Problems with Complex & Uncontrollable scenes2. Postproduction: capturing HDRI for outdoor scenes 3. Urban planning: simulating common illumination4. Indoor Lighting Design



The next application is that of urban planning. It discusses a method to generate shadows (common illumination solution) in real-time for virtual objects in a scene. This method does not require an accurate scene geometry and allows shadows in the texture model of the scene. Only an approximate light source position needs to be known. The generated virtual shadows are calculated in real-time and are consistent with the shadows already present in the scene. This method was developed as part of the CREATE project (a European project), and was used to generate consistent shadows for virtual objects inside a model of an existing city.

151

Urban planning: simulating common illumination



152


1. Introduction 2. Related work 3. Methodology4. Results5. Conclusion

153


1. Introduction 1. Problem description2. Illumination solution3. Contribution

2. Related work 3. Methodology4. Results5. Conclusion

154

Introduction Context: illumination for augmented reality:

– Augmented reality: real environments augmented by virtual objects/avatars

– Illumination: induced by virtual object

real scene geometry extraction texture mapping&

augmentation

© The CREATE project at VECG, UCL

The context of the presented algorithm is illumination for augmented reality. AR stands for the reality created when you insert virtual objects in a real scene. Illumination stands for the illumination effects that the virtual objects can create. An example is given in the images below. On the left hand side we see a picture of a real scene. Now, in order to insert virtual objects and to generate the illumination effects, the geometry of the scene needs to be reconstructed, the light source positions need to be estimated and the texture of the real scene needs to be extracted as well. A possible illumination effect that a user would like to create is for instance the shadows cast by the avatar on the ground floor as we can see in the example on the right hand side. Now, geometry reconstruction and light source position estimation is error prone and the light source estimation becomes even more complicated when the texture of different parts of the real scene are captured at different times of the day, since then the light sources might actually be different for different parts of the scene.

155

Introduction Context: illumination for augmented reality:

– Augmented reality: real environments augmented by virtual objects/avatars

– Illumination: induced by virtual object

Illumination effects:– virtual object → real scene– real scene → virtual object– virtual objects → virtual objects

[Haller03]

Now what kind of illumination effects can exist? First of all the virtual object can cast shadows on the real scene, secondly the real scene will illuminate the virtual objects and finally the virtual objects can interfere with each other. An example is given in the image on the right: the torus and the sphere are virtual objects and they generate shadows in the real scene and on top of each other.

156




157

IntroductionCommon illumination:

– Virtual shadows consistent with shadows present in real scene– Illumination in the real scene is unaltered– No physical understanding of the scene necessary

Relighting/inverse illumination: – Virtual shadows consistent with shadows present in real scene– Appearance of real objects can be altered, to reflect illumination

changes– Often physical understanding of the scene calculated (BRDF)

• see STAR Jacobs et al. at EG2004: classification of illumination methods for mixed-reality.

There are many different illumination solutions provided in the literature and we can classify them into different classes. The first class of methods provide common illumination: the virtual object is illuminated conform to the illumination present in the real scene and the virtual shadows cast by the virtual object are generated as well. However, the illumination already present in the real scene can not be changed. Also, usually there is no physical understanding of the scene. A second class of methods provide relighting. In this case, the virtual object is again illuminated with similar illumination as is present in the real scene and its shadows are generated. This time, a novel illumination can be applied to both the real scene and the virtual object. Usually some form of physical understanding of the scene is at hand, for instance, often the BRDF or reflectance of the materials in the scene are known or at least calculated. For a complete classification of illumination methods I would like to refer to the following state of the art report presented at Eurographics 2004. Now, the method presented in this talk can be classified under the first group of illumination solutions: it offers common illumination.

158




159

-- green box is virtualgreen box is virtual

IntroductionShadow volumes/maps?

– Calculation of position of virtual shadow – Scale pixels underneath (make darker)

The contribution of the presented method is the generation of consistent shadows for virtual objects in an AR environment using shadow volumes or shadow maps. Shadow maps or shadow volumes generate shadows in real time as the calculation can be done using the graphics hardware. Usually these shadows are hard shadows, but soft shadow generation is possible as well.

160

- green box is virtual



In short, what shadow volumes and shadow maps does is that it calculates the position of the virtual shadow …….

161

- green box is virtual



….. and then it scales the pixel intensities of those pixels that fall inside this shadow region as is illustrated here.

162

- orange box is real

IntroductionShadow volumes/maps?Consistent?

– Consistent with shadows already present in the scene – Prevent pixels inside shadow in texture from being scaled – Texture contains semi-hard shadow

As said earlier, the method provides consistent shadows. Consistent means in this context that the shadows are in the same direction as the shadows already present in the real scene, and with a similar appearance, or colour, which means that we need to find a good scaling factor. In this example we see a real object, the orange box, which casts a clear shadow on the ground.

163

- orange box is real- green box is virtual



….. when a virtual object is inserted, the position of its shadow is shadow is calculated using an approximate light source estimation. …….

164




… and then the pixels inside this shadow position are scaled. And as we can see, when virtual and real shadows overlap, using shadow volumes or shadow maps, will generate inconsistent shadows in the overlapping pars. For instance in this example, we see that the colour of the overlapping regions is darker than the rest of the shadow …..

165

-- orange box is realorange box is real-- green box is virtualgreen box is virtual



… the presented method will detect the position of the real shadow present in the scene and will not allow scaling pixels in those areas, the result is depicted in the example. The result is that the shadow in the overlapping area is appropriate according to the shadows already present in the scene.

166


1. Introduction 2. Related work3. Methodology4. Results5. Conclusion

167

Related work

• Common illumination• Illumination generated using environment maps• Not real-time • Inconsistent shadows when real texture contains shadows

Sato et al.: Sato et al.: Acquiring a radiance distribution to superimpose virtual objectsAcquiring a radiance distribution to superimpose virtual objects onto a real scene.onto a real scene.

[Sato[Sato--SatoSato--Ikeuchi99aIkeuchi99a]]

In this example from Sato et al. we see a real scene on the left hand side and the real scene augmented with a virtual sphere on the right hand side. The illumination on the sphere is generated using environment maps, the shadow of the virtual object is generated using ray tracing. The method is not real-time. If the virtual shadow would have overlapped with real shadows in the scene, the shadow would have been inconsistent.

168

Related workYu et al.: Yu et al.: Inverse global illumination: recovering reflectance models of reInverse global illumination: recovering reflectance models of real scenes from al scenes from photographsphotographs. .

• Relighting illumination using inverse illumination • Reflectance calculation• Not real-time

[Yu99]

This example form Yu et al. illustrates relighting. The top image gives the real scene, the bottom image illustrates the same scene but this time virtually illuminated with a novel illumination pattern. The method does not operate in real time and uses the geometry of the real scene and BRDF information for the materials in the scene to calculate the illumination effects.

169

Related workAgusantoAgusanto et al.:et al.: Photorealistic rendering for augmented reality using environmentPhotorealistic rendering for augmented reality using environmentillumination.illumination.

• Common illumination• Illumination using environment maps• Real-time using ARToolkit

[Agusanto03]

Agusanto et al. provide common illumination using environment maps. A glossy and specular environment map are given on the left hand side. This method operates in real time, the illumination on the virtual objects is generated, no effort is done to include shadows.

170

Related workHaller et al.:Haller et al.: A realA real--time shadow approach for an augmented reality application using time shadow approach for an augmented reality application using shadow shadow volumesvolumes. .

• Common illumination• Real-time using shadow volumes• Inconsistent shadows when real texture contains

shadows

[Haller03]

Finally, an example from Haller et al. which uses shadow volumes to generate the virtual shadows. This method requires a detailed model of the real scene and the light source position. But when we have a look at the image on the right hand side, we see that when virtual and real shadow overlap, the method generates an inconsistent shadow pattern.

171


1. Introduction 2. Related work 3. Methodology4. Results5. Conclusion

Next we will discuss the methodology of the shadow generation algorithm presented in this talk. The methodology consists out of 4 different steps.

172

Methodologygeometry

light source position

texture

virtual element

The first steps is the input generation. At least four different inputs need to be generated. The first is the geometry of the real scene. Geometry reconstruction, which can be done with methods like image modeler, is very tedious and error prone.

173


Methodologygeometry


texture

virtual element

1. shadow detection

• shadow estimation• shadow calculation• scaling factor

Then the shadow detection process proceeds. The following slides give an overview of how this was implemented in the presented method.

174

Methodologygeometry


texture

virtual element

1. shadow detection


- orange box is real- yellow box is construction

The orange box is a real object, the yellow box is its reconstruction (misaligned with the original object as we can see here, due to numerous errors).

175

Methodologygeometry


texture

virtual element

1. shadow detection


- orange box is real- yellow box is construction- yellow region is estimated shadow position

The shadow estimated from the light source estimate and the reconstructed geometry is given in yellow.

176

Methodologygeometry


texture

virtual element

1. shadow detection


- orange box is real- yellow box is construction- yellow region is estimated shadow position- green box is bounding box

From this estimate a bounding box can be created that is larger than the estimate and will contain the real shadow.

177

Methodologygeometry


texture

virtual element

1. shadow detection


- orange box is real- yellow box is construction- yellow region is estimated shadow position- green box is bounding box- red contour is shadow contour

A canny edge detector is used to calculate the position of the shadow contour. This implies that only hard shadows can be detected.

178

Methodologygeometry


texture

virtual element

1. shadow detection


- orange box is real- yellow box is construction- yellow region is estimated shadow position- green box is bounding box- red region is calculated shadow region

A region filling algorithm is used to find the shadow pixels based on the shadow contours.

179

- orange box is real- yellow box is reconstruction

- scaling factor = A/B - one scaling factor per material

Methodologygeometry


texture

virtual element

1. shadow detection


A scaling factor is calculated. This scaling factor relates the intensities of the pixels in shadow with those not in shadow. It is this scaling factor that will be used by the shadow volumes method to generate the virtual shadows. This scaling factor actually varies per material and per pixel, but in the presented method only one scaling factor was used PER MATERIAL. The results, though being an approximation, were satisfying.

180


Methodologygeometry


texture

virtual element

2. shadow protection

• shadow mask generation

1. shadow detection


Now, the third step of the algorithm deals with the protection of these real shadow pixels from being scaled during the shadow generation with the shadow volume method.

181

Methodologygeometry


texture

virtual element

2. shadow protection


1. shadow detection


.. this protection is performed by generating a shadow mask. An example of a binary mask is given here. White indicates that the pixels is inside a real shadow, and hence no scaling is allowed, black indicates that scaling is allowed.

182

white = no scalingblack = scaling allowedgrey = partial scaling

Methodologygeometry


texture

virtual element

3. shadow generation

• using shadow mask • using scaling factor generated in steps 1 & 2

2. shadow protection1. shadow detection



Sometimes the real shadow is not a true hard shadow. To reflect the difference in shadow intensity in penumbra and umbra regions, the shadow mask is in grey scale and a gradient from white to black is introduced along the border of the real shadow. Now, in this shadow mask, white indicates that the pixels cannot be scaled; black indicates the pixels can be scaled and grey indicates they can be scaled, but with a smaller scaling factor than that used for pixels in the black region.

183

Methodologygeometry


texture

virtual element

3. shadow generation2. shadow protection


1. shadow detection


Intensity Intensity = =

scalingfactorscalingfactorx x

shadow maskshadow maskxx

texturetexture


• using shadow mask • using scaling factor generated in steps 1 & 2

The fourth and final step in the methodology generates the virtual shadows. Now the intensity of a pixel inside the virtual shadow is calculated as the original pixel intensity multiplied by the scaling factor and multiplied by the value in the shadow mask. As we can see, with this method only pixels outside of a real shadow will be scaled.

184


1. Introduction 2. Related work 3. Methodology4. Results

1. Demo 12. Demo 2

5. Conclusion

185

• Characteristics: – light source static– real scene static– everything recorded offline– RT shadow generation and scene navigation

• Task flow:– 0. input generation– 1. shadow detection– 2. shadow protection– 3. shadow generation

Results

repeat every frame

In the first demo, the light source and the real scene are static and the texture is captured offline. The shadow generation and scene navigation is calculated online and in RT. Basically this means that the first three steps of the methodology are calculated once, and the final step is repeated every frame. This type of applications performs the shadow detection offline and therefore the necessity of calculating the real shadow positions in real time is less important.

186

• Characteristics: – light source semi-static– scene static– everything recorded online– camera calibration online using ARToolkit

• Task flow:– 0. input generation– 1. shadow detection– 2. shadow protection– 3. shadow generation

Results

repeat every frame

In the second demo, the light source is semi-static and is allowed to move in a close range around the real light source position. The real scene is static, but the texture is captured at run time. The camera calibration was executed using ARToolkit. In short this means that the input generation can be done offline and only once, but the shadow detection, protection and generation is repeated every frame.

187

Conclusion and future work

• Conclusion:– A real-time shadow detection and generation is presented – Common illumination for augmented reality

• Future work:– Improved shadow detection system (soft shadows) – Light source tracking – Improved per-pixel scaling factor calculations

A real-time shadow detection and generation method is presented, which provided common illumination for augmented reality. There are a few things that can be improved in the current implementation of the method. For instance, we have only considered semi-hard shadows, but the application field of the method could be broader if a soft shadow detection would have been used in the shadow detection step. Secondly, a light source tracking could be included. And finally the scaling factor calculation could be done per pixel instead of per material, as this would better reflect that pixels inside a shadow cast on one object can have a slightly different appearance due to the orientation of the object towards the light source, or the indirect light the points receive from their neighbouring objects.

188

Indoor Lighting Design

Celine LoscosKatrien Jacobs


189

Indoor Lighting Design

Geometric modificationsLighting modifications

Can this be done virtually?

When designing interior one would try to imagine different scene set up and lighting set up. It is tedious and often impossible to do it in real life. We could build a virtual model of the room and use traditional computer graphics lighting simulators. But many details and the overall impression would be lost. Could this be done virtually, based on the existing room?

190

Different approaches

• Common goal:– Realistic output– Use of global illumination

Different approaches exist. All have a common goal to produce a realistic output – meaning that the output can be comparable to what would a photograph of the redesigned room would look like. Global illumination is preferable has it models light transport more realistically.

191


• Approach 1: [Loscos00]– Input:

• Partial geometry known• One lighting condition known• Few input photographs

– Output:• Approximate solution• Fixed viewpoint• Interactive control

We will present 4 different approaches to the problem. The first one was published by Loscos et al. in 2000. Its advantages are that the input can be restrictive. But as a consequence the solution is approximate.

192


• Approach 2: [Loscos99]– Input:

• Partial geometry known• Several lighting conditions known• Few input photographs

– Output:• Approximate solution• Fixed viewpoint• Interactive control

A second approach was published by Loscos et al. in 1999. The input is more restrictive as several lighting conditions need to be known. The results are therefore more reliable than those of the previous approach.

193


• Approach 3: [Yu99]– Input:

• Full geometry known• One lighting condition known• Many input photographs

– Output:• Accurate solution• Pre-computed results• Possible of changing viewpoint before computation

A third approach is of Yu et al. published in 1999. The input needs to be very complete, but the provided solution is very accurate.

194


• Approach 4: [Boivin01]– Input:

• Full geometry known• One lighting condition known• One input photographs

– Output:• Nearly accurate solution• Pre-computed results• Possible of changing viewpoint before computation

The last approach presented is of Boivin et al. in 2001. The output is similar to the one of Yu et al., but the input needs to be less complete.

195

Approach 1: Loscos et al. 00

• Input:• Partial geometry known• One lighting condition known• Few input photographs

• Output:• Approximate solution• Fixed viewpoint• Interactive control

196

Original photograph Relighting

Relighting using a single known lighting

For an original photograph on the left hand side, this method allows to reach results as in the picture shown in the right hand side, where all original light sources were virtually turned off and a new virtual light was inserted. In addition a virtual object was inserted in the scene.

197

Relighting using a single known lighting

• Input data– 3D-model with textures– single known viewpoint– single photograph – single known lighting

A scene is reconstructed from photographs, on which textures taken from one view are mapped.

198

Global illumination estimation

• Initialisation of lighting parameters[Fournier-Gunawan-Romanzin93] [Drettakis-Robert-Bougnoux97]

– reflectance estimate• from pixels of the textures

– estimation of the light sources exitance

• Initialisation of the lighting system– hierarchical radiosity system

The technique builds on Fournier et al, and Drettakis et al. to initialise the parameters (initial reflectance, light source exitance). The method also uses a hierarchical radiosity system.

199

Global illumination estimation• Initial radiosity solution (without textures)

– radiosity for each mesh element

From the initial parameters a radiosity solution is computed.

200

Adding virtual objects• Shadow of the virtual object on the table• Modulate the texture with a display ratio

[Drettakis et al. 97]

Modified radiosity

Initial radiosity

To make light changes perceptible after virtual modifications, textures are modulated by a factor of the modified radiosity over the initial radiosity.

201

Limitations• Problem [Drettakis-Robert-Bougnoux97] : shadow already

included in the textures

Left real light source virtually switched off

But this doesn’t allow relighting.

202

Creation of new textures without shadows

• For each element in a shadow region– add light previously blocked by a real object– correction from a reference element chosen automatically

referenceelement

elementin shadow

In order to allow relighting new textures are created on which shadow effects are removed.

203

Texture correction

Original textures Textures without shadows

204

New radiosity solution

Radiosity Bi Radiosity B0 « without shadows »

We can update now a new radiosity Bo corresponding to the textures without shadows.

205

New lighting

Display ratio

. Texture

Relighting allowed

Bi

B0

B0Bi

The original lighting or any new lighting can then be reproduced by applying a factor to the textures without shadows. The factor is based on the new calculated radiosity over the radiosity without shadows.

206

Comparison with reality

Original photograph Simulated original lighting

207

Comparison with reality

Photograph with new lighting Simulated relighting

208

HDRIs against RGB format

Original photograph

Textures without shadowsRGB

radiance

Using HDRIs helps producing more accurate results.

209

Interactive relighting

• Light source exitance modification– fast solution

• Add/Move virtual objects and light source– incremental algorithm [Drettakis et Sillion 97]

210

Approach 2: Loscos et al. 99

• Input:• Partial geometry known• Several lighting conditions known• Few input photographs

• Output:• Approximate solution (diffuse reflectance only)• Fixed viewpoint• Interactive control

211

Input data• Radiance images from a single viewpoint

– a single light source per image

Differentlighting

conditions

In a second approach, we will use the fact that we can retrieve reflectance parameters easier when several lighting conditions are known.

212

Reflectance estimate pixel per pixel• For each radiance image

• Indirect approximated by an ambient term– Leads to errors

reflectancereflectance == radiosityradiosity // (direct(direct lightlight ++ indirect lightindirect light ))

Original Original photographphotograph EstimatedEstimated reflectancereflectance

The reflectance estimate is done pixel per pixel using an approximation of the calculation of the direct lighting and indirect lighting. Because of the approximations the reflectance values are very inaccurate.

213

Use of Weighted Average to Merge the Reflectance Values

x

x

avg.

reflectance confidence

mergedreflectance

We use the combination of images to reduce the errors. We assign to each image a confidence value that remove areas in shadows (more prone to errors because of the approximation on the indirect lighting), and for highlights since only diffuse reflectances are treated.

214

Lighting simulation

• Direct lighting: Ray casting• Indirect lighting: optimised radiosity solution

pixel

Reflectance

Directlight

Indirectlight

After the reflectance values are calculated, the illumination is calculated per pixel for the direct lighting. The indirect lighting is however calculated using radiosity as it is faster than ray tracing.

215

Iterative algorithm for reflectance estimate

• For each pixel:

convergence of reflectance values

Initial Initial reflectancereflectance

Indirect Indirect lightinglighting

New New reflectancereflectance

iterationiteration

(indirect = (indirect = ambientambient))

An iterative approach is set to update the reflectance values with the indirect lighting calculation improving through the iterations.

216

Calibration results (with HDRI input)

RGB Initial radiance After iterations

Reflectance

The calculated reflectance is shown on those images. HDRIs images help producing results with less visible errors.

217

Reflectance for a scanline (after iterations)

Calibration results

The reflectance values are shown in RGB for a scan line. For a same material, values are consistent.

218

Lighting simulation

Photograph SimulationSimulation

219

Approach 3: Yu et al. 99• Input:

• Full geometry known• One lighting condition known• Many input photographs

• Output:• Accurate solution• Pre-computed results• Possible of changing viewpoint before computation

220

Input• Reconstruct scene geometry and light source positions

In another approach, it is possible to deal with more complex BRDFs and lighting conditions.

221

BRDF estimation• Diffuse albedo estimated using inverse radiosity

• Roughness and specular albedo estimated using non-linear optimisation:

– based on a large set of images from different viewpoints and specular highlights identified in these images

In this method, the diffuse reflectance is computed using a radiosity method. Whereas the other BRDF parameters are estimated using a non-linear optimisation

222

Results• Rendering using RADIANCE

A great advantage of this method is that the computed BRDFs are accurate. The scene can therefore be relighting with very good results.

223

Approach 4: Boivin et al. 01• Input:

• Full geometry known• One lighting condition known• One input photograph

• Output:• Nearly accurate solution• Pre-computed results• Possible of changing

viewpoint before computation

224

Method Overview• Reconstruct scene

geometry, light source position

• BRDF model according to Ward et al. : 3 or 5 parameters: diffuse, specular, roughness

31

The method of Boivin et al. is similar to the one of Yu et al.

225

Method Overview31

• Iterative approximation based on one single image:

1. start from initial BRDF estimate2. render scene using BRDF, light sources and geometry3. calculate difference with input image4. if difference too large:

1. make new BRDF estimate, or 2. refine BRDF model 3. go to step 2

5. else stop!

It uses an iterative algorithm but it is based on a single image (rather than a set as in Yu et al.)

226

Results• Output reflectance at each iteration step

After each iteration, the errors in computation decrease.

227

Results

original re-rendered

32

• Use scene knowledge to fill in invisible parts of the scene

With this method it is possible to modify the view point by completing the unknown regions with the calculated materials.

228

Conclusions• Relighting methods can be used for lighting design of

existing rooms• Solutions range from accuracy to interactivity• Usually it needs a good understanding of the geometry

and the original lighting

We have presented four different approaches to calculate indoor relighting. The different solutions range from accuracy to interactivity and practicability. All require a fair understanding of the geometry of the scene.

229

Future Work• Solutions are now limited to controlled rooms• Future methods:

– Should work on any type of surfaces and objects• including for e.g., plants, set of small objects, table cloths,

untidy rooms– Should work for any type of lighting

• combining natural light from windows with different types of light sources

– Should provide a system usable by a designer with a library of furniture and lightings, and an interface

Relighting methods are still at their early stage since for each presented method, the rooms were chosen carefully with controlled geometry and lighting conditions (no windows for example). It is expected that a new range of methods should come up to allow more complex scenes and conditions to be treated.

230

1. Inverse Rendering Definition2. Applications to Inverse Lighting3. Applications to Inverse Geometry

1. General design of reflectors2. User-guided design of reflectors

4. Conclusion and Future Work


In this Section, applications are given of inverse geometry.

231

Applications to Inverse Geometry: Surface Design




232

Applications to Inverse Geometry: Surface Design

• Introduction• Previous Work• Problem Statement• Foundations• Numerical Aspects of Inverse Surface Design • General design of reflectors• User-guided design of reflectors• Conclusions• Future Work

233

Height

Reflector

Bulb

Target Optical Set

Firstly, we should define what an optical set is. The reflector shape to be found is just a piece of a set called in lighting engineering an optical set, which consists of a light bulb, the reflector and, possibly, the diffusor. The reflector has a border, contained in a plane, that limits its shape. In general, a reflector must fit inside a holding case, so its shape cannot be lower at any point than the plane defined by the border nor higher than a certain threshold defined by the case. We can say that the case defines a bounding box for the reflector.

234

Objective

• Design of reflector shapes from prescribed optical properties and geometrical constraints.

We will focus our efforts on the following problem: Given a desired optical set-outgoing radiance distribution, find the corresponding shape for the reflector that provides a light distribution similar to the given one up to a user-defined threshold.

235

Restrictions (I)

• Surface must be “build-able”:z = f(x,y)

Metallic sheet

z

x/y

The following constraints are imposed on the surface shape to be built: The shape must satisfy certain constructive constraints that amount to requiring that the shape of the reflector be the graph of a function with respect to the plane of the reflector's border.

236

Restrictions (II)

• Shape must fit exactly into the border

The resulting shape must exactly fit the given border because the case holds the reflector at that curve.

237

Restrictions (III)

• Shape can’t be lower than border plane (should leave space for light bulb)

• Shape can’t be higher than holding case

Border PlaneLight bulb

Holding Case

The shape cannot be lower than the border plane (z=0), or higher than a certain maximum height (it must fit inside the case).

238

Previous Work: Inverse Surfaces

Source

BRDF

Reflector


This problem is clearly within the Inverse Geometry problems we mentioned before

239

Previous Work: Our case

• To the best of our knowledge, there are no other works dealing with: – Inter-reflections inside the reflector– General BRDFs– Polygon-based surfaces– A global strategy for the optimization

To the best of our knowledge, there are no other works dealing simultaneously with the treatment of inter-reflections inside the reflector geometry, using general BRDFs for the reflector surface material, a polygonal-based representation of the surface, and finally, a global strategy for the optimization.

240

Problem Statement• Given

– The radiance distribution of the light bulb– A reflector border– A desired outgoing radiance distribution for the

Optical Set

• Find a shape within a user-prescribed tolerance

We can state more precisely our problem as: Given the outgoing radiance distribution of a light bulb and a reflector border, and given a desired optical set-outgoing radiance distribution, find the corresponding shape for the reflector. Do this up to a user-defined tolerance.

241

Surface RepresentationRegular Grid:

+ Avoids optical estriations+ Easy to manufacture+ Allows studying the procedure+ Border fitting almost trivial− Polygonal approximation− C0 Continuity − Not very flexible− Industry requires a fine subdivision.

We choose to implement the regular grid representation/scheme because: Allows to avoid undesirable striations since images (in the optical sense) are formed behind the reflector[CM97]. An accurate template or tool to build a physical reflector from the resulting data can easily be made [CM97]. The overall convergence and stability of the algorithm can be easily tested. The routines for border matching are very simple: Only the grid points inside the border are available for optimization (the ones marked with dots in The Figure above). When assembling the surface, the polygons that join the grid points that define the surface in the interior of the border with the border itself are created, making a polygonal approximation to the originally given border, see Figure. In order to do this, the border is intersected with the grid lines and the intersection points (marked with circles in the lower image) are used to build the polygons. Those polygons are created following a pattern like the one shown in the Figure. On the other hand, regular grid representations present the following disadvantages C0 continuity at all the triangle lines in the Figure, that are all over the surface. To be flexible to adapt to the illumination requirements imposed by the OutRaddesired radiance distribution, the surface built this way needs many vertices, which increases computing times.\item A fine grid is needed to achieve the smoothness needed to achieve the manufacturing standards of the industry. [CM97] J. R. Coaton and A.M. Marsden, “Lamps and Lighting” ,Ed. Arnold, London, 1997

242

Outgoing RadianceDistributions specification

We choose to use the C-γ coordinate system [CM97] as our discrete representation for the outgoing radiance distributions, because it represents a standard in the lighting engineering industry. This coordinate system is depicted in the Figure. It is worth mentioning that the C-γ representation is equivalent to any other spherical coordinate system (see [Cohen93-RRIS] Section 10.1.4, General Luminaries). As we can see, the C-γ representation is an angular representation given by two angles, c and γ (c ∈ [0,2π], γ ∈ [0, π]). [Cohen93-RRIS] Michael F. Cohen and John R. Wallace, “Radiosity and Realistic Image Synthesis”, Academic Press Professional, Boston MA, 1993, ISBN 0-12-178270-0

243

Monte Carlo Light Tracing

This step has as a main objective the computation of the outgoing C-γ radiance distribution from a given reflector shape. Light rays are sampled at the light source according to its energy distribution per solid angle, shooting more rays in the direction where more light is emitted. Then, ray paths are followed until they leave the optical set and then their intensities are recorded in the corresponding entry of the C-γ distribution.

244

Monte Carlo Light Tracing• Advantages

• Accurate• No Lost Rays• General BRDFs• Interreflection• All kind of optical phenomena

• Drawbacks• Slow

• Best among ray-based options

For this, several possibilities were studied, arriving to the conclusion that Monte Carlo Light Tracing is the best option: This algorithm is, by far, the most efficient and straightforward to code, as it propagates the radiance from the light sources to the rest of the optical set [Lafortune96-MMMCA]. In this method, each fired ray contributes to the final result and there are no lost rays. Thus, we get an optimal usage of the computational effort of tracing rays, since each ray propagates from the light source and each of them contributes significantly to the final result. On the other hand, is important to notice that this algorithm can easily accommodate general BRDFs (as long as then can be sampled), interreflections and other kind of optical phenomena. For example, if we would like to add the glass diffusor, it would be very easy to include refractions in our current model. Unfortunately, if we want a small variance, we must use many rays for the computations, making this algorithm a slow choice. It is important to take into account that the Light Tracing algorithm was developed with extended, non-isotropic light sources in mind, uniformly sampling locations over the light bulb surface. Thus, although all our experiments were done with point light sources, our algorithms should perform equally well on photometric lamp data provided

by near-field goniophotometers (see [RadiantImaging]). [Lafortune96-MMMCA] Eric Lafortune, “Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering”, Ph.D. thesis, Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium, February, 1996. [RadiantImaging] Radiant Imaging Photometric, URL: http://www.radimg.com/

245

Error Definition

• Tested several options:– Drettakis (% of pixels above threshold)– ln (l2, l1, l∞)

• We are going to use the l2 metric + penalization terms

∑ −=ji

ijdesired

ij OutROutRError,

2

2 )(η

Parameters that define a reflector shape

The error definition is, by far, one of the most delicate parts of an optimization algorithm. This error is what drives the optimization and is being evaluated every time we need to assess the behavior of any reflector, and so, its definition is crucial for the right behavior of the algorithm. We decided to try several options, among which are those listed in the slide, but with poor success. We finally resorted to the well known l2 error measure to drive our optimization process. This error is just computed as the square root of the element-wise difference between a light distribution generated with the current reflector (whose shape is given by the parameter vector η ) and the desired one, provided by the user. To take into account the restrictions imposed by the bounding box, we added penalizing terms to this error, thus changing the problem into an unconstrained one.

246

Algorithm Foundations (I)

• Let Δi be a vertex influence region:Δi = OutR(Refl) | OutR(Refli)

Our Operator:

||)|( 2121ijijij cccc γγγγ −=

C

γ

In order to be able to explain the behavior of the function and of our algorithm in simple terms, it is convenient to introduce some further definitions. One of the most important ones is the differential vertex influence region, Δi . This Δi is computed for the i-th vertex with our specifically defined operator “|”, which is the light distribution that arises as the element-wise absolute value of the difference of two light distributions. Thus, Δi is defined as the (positive) difference between the light distribution computed for the current reflector, and the light distribution computed for the same reflector, but with one of its vertices (the i-th one) displaced a little bit. An schematic example of this can be found in the figure at the left. On the lower right hand side we can find an actual result of a difference between two light distributions, were dark blue means small values (close to zero), brown intermediate values, yellow higher ones and light blue the highest ones.

247

Reference

Curr

Curr | Reference

Curr 5mmA

Curr 5mmACurr |

(Curr | Reference) Curr )5mmA(Curr |*

Algorithm Foundations (II)

summing thisgives statusi

Δa

Here we can see how the different operators work together. Starting from the upper right image, which is the desired light distribution provided by the user, we can compute its difference (with the “|” operator) with the light distribution generated by the current reflector (called “Curr”), getting the light distribution un the upper row of the middle column (Curr | Reference). This distribution shows us the error between the current reflector and the ideal one we are looking for. We can compute Δa by making the same operation between Box and the light distribution generated by the same reflector as Curr , but one of its vertices shifted a little bit (Curr | CurrA

5mm). This time this was 5 millimeters upwards. This computation shows us the contribution of this particular vertex to the current light distribution. Now, if we perform an element-wise multiplication of the just computed light distributions (Δa and Curr | Reference), we get the light distribution on the last column, which shows us the area of contribution of this particular vertex to the overall error. If we add the values in this light distribution, we get a quantity we called the statusi .

248

Algorithm Foundations (III)

• Observations:– Statusi ≥ 0– Statusi is relative, not absolute!

The statusi provides us valuable information, so it is interesting to look at it a little bit more. The first thing to notice, is that the statusi is a positive defined quantity, that is, is always bigger than zero. The second one is that it is a relative measure, because it measures local shape, not absolute position deviations. That is, given the reflector shown in the middle, statusi would present the vertices of the reflector on the left hand image as much better than the vertices at the right hand one, as the shape is much closer on the left than on the right, although the absolute positions of the vertices are the other way round. Thus, statusi is not a measure we can use to drive our optimization. We only can get hints on where to put more effort, but the global optimization must be still computed by the l2 error we presented a few slides ago.

249

Analysis: Vertex Couplings

Superposition = Δa * Δb

Δa

Δb

We can perform a similar computation with two Δa and Δb vertex influence regions (left column), and by element-wise multiplication we can get the product Δa * Δb , which shows the superposition between both light distributions. As we can see, there are brown areas in the image, which means a non-zero overlapping area. We can sum those values, and perform that for every pair of vertices. In the lower right image we can see a graph for one particular vertex, and we can observe that we have no zero values, meaning that every pair of vertices have overlapping areas. That means that every vertex influences the same regions as every other vertex, thus showing us that we can

not treat a vertex in isolation, as the other vertices would give us a wrong picture during the optimization. We can conclude that our degrees of freedom, our vertices, are strongly coupled. This is a very bad situation for optimization algorithms which try to optimize each degree of freedom separately, hoping to converge at the end.

250

Analysis: Function analysis

Full shape, Perfect Specular One Vertex, Phong BRDF

Changing the shape

Before working on any optimization algorithm, we should make ourselves an idea of the shape of the function we are trying to optimize. In the left picture we have the case when we move the full surface upwards and downwards, with a prefect specular BRDF. In the right picture we move just one vertex, but with a classic Phong BRDF this time. What is important of those pictures is that they both have a clear global minimum, but surrounded by many local minima, which is a very unfortunate situation for local optimization algorithms, as they tend to get trapped by those local minima instead of reaching the deeper global one.

251

Analysis: Function analysis.Monte Carlo Evaluation

1e5 rays 1e7 rays

Another point to take into account is the fact that we are using a Monte Carlo (MC) based algorithm for the light propagation evaluation. As is well known, every MC evaluation has an inherent variance associated with it, giving us values that are around the real one but within the associated variance. Of course, the more rays, the more accurate our simulation would be. For example, if we draw a part of the complete function with 1e5 rays (left), we would get a picture which shows a clear MC noise all over its shape. But, if we draw the same function, this time with 100 times more rays, we will get the picture on the right, showing much more clearly the real shape of the function. So, lets suppose, to start, that we want to perform our optimization only with 1e5 rays to fasten calculations. But, we can see from the picture that, if we do movements of about 1 or 2 millimeters (the horizontal axis is millimeters), we won’t get any meaningful information, as we are optimizing within MC noise, which hides the real shape. From the left picture we could say that movements of about 5 millimeters are needed to get meaningful information. But we need a well founded way to assess the distances we should move for the small variations in our algorithm…

252

Analysis: SensitivityThe Semivariogram:

A statistic measure of the decrease in similarity of two random variables with distance

From this, a = 5 mma

In order to do so, we can compute a semivariogram, which is a statistical measure of the way two random variables decrease in similarity as they get apart. The typical shape of a semivariogram is shown in the lower left, where we can define a value called range (“a” in the figure), which is the distance after which we can not get meaningful information about the underlying shape of the function. So, if we want to take a measure about the underlying function, like our differential vertex influence region, we should use values smaller than this range. Performing the measurements for our case, we observe that 5 millimeters is the value of the range. But, as we want to take meaningful measures taking into account the MC noise, we decided to use exactly 5 millimeters for our differential measurements. That is why we used that value in the previous slides.

253

Classic optimization behaviour

• We have tested several alternatives:– Conjugate gradients– Powell’s method– Simplex method– Stimulated annealing

• Vertex coupling + the variance of the MC evaluation made them fail !

When starting with the optimization stage, we tested several possibilities, those on the slide among others. Unfortunately, the combination of the strong vertex coupling plus the fact that we are performing MC-based computations (every evaluation has a variance associated which creates a noisy landscape) made all of them fail. Thus, we needed to find a different, custom optimization method for our problem.

254

Summary of problems encountered

• High non-linearity:– Many local minimum– Local methods tend to fail

• Strong vertex coupling– Can’t optimize one by one– Can’t optimize subsets of vertices

• Noisy Light simulation– Values not exact (variance)

So summarize the problems we found, we can mention A strong non-linearity, with many local minima surrounding a clear global one. As a consequence, unless the starting point is chosen extremely wisely (which is very difficult), local methods tend to fail. Strong vertex coupling that precludes the optimization of vertices one by one, or even in small subsets! We are using a noisy light simulation, measurements have an associated variance: the values we measure are not exact, the real value could lie anywhere within the value plus/minus its variance. Although the probability distribution is a typical Gaussian, we can’t rely only on the central value.

255

Algorithm - Global Optimization

So, the core of our optimization algorithm works as follows: Sorts the available vertices by their respective status. Then takes the N with highest values. Assigns to each chosen vertex a span of possible positions (based on their respective status). Then, we compute tests/evaluations of the performance of each member of a family of reflectors obtained by iteratively combining the addition of an increment to each one of the vertices. Then, we kept the best one: the one with smallest error. Unfortunately, just keeping the one with lower central

value is not right, as each value has an associated variance bar. So, we must keep the best one as well as all the other reflectors that gave an error whose variance bar overlaps with the one of the best one. What we can do is to consider those values as being measurements of an ideal reflector we don’t know, so we can average them to get the final reflector for this iteration.

256

Reflector := create a low-res reflectorwhile (not converged) and (not userDefinedStop)

FreeVertexList := all vertices in ReflectorWrappedRefl := wrap (Reflector, FreeVertexList)while (not converged) and (FreeVertexList is not empty)

addVertices (WrappedRefl, FreeVertexList)optimize (WrappedRefl)

if (not converged)increaseResolution (Reflector)

Algorithm

Unfortunately, this algorithm has an exponential behavior each time we increase the resolution of the reflector: we increase resolution by doubling the number of vertices in each direction. This is done whenever we finish an iteration and do not reach the user defined threshold and the number of iterations do not exceed a certain defined number. So, each time we have 4 times more vertices, thus getting an exponential behavior. In order to avoid such behavior, a strategy called wrapping is introduced. The basic idea is to expose the optimization stage only a carefully chosen subset of the available vertices, interpolating the others.

257

Algorithm - Wrapping

• Avoids an exponential behavior• Consists of two parts

– Wrapper– New vertex addition strategy

• Surface Wrapper:– Initialized w/ vertices at previous resolution– Interpolates wrapped vertices from the non-

wrapped ones (Akima)

Thus, the wrapping strategy consists of two parts: the wrapper itself and the strategy for the addition of new vertices every time more flexibility is needed. The surface wrapper is initialized at each iteration with the vertices at the previous resolution/iteration. The non-exposed vertices are interpolated by a polynomial scheme.

258

• Addition of new vertices:– Only when more flexibility is needed– Sort unwrapped vertices by Statusi

– Choose worst N– For each, select wrapped neighbors– Add m with maximum free-area-coverage.– Remove from Free-Vertex-List

Algorithm - Wrapping

With respect to the addition (exposure) of new vertices, the basic idea is to add new vertices only when more flexibility is need. The vertices are added by sorting the current ones by their status and by choosing the N with worst values, and the areas surrounding them are refined (remember that status is a local measure of the wrongness in shape of a vertex neighborhood). Thus, we add some of those vertices, in a way controlled by the user. In our case, we decided to add a fixed number of vertices each iteration, having a linear behavior in the number of vertices to optimize.

259

Accuracy: #Rays and BRDFDiffuse to specular ratio

Before showing the results for this algorithm, let’s study its accuracy. We can see that, as expected, the variance diminishes as the number of rays increases, a classical behavior for MC algorithms. What is interesting is that the variance also increases as the BRDF goes more diffuse. This result can be explained as diffuse BRDFs tend to “blur” the information, mixing the rays because of the high number of interreflections. It is important to mention that this variance also

represents a bound for the performance of our algorithm. For example, if we are using the Phong BRDF defined by the diffuse to specular ratio 0.05, and we decide to use 10000 rays, we have a variance of about 0.14. This means that we will not be able to get closer to zero than 0.14, because if we get closer we won’t be able to distinguish the real function of the MC noise. Thus, the variance gives us a bound on the convergence of our algorithm.

260

Results – General

DesiredReflector 1

Obtained Reflector 1

Initial Reflector

DesiredReflector 2

Obtained Reflector 2

Cγ1

Cγ2

Here we can see a couple of examples: starting from an initial reflector with a corresponding outgoing light distribution (left of the slide), and given a desired light distribution like the one in the middle-lower part of the slide, we get a reflector like the one on the lower right part of the slide, with a distribution that is very similar to the desired one. If we compare the obtained reflector with the one we used to generate the desired light distribution (the reflector shown in the middle-lower image), we can see that they are quite similar. The same can be seen in the upper part of the image for a different situation. Unfortunately, this algorithm is slow: it took about 10 days to get from the left part of the slide to the right one!

261

User-guided optimization

So, a logical possibility is to incorporate knowledge provided by the user to the algorithm: We expect the natural user of this system to be a lighting engineer, who generally has, by experience, a reasonable idea of what the resulting reflector should look like. So, we request him to provide a starting reflector plus two confidence values that tell us his own confidence on his own guess. We are going to use this information to define bounds on the optimization region for the possible reflectors during the optimization stage.

262

User-guided: Accomodation

In order to take maximum advantage of that information the user provided, we added an extra step before the global optimization described a few slides ago. Basically, what we intend to do is to modify the user-provided surface without changing its overall shape, just trying to adjust it to be as close as possible to the desired one before starting the global optimization. So, this new step consists of two parts: Firstly, we move and stretch the surface upwards and downwards. Then, we shift the vertex positions horizontally, in the plane of the reflector border, trying to get the maximum flexibility of the vertices we have. Observe that we continue having a regular grid, we just compressed/expanded and shifted the vertices as a whole.

263

User-guided: Vertex Selection

• Problem:– We don’t have a “previous” surface to choose

vertices from.– We can’t use the full user-provided surface.

• Solution: – an heuristic that iteratively chooses vertices

• With maximum coverage area• As far as possible to the already placed ones

Now, before we can start with the global optimization, we must face another small problem: In the previous version of the algorithm, we initialized the wrapper with the vertices used at the previous iteration. But now, we don’t have a previous iteration to start with. So, we must find a way to choose the initial vertices for the first iteration. We decided to use a simple heuristic that iteratively chooses vertices with maximum free area (without other vertices) around them, being at the same time as far as possible to the already placed ones. Distances between vertices are measured with the standard 2D distance.

264

User-guided: bounded optimization

The new algorithm works as follows: We start from a user-provided initial surface, plus two confidence values. We perform firstly a vertical accommodation step and then a horizontal accommodation one. Finally, we start a global optimization as before, but taking into account the original bounds we were provided, not generating any vertex outside this allowed region.

265

User-guided : Test Cases

A

A1

A2

A3

B

B1

B2

C

C1

As test reflectors, we built for each desired one (see upper row), a set of user-provided starting reflectors with different geometric properties (other rows).

266

General vs. User-guided

Diffuse tospecularratio

As we can see from this table, times were reduced from the order of 10 days to the order of only one. Also, by observing the fourth column, we can see the error is much smaller than the previous version of the algorithm (called “old”). But this affirmation is not completely fair, as we were forced to use many more rays for the new optimization as the user provided a surface close to the desired one, with an associated error that quickly collided with the variance for that number of rays. So, we must use more rays to be able to do any meaningful optimization. So, the advantages are twofold: on the one side, we reduced the computing time from 10 days to about one. On the other hand, we even were able to increase the accuracy of our algorithm!

267

General vs. User-guidedDesired General User-guided

To visually compare both algorithms, we can provide the algorithms with the desired light distribution resulting from a reflector we know (but the algorithm doesn’t), shown in the right column. The general algorithm started from the one shown in the middle column, upper reflector, and got to the lower one. Instead, the second algorithm started from the reflector in the right column, upper row, and got to the lower one, which is much more similar to the desired one than the one we got from a generic starting point.

268

General vs. User-guidedDesired General User-guided

Initial Initial

Final Final

If we want to observe the outgoing light distributions and their respective errors, we can compare the respective light distributions shown below each reflector (left side when there are two distributions). By visual comparison, we can see that the resulting light distribution from the final reflector in the user-guided algorithm is much closer to the desired light distribution than the final distribution from the general algorithm. The respective error graphs are shown on the right of these distributions, and we can see that the resulting distributions from the user-guided case present a much smaller error than their general counterpart (remember: light blue mean high values, so the errors for the user-guided case are much smaller than the general ones as they do not present colors for higher values in their distribution).

269

Conclusions

• A good solution for design of reflectors with:– Interreflections– General BRDFs– A polygonal surface– A global strategy for the optimization

• Robust solutions:– From a generic start– With a user-guided setting

We have presented a new solution for design of reflectors taking into account multiple interreflections, a general BRDF model, a polygonal surface and a global strategy for the optimization. Also, we have presented robust solutions, both starting from a generic starting point and in a user-guided setting.

270

Future Work• Different reflector shape definitions:

– Non-regular distribution of vertices+ triangularization

– Splines• Other error metrics (entropy)• Recent theoretical developments for optimization in

restricted cases• Generalization to the near-field (in the lighting

engineering sense) problem• Parallelism

– Distribution of the optimization work among several CPUs– Change the Light Propagation Stage to a GPU-based solution

271

bibliography• A Survey on Inverse Rendering Problems, Gustavo Patow and

Xavier Pueyo. Computer Graphics Forum 22(4), pp. 663-687.• Reflector Design From Radiance Distributions, Gustavo

Patow, Xavier Pueyo and Alvar Vinacua, International Journal of Shape Modeling, vol 10 (2004), number 2, pp. 211--235.

• A Survey of Inverse Surface Design From Light Transport Behavior Specification, Gustavo Patow and Xavier Pueyo. Computer Graphics Forum. December 2005.

• User-Guided Inverse Reflector Design, Gustavo Patow, Xavier Pueyo and Alvar Vinacua, Research Report TR-IIiA 04-07-RR, Institut d'Informàtica i Aplicacions, Universitat de Girona, 2004.

272


Conclusions

273

Conclusions (I)

• A definition of Inverse Rendering: Goes the opposite way of classical rendering – Based on an image (or a lighting description) and

some extra information, the missing information in the radiance equation can be calculated.

– Depending on the amount/type of information available, different strategies apply to calculate the missing information.

274

Conclusions (II)

• Classification of existing problems– Inverse lighting problems– Inverse reflectometry problems– Combined lighting-reflectometry problems– Inverse surface design problems

• Classification of existing solution methods– For general applications– For mixed reality

275

Conclusions (III)

• From theory to practice is not straightforward due to:– Capturing failure– Uncontrollability of scene– Complexity of the scene

276

Conclusions (IV)

• Some solutions to overcome these problems were presented

– Capturing illumination in complex (e.g.: outdoor) scenes– HDRI construction with moving objects– Common illumination with inaccurate geometry and lighting– Indoor lighting design (accuracy vs. interactivity)– Inverse reflector design

• But further research is required!

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Volume xx (200y), Number z, pp. 1–25

Classification of illumination methods for mixed reality

Katrien Jacobs† and Céline Loscos‡

Department of Computer Science, University College London, UK

AbstractA mixed reality (MR) represents an environment composed both by real and virtual objects. MR applications areused more and more, for instance in surgery, architecture, cultural heritage, entertainment, etc. For some of theseapplications it is important to merge the real and virtual elements using consistent illumination. This report pro-poses a classification of illumination methods for MR applications that aim at generating a merged environmentin which illumination and shadows are consistent. Three different illumination methods can be identified: commonillumination, relighting and methods based on inverse illumination. In this report a classification of the illumina-tion methods for MR is given based on their input requirements: the amount of geometry and radiance known ofthe real environment. This led us to define four categories of methods that vary depending on the type of geometricmodel used for representing the real scene, and the different radiance information available for each point of thereal scene. Various methods are described within their category.The classification points out that in general the quality of the illumination interactions increases with the amount ofinput information available. On the other hand, the accessibility of the method decreases since its pre-processingtime increases to gather the extra information. Recent developed techniques managed to compensate unknowndata with clever techniques using an iterative algorithm, hardware illumination or recent progress in stereovision.Finally a review of illumination techniques for MR is given with a discussion on important properties such as thepossibility of interactivity or the amount of complexity in the simulated illumination.

Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: augmented reality, mixedreality, common illumination, relighting, inverse illumination

1. Introduction

To understand the concept mixed reality it is necessary toclassify the different types of environments that can begenerated with a computer. Milgram et al. [MK94, OT99]present such classification based on the amount and type ofvirtual and real elements that constitute the resulting world.In their classification, all possible environments form onecontinuum called reality-virtuality continuum (RV), see Fig-ure 1. In this continuum, four worlds can be identified thathave an outspoken character. These four worlds lie next toeach other in the RV continuum and might even overlap.The first and most straightforward of these is the real worldwithout any addition of virtual elements; it will be referredto as reality and it lies on the left end of the RV contin-

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uum. In the second This world is referred to with the termaugmented reality (AR)[Azu95][ABB∗01][BKM99]. In anopposite scenario, the world consists of a virtual environ-ment, augmented with real elements. This world is conse-quently called an augmented virtuality (AV). The last andfourth world doesn’t contain any real elements and is there-fore labelled as a virtual environment (VE); it lies on theright end of the RV continuum. The term Mixed Reality (MR)refers to those worlds that are a mix of virtual and real ele-ments, or, MR spans the RV continuum. In general methodsthat are developed for AR focus on real-time applications.Therefore they usually differ from methods that are specif-ically designed for MR applications whose focus can be onnon real-time applications. This report will discuss the var-ious existing illumination methods for MR applications ingeneral.

Two different classes of AR exist; they differ in the reali-sation of the AR [MK94]. The first class groups the methods

submitted to COMPUTER GRAPHICS Forum (8/2005).

2 Katrien Jacobs and Céline Loscos / Classification of illumination methods for mixed reality

Figure 1: Simplified representation of a Reality-Continuum[MK94][OT99]. Courtesy of Milgram et al.

for semi-transparent or see-through displays, examples are[SCT∗94][BGWK03]. This first class contains two differentsee-through display methods. The first method (optical ARmethod [Azu95]) projects the virtual objects on a transparentbackground, most likely the glasses of goggles. The secondmethod (video AR method [Azu95]) uses a head-mounteddisplay: a head-mounted camera records the environmentand this image is projected inside the display together withthe virtual objects. The second class of AR replaces the ex-pensive see-through devices with a non-immersive display; itis usually called a computer-augmented reality (CAR). Thequality of the immersion is higher for the first class than forthe second. Nevertheless see-through devices are not alwaysrequired by the application: urban planning, architecture andsome applications in the entertainment industry are satisfiedwith the second type of CAR display methods. In earlier ap-proaches of AR, virtual objects were positioned on top ofa real environment. Calibration and registration are difficultprocesses and for long the focus lied upon taking into ac-count the possible occlusion and collision effects, while nofurther adaptations on real and virtual objects were carriedout. In other words, after the inclusion, no resulting shadowswere generated and no lighting changes were put through.An AR system of such kind does not yield a high level ofrealism, consistency between objects is restricted to geomet-ric aspects. Nowadays three illumination techniques can beidentified that attempt to raise the quality of AR and in gen-eral MR: common illumination, relighting and inverse illu-mination for relighting or common illumination. These tech-niques vary in the quality of the illumination and in the con-sistency obtained between the illumination of the real andvirtual objects.

The most straightforward method of these three results inthe addition of shadows in the MR environments. Generat-ing shadows is just as important as taking into account oc-clusions, since they help situating the objects in the sceneand give information about the distance between differentobjects [SUC95]. A higher level of realism can also be ob-tained when the local light interaction between real and vir-tual objects is incorporated in the MR scene. Simulatingsuch effects results in common illumination. An exampleof an application that uses common illumination to improvethe MR can be found in the movie industry. Special effectsin movies make an effort to mix lighting effects and reflec-tions as realistic as possible, resulting in brilliant graphical

effects in recent movies such as Jurassic Park, Harry Potterand The Lord of the Rings trilogy. In these movies computer-generated effects are blended entirely with the real footage;usually this is carried out by hand.

Some methods allow to change the original illumination,hereby influencing the appearance of virtual and real objects.An example of an application domain for this method is ar-chitecture. Being able to virtually change the lighting condi-tions in the real scene makes it possible to see the impact ofa new building in a street under different lighting conditionswithout the need of recording the real environment under allthese different conditions. Another application area is crimeinvestigation [HGM00]: a recording of a scene at a certaintime can be changed to the illumination at a different day-time, making it possible to visualise the perception of thecriminal at the time of the crime. Techniques that focus onvirtually changing the illumination of an existing scene aresimply known as relighting techniques.

The techniques brought together in a third category arebased on more complex estimations of the reflectances inthe environment in order to provide more accurate results.The process of estimating the reflectances (bidirectional re-flectance distribution function or BRDFs) from an existinglighting system is called inverse illumination. It was origi-nally developed to give more realism in computer graphics.Reflectance properties of objects were estimated in order toreproduce a more realistic simulation of virtual scenes. In thecontext of MR, inverse illumination techniques aim at mak-ing a correct estimate of the photometric properties of theobjects in the scene. While other techniques search for ac-ceptable solutions for the new illumination problem, inverseillumination makes it possible to produce relit images thataim to be an exact replica of the real conditions. A full dis-cussion of the current state of the art of inverse illuminationtechniques can be found in [PP03], while Ramamoorthi andMarschner [RM02] present a tutorial on some of the leadingresearch work in this area.

At the moment, fairly good techniques exist that can re-light an augmented scene with a different illumination. It isgetting more difficult to differentiate between virtual objectsand real objects. The main limitation of most techniques isthe tedious pre-processing time and the slow update rate,which excludes real-time applications. When a geometricmodel of the scene is required, the user will have to createone, usually in a semi-manual and error-prone manner. Thescene update rate is often too slow to allow real-time user in-teraction, even with the current progress in computer hard-ware and software. The research focus is moving towardsusing hardware for the calculation instead of software to ac-celerate computation. Early results are promising, but moreresearch needs to be carried out in this area. This report doesnot review all existing work. Instead it concentrates on il-lumination techniques in MR that are meant for large envi-ronments. When optimized and extended, these techniques


Katrien Jacobs and Céline Loscos / Classification of illumination methods for mixed reality 3

will be widely applicable in real-time applications, for in-stance see-through display in AR. Several techniques existfor relighting human faces [Mar98][DHT∗00], or that focuson local objects or simple scenes [ALCS03][SWI97]. Thesetechniques are classified mainly in the domain of inverse il-lumination as the emphasis was placed on this aspect in thereferenced papers. Although these techniques are designedfor small objects they can be used to build extremely usefuland strong methods for illumination in MR but they will notbe further discussed in this paper.

This report discusses the state of the art of those tech-niques that strive to solve the problem of illumination in MRenvironments and gives an objective evaluation of their qual-ity. Section 2 describes in more detail the context of this re-view and the assessment of the criteria on which the clas-sification is based. Section 3 gives a structured overview ofall the illumination methods that were developed for MR.A further qualitative evaluation and discussion of the differ-ent techniques is given in section 4. Finally section 5 givesconclusions and presents the necessary future work for illu-mination methods for MR.

2. Problem Assessment

2.1. Objective and difficulties

The classes described above are not necessarily designed tolure the users into believing that what they see is real. Forinstance VR often aims at trying to create the perception ofa real world, without necessarily using convincing real im-agery. Some AR systems merely add data displays to realscenes, making no attempt to mix the two seamlessly. Thisreport considers MR scenes that do try to convince the usersof believing that a real world is surrounding them and willuse this as a measure to assess the quality of the method.

An MR is convincingly real when it is impossible to sepa-rate the virtual elements from the real elements in the result-ing environment. Four critical success factors were identifiedthat need to be present in the MR in order to be convincinglyreal:

• After including the virtual object(s), the resultingscene needs to have a consistent shadow configura-tion[SUC95]. The main difficulty to obeye this require-ment is to find the correct appearance of the new shadows:their position in the scene, shape and colour. Sometimesthese are estimated, but they can be calculated exactly ifthe geometry of the scene, the illumination characteristicsand the material properties of all objects in the scene areknown.

• The virtual object(s) must look natural. A cartoon-likevirtual object is easily detectable and therefore effortshave been made to model objects that look realistic. Onesuccessful technique is image-based modelling, in whichobjects are rendered with textures based on real images.

• The illumination of the virtual object(s) needs to re-semble the illumination of the real objects. There aretwo possible methodologies to achieve this requirement.Either the illumination pattern of the real scene is known,which in turn is used to illuminate the virtual object or allmaterial properties of all objects in the scene are knownor estimated, which allows the entire scene to be relightedwith a consistent known illumination pattern.

• If the user can interact with the MR environment, it isclearly important that all update computations occurin real-time. Any delay in the interaction will remind theuser of the fact that what is seen is unreal [MW93]. Therequirement of a real-time system is one of the most diffi-cult to achieve, especially when no pre-processing time isallowed.

2.2. Assessment of existing techniques

The ultimate objective of the aforementioned techniques isdefined by the amount of realism perceived by the user. Thisinherent subjectivity complicates an objective assessment ofthe various techniques. In this section a few quality criteriaare listed that will be used in section 4 to assess the presentedmethods:

• Amount of realism. In some cases it is impossible to eval-uate the amount of realism without using a statistical mea-sure. For instance, a test audience can evaluate the tech-nique, if the test group is large enough, a statistical valuecan be derived from the group evaluation. Alternatively,if the inserted virtual object is an exact replica of an ex-isting real object, it is possible to give an exact value ofthe amount of realism in the produced scene. It sufficesto compare the generated scene with an image of the realobject in the same scene. The difference between the twogives a measure of the level of realism.

• Input requirements. It is expected that the more inputdata is available, the higher the quality of the end resultwill be. On the other hand, the usability of the systemreduces with the complexity of the input data. Possibleinput data are: the geometry, the light position, the illu-mination pattern and the material properties. This reportgives a classification of the various techniques based ontheir input requirement.

• Processing time. the time needed to create the end re-sult is another important characteristic of the method. Tooffer the user a highly realistic interactive environment,the computations need to be done in real-time. Unfortu-nately, this is very hard to achieve. If geometric and mate-rial properties of a scene need to be known, it is unavoid-able that some pre-processing time needs to be incorpo-rated. In general the usability of the proposed techniquesdepends on the amount of pre-processing time needed andthe computation speed of the illumination technique.

• Level of automation: if the technique under considera-tion requires a considerable amount of manual interaction



Figure 2: Results for Sato et al. [SSI99]. The top row shows results for an indoor scene, the bottom row for an outdoor scene.The images on the left are the input images, the images on the right illustrate the resulting MR. Soft shadows are produced usinglocal common illumination. Courtesy of Sato et al.

while processing the input data, the technique is less in-teresting than one that is automated.

• Level of interaction: a technique can be judged based onits dynamic character: the possibility to change the view-point of the camera, or the possibility to let the user inter-act with the environment for instance by moving aroundobjects. A higher degree of interaction gives a greater us-ability of the method.

2.3. Methodology

The various existing techniques can be grouped into threedifferent classes, based on the methodology used to solve theproblem. They were already listed in the introduction and arefurther discussed in this section:

1. Common illumination: to this category belong all meth-ods that provide a certain level of illumination blending,like the addition of shadows projected from real objectson virtual objects and shadows cast by virtual objects onreal objects. These techniques do not allow any modifi-cation of the current illumination of the scene. Two dif-ferent types of common illumination can be considered:local and global common illumination, referring to thetype of illumination simulated. For local common illu-mination, there is usually no requirement of any BRDFinformation. For global illumination, it is often importantto have an estimate of the material properties of the real

objects. The accuracy of this type of techniques dependson the accuracy of the known geometric model of the realscene. In Figure 2 an example is given of a rendering us-ing global common illumination [SSI99].

2. Relighting after light removal: relighting techniquesmake it possible to change the illumination of the scenein two steps. Firstly, the current illumination effects of thereal scene are analysed and possibly removed. Secondly,new illumination effects (shadows, intensity changes, ad-dition of a new light, indirect lighting effects, etc.) aregenerated based on a new illumination pattern. Thesemethods do not necessarily require an exact knowledgeof the BRDF values of the real scene objects as forsome methods the focus lies on generating a scene thatlooks realistic. These techniques require in general a de-tailed geometric model of the real scene. An exampleof a relighted scene using global illumination techniques[LDR00] is given in Figure 3.

3. Physically based illumination: this last category en-closes those methods that make an attempt to retrievethe photometric properties of all objects in the scene of-ten referred to by the term inverse illumination. Thesemethods estimate BRDF values as correctly as possibleas well as the emittance and positions of the light sourcesin the real scene. The BRDF values can be estimated us-ing a goniometer [War92] or can be calculated based onthe photometric equilibrium equations [Mar98] [SWI97].



Figure 3: Results for Loscos et al. [LDR00]. The image on the left hand side represents the real scene. The image on the righthand side shows the relighted synthetic scene for which real light sources have been virtually turned off and a virtual lightsource is inserted. Global common illumination updates are performed at interactive rates using an adapted version of [DS97].Courtesy of Loscos et al.

Figure 4: Results for Yu et al. [YDMH99]. Left: the original input scene. Right: the result of illuminating the original sceneusing a different illumination pattern. The specular and diffuse parameters of the real objects are calculated. Courtesy of Yu etal.

The BRDF information can be used for both common il-lumination or relighting methods. The accurate BRDF es-timation often permits to perform a complete and realisticrelighting, which takes both reflections and global illumi-nation techniques into account. Patow et al. [PP03] givean in-depth overview of inverse illumination techniques.An example of inverse global illumination [YDMH99] isillustrated in Figure 4.

3. Classification of Illumination Methods for MixedReality

MR brings together those applications that create a new en-vironment, around or in front of a user, containing both realand virtual elements. Sections 2.1 and 2.2 formulated theobjectives, the difficulties encountered and the assessmentcriteria of the MR systems. One of these criteria, the typeof input requirements, regulates the accessibility and accu-racy of the technique. This criteria will be used to classifythe different methods. An overview of the input informationneeded to calculate a common illumination, relighting or in-verse illumination solution is given in Figure 5.

The classification put forward firstly takes into accountthe required geometric model of the real scene, starting withthe techniques that require no geometric model and endingwith techniques that require a precise geometric model. Inthis report a geometric model is defined as a reconstructionof a part of the (or the entire) real scene with significant de-tail. The pre-processing workload for techniques that extracta basic geometric model, e.g. the depth at a low resolution,is significantly lower than those methods that do require ahigh-level geometric model. Therefore techniques using ba-sic geometric information are classified under that group ofmethods that do not require a geometric model, as this willgive a better indication of the amount of pre-processing timerequired for each different class.

Two different approaches exist to reconstruct a geometricmodel of the real scene. Either the scene is scanned with ascanning device [Nyl] [MNP∗99] [3Ds] or it is reconstructedusing stereovision [HGC92][Har97][Fau92][Fau93]. Thefirst option of using a scanning device gives a precise geo-metric model but is expensive and tedious. Often the modelwill capture too much detail, which is not always necessaryand is difficult to manage for real-time applications. Ob-



Figure 5: An overview of the dataflow in illumination calculation for MR. Three input sources are considered: the scenegeometry, the scene radiance and information about the to be inserted object(s). These are used to calculate the illuminationsolution. The accuracy of the integration depends on the amount of input information available.

jects such as trees and objects with a highly specular surfaceare for some scanning techniques difficult to model accu-rately. Instead of using a scanning device, modelling tech-niques based on stereovision can be used to reconstruct thegeometry of a scene. Most methods described in this sur-vey requiring a 3D model of the scene make use of thislow cost solution. In general, the 3D reconstruction requiresat least two images from two different viewpoints. How-ever, the entire geometry of a scene cannot be capturedwith one image pair only, this would create gaps in theknown geometry. Usually more than one image pair is re-quired for a complete geometric reconstruction. The ease

at which this reconstruction can take place depends on theamount of information that is available for the camera(s)used. If the internal and external camera parameters areknown, the reconstruction is easier. Internal parameters canbe estimated in a relatively simple way. Recording the exter-nal parameters is more difficult and involves a precise andtedious capture process. Fortunately, the fundamental ma-trix of the stereovision system can be estimated based onthe internal parameters only, if at least eight correspondingpoints are known [HGC92][Har97]. This was reduced to sixknown points [Fau92][Fau93] for a calibration relative to ascale factor, which is often sufficient. Having the fundamen-



tal matrix can ease the reconstruction but does not makeit trivial. Research led to different types of systems: nonconstraint systems [FRL∗98][SWI97] and constraint sys-tems [POF98][DTM96][DBY98][MYTG94]. Good com-mercial reconstruction software [Rea][Met][Eos][Int] exists,but most of them lack the option of reconstructing complexshapes and large environments. In general, we can concludethat systems requiring geometric information demand a longpre-processing time, and are not guaranteed to get an ac-curate geometric model. It is really important to recognizethe geometric acquisition as a difficult problem, that still re-quires much more research efforts.

Our classification of methods is, parallel with the classi-fication based on the geometric information, based on thisamount of image data needed to reconstruct a MR environ-ment. Hereby excluding the image data needed for retriev-ing geometric information. More precisely, the classificationwill use the amount of different input images used for therendering or calculation process. These processes might usemore than one image (or texture containing radiance infor-mation) for the same point in the real scene, for instance forthe BRDF estimation.

Some projects adopted the concepts of High DynamicRange Images (HDR images) [Lar91] which can be com-puted using techniques such as [DM97][MN99]. Each HDRimage is generated based on a set of images taken from thesame viewpoint of the same scene, but with a different expo-sure. The end-result is one image containing radiance valuesinstead of ordinary RGB values. In other words, radiancevalues are not clamped in the RGB space. It may be arguedthat methods using HDR images should be classified underthat class with methods that use more than one image foreach point of the scene. However, this report considers thata HDR image provides one radiance value per point, andmethods that use only one HDR image for a certain point ofthe scene, are therefore classified as methods requiring onlyone input image. Similarly, techniques that require a few ormany HDR images are classified as methods using respec-tively a few or many images.

The following classification is used throughout the rest ofthis section:

1. Model of the real scene unknown, one image known(section 3.1): this category lists those techniques that donot require any model of the real scene, except for somelow-level geometry like depth information. Any neces-sary radiance information of a certain point in the realscene is extracted from one single image.

2. Model of the real scene known, one image known (sec-tion 3.2): a geometric model of the real scene is available.Any necessary radiance information is extracted fromone image only.

3. Model of the real scene known, few images known(section 3.3): again a geometric model of the scene is re-

quired. For a certain point in the scene, radiance informa-tion is available from a few different images.

4. Model of the real scene known, many images known(section 3.4): this class groups those techniques that re-quire both a detailed geometric model of the real sceneand radiance information from a large set of different im-ages.

The rest of this section lists the most significant meth-ods based on the above mentioned classification and brieflydiscusses their methodology. A discussion of the techniquesbased on the assessment criteria mentioned in section 2.2 isgiven in section 4.

3.1. Model of real scene unknown, one image known

To this challenging category, in terms of output quality, be-long those methods that require very little relevant informa-tion about the real scene. Since no geometric model of thescene is available it might be necessary to calculate depthinformation of the scene, to allow a correct inclusion of thevirtual objects, or some lighting information. For this group,all radiance information is extracted from one single image.

Nakamae et al. [NHIN86] were the first to propose amethod for composing photographs with virtual elements.Input photographs are calibrated and a very simple geomet-ric model of the real scene is extracted. The viewpoints ofthe photograph and the virtual scene are aligned to ensure anappropriate registration of the virtual objects within the pho-tographed elements. The sun is positioned within the systemaccording to the time and date when the picture was taken.The sun intensity and an ambient term are estimated fromtwo polygons in the image. The illumination on the virtualelements is estimated and adjusted to satisfy the illuminationin the original photograph. The composition is done pixel bypixel and at that stage it is possible to add fog. All parame-ters are very inaccurate and therefore the results are limitedin accuracy. However, they were one of the first to mentionthe importance of using a radiometric model to improve theimage composition. Figure 6 displays gives an example ofthe obtained results.

Techniques exist in computer graphics that use envi-ronment maps to render objects in a scene. They wereintroduced to approximate reflections for interactive ren-dering [BN76][Gre86][VF94]. These techniques can alsobe used to assist the rendering of glossy reflections[CON99][HS99][KM00] by pre-filtering a map with a fixedreflection model or a BRDF. At this moment, graphics cardsextensions support the real-time use of environment maps,this encourages its use even more. Graphics cards nowsupport cube maps [NVi]; ATI [ATI02] presented at SIG-GRAPH 2003 a demonstration of a real-time application forhigh resolution. Environment maps can be used to representthe real scene in a MR environment as a panorama and theinformation from these images can be used to simulate re-



Figure 6: Results for Nakamae et al. [NHIN86]. The first image depicts the background scene, the second image shows theaugmented scene where the illumination of the augmented objects are matched to their surroundings and the shadows are castaccordingly. Courtesy of Nakamae et al.

flections on a vertical object positioned at the center of theenvironment map [Che95].

Agusanto et al. [ALCS03] exploited the idea of environ-ment maps to provide reflections in AR. They use HDR im-ages of the environment captured by a light probe to cre-ate the environment map. These maps are filtered off-lineto decompose the diffuse from the glossy components. Therendering is then performed with a multi-pass rendering al-gorithm that exploits hardware capabilities. After some pre-processing, like the inclusion of shadows, they present re-sults for MR environments rendered on a desktop. An im-pressive aspect of their work is that the method also worksfor real-time AR. The implementation of their method workswith ARToolKit [KBBM99] and the results show interactivereflections from the real scene on virtual objects at interac-tive frame rate. An example of such a projection is given inFigure 7. Although it should be feasible, they have not yetprovided a shadow algorithm for the AR application.

Sato et al. [SSI99] adopt a technique that extends the useof environment maps to perform common illumination. Intheir method, it is assumed that no geometry is known a-priori. However, at least a few images are known from dif-ferent but very restricted and known viewpoints, which canbe used to estimate a very simple geometry of the scene andthe position of the light sources. The obtained geometry doesnot offer a reliable occlusion detection and the positions ofthe virtual object are therefore restricted to lie in front ofall real objects in the real scene. After this low-level geo-metric reconstruction, a set of omni-directional images arecaptured with varying shutter speed. From these images, aradiance distribution is calculated, which in turn is mappedonto the geometry. To calculate the shadows and the local il-lumination a ray casting technique is adopted. The radiancevalues of the virtual objects are calculated using the informa-tion known about the light sources, the radiance values of thereal scene, the geometry and the BRDF values of the virtual

Figure 7: Results for Agusanto et al. [ALCS03]. The vir-tual objects are rendered with skin textures. The left objectis blended with a diffuse map and no soft shadows. The rightobjects is blended with a glossy map and with soft shadows.Courtesy of Agusanto et al.

objects. To simulate the shadows cast by virtual objects onreal objects, the radiance values of those points in the scenethat lie in shadow are scaled. The simulated soft shadowslook realistic, see Figure 2. Their geometric estimate is poorand therefore usability of the method is limited and the po-sitions of the virtual objects are restricted. Nevertheless themethod produces convincing local common illumination.

3.2. Model of real scene known, one image known

Most of the existing illumination methods assume that a geo-metric model of the scene is available. The more detailed thegeometric model is, the more reliable the occlusion detec-tion will be. Although not all techniques explain where thismodel should come from, it is doubtful that a perfect geo-metric model can ever be acquired and this should be taken



into account when evaluating a specific method. In this sec-tion a discussion is given of those methods that take a certain3D geometric model of the real scene as input and extract ra-diance information from one single image. All methods thatbelong to this category are further divided into three groupsbased on the type of illumination they produce:

• local illumination for AR applications: 3.2.2• common illumination: 3.2.1• relighting: 3.2.3

3.2.1. Local illumination for AR

As mentioned before, AR has long been an area whereinpeople focused on registration and calibration as these arestill difficult problems to solve in that area. However, a fewpapers tried to introduce shadows in their systems, to showhow well the registration was done and to improve the ren-dering quality. Recent improvements in graphics hardwarefor rendering shadows made it possible to perform real-timerendering of shadows on well-registered systems where thegeometry is known. Early work was presented by State etal. [SHC∗94] in which virtual objects are inserted in thesee-through real scene. A real light source is moved aroundand tracked, and shadows of the virtual object due to thisreal light source are virtually cast onto real objects by us-ing the shadow mapping technique [Bli88]. In this case, thelight source is assumed to be a point light source. It wasvery promising that some researchers in AR were interestedin using local common illumination in their systems, but itwas followed by a long period in which no innovative ma-terial emerged. Only recently, additional work of Haller etal. [HDH03] and Jacobs et al. [JAL∗05] was carried out toadd shadows from a virtual object onto real objects. Bothmethods use shadow volumes, and in order to get good qual-ity results knowledge about the scene geometry is essen-tial. However, Jacobs et al. start from a rough approxima-tion of the geometry and use image processing techniques tocompensate for approximation errors. Other methods exist[BGWK03] that we will not discuss here, since they will notbe applicable in general MR systems because these systemswould require the capture of a large environment.

3.2.2. Common illumination

Jancene et al. [JNP∗95] use a different approach to illumi-nate the virtual objects, they base their method, called RES(Reality Enriched by Synthesis), on the principle of com-position. The objective is to add virtual animated objects ina calibrated video sequence. The final video is a composi-tion of the original video sequence with a virtual video se-quence that contains both virtual objects and a representa-tion of the real objects. The geometry of the real object isreconstructed a-priori so that for each frame in the video thegeometry is known. The rendering in the virtual sequence isperformed using ray tracing. It is possible to modify the re-flectance properties of real objects. Shadows are simulated

in the virtual sequence, the impact of the shadows in the fi-nal video is acquired by modifying the original video with anattenuation factor. An occlusion mask is created to reflect oc-clusion between virtual and real objects. This method camequite early in the history of common illumination and videocomposition. Even though it is not applicable for real-timeapplications, it allows local common illumination and virtualmodification of the reflectance properties of real objects. Theimages on the left in Figure 8 illustrate the original scene, theimages on the right illustrate the composition.

Gibson and Murta [GM00] present a common illumina-tion method, using images taken from one viewpoint thatsucceeds in producing MR images at interactive rates, by us-ing hardware accelerated rendering techniques. Apart fromconstructing the geometry of the scene, the pre-processinginvolves creating a set of radiance maps based on an omni-directional HDR image of the entire scene. New virtual ob-jects are rendered via a spherical mapping algorithm, thatmaps the combination of these radiance maps onto the vir-tual object under consideration. Later shadows are added us-ing a two step algorithm. To simulate the shadows, a set ofM light sources are identified, which imitate the true, un-known illumination in the scene. Each light source is as-signed a position and two parameters αi and Ii, which definethe colour of the shadow. For each light source, a shadowmap is calculated using efficient hardware calculations (z-buffer). Shadow mapping is an intensively technique sup-ported by the graphics hardware that helps to create shad-ows in a fast and efficient way. The shadows created withshadow maps are in nature hard shadows and therefore un-suitable for realistic shadow generation. Gibson and Murtacombine the M shadow maps in a specific way, using theabove-mentioned parameters and now the system succeedsin simulating soft shadows, looking almost identical to thesolutions obtained with a more computational and tradi-tional ray-casting algorithm, see Figure 9. The system ofM light sources needs to be defined so that it represents aclose replica to the current illumination system, an increasein number of light sources affects the rendering time. Todemonstrate their method, Gibson and Murta used eight lightsources to simulate an indoor environment. The position andthe parameters of the light sources are defined via an optimi-sation algorithm, which needs to be executed only once foreach different scene.

Debevec [Deb98] presents a more advanced common il-lumination technique that estimates the BRDF values for asmall part of the scene. It is argued that if a virtual object isinserted into the scene, only a small fraction of the scene ex-periences an influence from that inclusion. Relighting tech-niques using inverse illumination therefore only require theBRDF values of those points that lie in this fraction. Sincefor most applications it is possible to know the position ofthe virtual objects, Debevec uses this position to divide theentire scene into two parts: the local scene and the distantscene. The local scene is that fraction of the scene whose



Figure 8: Results for Jancene et al. [JNP∗95]. The images on the left hand side show the original scene and the registrationof the cardboard box within this scene. The images on the right hand side show two screen shots from the video sequence inwhich a virtual dynamic green ball and static pink cube have been added to the original scene. The reflection of the green ballis visible on the board behind it. Courtesy of Jancene et al.

Figure 9: Results for Gibson et al. [GM00]. Comparison of a ray-traced (left) and a hardware generated image (right). The ray-traced image was generated using RADIANCE [War94], the hardware generated image made use of the rendering methoddescribed in [GM00]. The generation of the ray-traced image took approximately 2 hours, the generation of the hardwarerendered image took place at nearly 10 frames-per-second. Courtesy of Gibson et al.

appearance might alter after inclusion and the BRDF of thematerials in that part need to be estimated. On the other hand,the distant scene is that part of the scene that undergoes nophysical alteration after inclusion. A schematic overview ofthe division in local and distant scene and their correspond-ing influences is presented in Figure 10. The local scene isrestricted to be diffuse only; the distant scene has no restric-tions. An omni-directional HDR image is captured using amirrored ball. The resulting light probe image is used topresent the illumination in the real scene. Based on the geo-metric model, the light probe image and the division into lo-cal and distant scene, the BRDF values in the local scene areestimated. The calculations are straightforward, since onlydiffuse BRDF values are considered. A differential render-ing technique was developed to reduce the possible incon-sistencies in the geometric model and the (specular) erroron the BRDF estimates to an acceptable level. The render-ing is a two pass mechanism. First, the augmented scene isrendered using a global illumination technique, the result is

denoted by LSob j . Next the scene is rendered using the sameglobal illumination technique, without including the virtualobjects, denoted by LSnoob j . If the input scene is representedby LSb, than the difference between LSb and LSnoob j is ex-actly the error that results from an incorrect BRDF estima-tion. The differential rendering therefore calculates the finaloutput rendering LS f inal as:

LS f inal = LSb +(LSob j −LSnoob j)

This differential rendering technique removes most of theinaccuracies and in a certain way it is similar to the one ofJancene et al. [JNP∗95] presented above. The results of thistechnique are promising, see Figure 10, but it still suffersfrom a few deficiencies. Firstly, only diffuse parameters ofthe local scene are estimated, this introduces an error thatshould be compensated by the differential rendering. Sec-ondly, the viewpoint can be altered but the technique is tooslow to work at interactive rates. If the rendering could be



Figure 10: Debevec et al. [Deb98]. Left: a diagram illustrating the relation between the different components presented in[Deb98]. The real scene is divided into a local scene and a distant scene. The illumination from the distant scene influencesthe local scene and the virtual objects. The virtual objects influence the local scene. The local scene and the virtual objects donot have an influence on the distant scene. Middle: an image of the real scene. Right: an example of the differential renderingtechnique for an indoor scene after inserting virtual objects. Diffuse effects are simulated. Courtesy of Debevec et al.

accelerated using low cost graphics hardware, it could bepossible to achieve interactive update rates for the MR.

Gibson et al. [GCHH03] developed a method to create softshadows using a set of shadow maps. They created a rapidshadow generation algorithm to calculate and visualize theshadows in a scene after the material properties of the sceneare calculated. A proper estimate of both the geometry andthe radiance information in the real scene needs to be avail-able. It is assumed that the BRDF for all materials is diffuse.This diffuse BRDF is estimated using geometry and radi-ance information (one radiance image per 3D point). In theirmethod, the scene is divided into two parts: one part containsall patches in a scene that are visible from the camera, calledthe receiver patches and another part contains those patchesin the scene that have a significant radiance, called the sourcepatches. Then they organize these patches to build a shaft hi-erarchy between the receiver patches and the source patches.The shaft hierarchy contains information on which patchesblock receiver patches from other source patches. Next theyrender the scene from a certain viewpoint. This renderingis a two-pass mechanism. In a first pass, they go throughthe shaft hierarchy to see which source patches partially orcompletely illuminate a receiver patch. Once these sourcepatches are identified, they set the radiance of each receiverpatch to the sum of all irradiance coming from these sourcepatches, without taking occlusions into account. The secondrendering pass, takes the shadows in consideration. To cal-culate the portion of blocked light, they use the shadow map-ping technique. In fact, they create a shadow map for eachsource patch. At each receiver patch, these maps are thencombined and subtracted from the radiance value that wasrendered in the first pass. This technique is capable of pro-ducing soft shadows in a fast and efficient way. In Figure 11examples are given of synthetic scenes rendered using theabove described method. Renderings of the same syntheticscenes using a ray tracing method are given as well. The im-ages in the last column are photographic reference images.

Another set of methods were built to exploit the structureof a radiosity method. Fournier et al. made pioneering workin this direction [FGR93]. When this method was developed,facilities for modelling a geometric model from a real scenewere not available. To overcome this issue, Fournier et al.decided to replace the geometry of the objects in the realscene by their bounding box, and an image of the object wasapplied on each of the faces of the box. An example of sucha model is shown in Figure 12. To set up the scene for globalcommon illumination computation, faces of the boxes rep-resenting the real objects are divided into patches. Using theinformation contained in the radiance textures, a diffuse lo-cal reflectance is computed by averaging pixels covered byeach patch. Light source exitances are estimated and the ra-diosity of the patches are set as an average of the per pixelradiance covered by each patch. After insertion of the virtualobjects and the virtual light sources in the model of the realscene, new radiosity values are computed for the elements inthe scene using progressive radiosity [CCWG88]. The ren-dering is carried out by modifying the intensity of each patchwith the ratio obtained by dividing the new radiosity by theoriginal one. In Figure 12 an illustration of the result of thismethod is given. The results of this technique look promisingbut it suffers from the lack of a detailed geometry. This leadsto misaligned shadows and other types of mismatching be-tween real and virtual objects. The technique is slow and willnot allow real-time interaction. Nevertheless, this pioneeringmethod has influenced subsequent research work, e.g. Dret-takis et al. [DRB97] and Loscos et al. [LDR00] as presentedin the remainder of this section.

Drettakis et al. [DRB97] present a method that buildson Fournier et al. [FGR93], but uses a finer model of thereal scene. The same equations are used to estimate thelight sources emittance, the reflectance of the patches andthe original radiosity. Drettakis et al. make use of the morerecent hierarchical radiosity method hierarchical [HSA91]accelerated by using clustering [RPV93][Sil95][SAG94].



Figure 11: Results for Gibson et al. [GCHH03]. A comparison of the rendering quality for three different scenes. The imagesin the left column are produced using the system presented in [GCHH03]. The images in the middle column are rendered usingray tracing. The images in the right column are photographic reference images. Courtesy of Gibson et al.

Based on [DS97] a hierarchy of shafts is built from the realscene model, which allows a local understanding when vir-tual objects are added. This permits an easy identificationof all patches that need to undergo a radiosity alteration dueto the influence of the newly added object. The advantageof this shaft hierarchy is that it permits interactive updates ofthe illumination in the augmented scene when virtual objectsmove. The final display is made similarly to the method ofFournier et al. [FGR93]: the intensity of the patches is mod-ified with the ratio defined by the modified radiosity dividedby the original radiosity. This type of rendering is fast, com-pared to a ray tracing method, as it uses the hardware ca-pability to render textured polygons. This method providesglobal common illumination with possible interaction. Un-fortunately, the technique does not allow changing either thecurrent illumination or the current viewpoint. In Figure 13 a

screen shot is given of the 3D reconstruction and an exampleof the resulting MR using the above explained method.

3.2.3. Relighting

In Loscos et al. [LDR00], relighting is made possible, whilekeeping the framework set by Fournier et al. [FGR93] andDrettakis et al. [DRB97]. The scene parameters are extractedin the same way but all calculations are extended to the useof HDR images [Los99] as well. Since this technique fo-cuses on relighting, a specific subdivision of the real sceneis made to detect as much direct shadows as possible. The ra-diosity of each element is modified to simulate non-blockedradiosity, in other words, to erase the shadows from the tex-tures. A factor is computed using the radiosity method with-out taking the visibility in consideration. Then the new ra-diosity value is used to update the texture. Approximations



Figure 12: Results for Fournier et al. [FGR93]. Left: wire-frame image, all objects in the scene are represented by a box, thatnarrowly fits the object. Middle: Image information is mapped on the boxes (note that for the ball, a more complex shape wasused). Right: an example of a MR, the book on top of another book, lying on a table is virtual. Also a virtual light source isadded. The global common illumination effects are generated with an adaptive progressive radiosity algorithm. Courtesy ofFournier et al.

Figure 13: Results for Drettakis et al. [DRB97]. In the left image a screen shot is given of the 3D reconstruction of the realscene. The right image gives an example of the MR, the floating box is the virtual object. The virtual objects can be moved atinteractive rate while keeping the global illumination effects. This is carried out by using an adaptation of hierarchical shaftsfor hierarchical radiosity [DS97]. Courtesy of Drettakis et al.

of the estimation and of the input data lead to an inexactmodification of the texture. In a second step, another fac-tor is applied to automatically correct the imprecisions. Thisis done by using a reference patch that reflects the desiredresult. Once this is done, the new textures are used insteadof the original ones, and reflectance and original radiosityvalues are updated accordingly. Shadows can be simulatedusing the factor of the newly computed radiosity solutiondivided by the original radiosity (without shadows). Thistechnique also extends the method presented in [DS97] forthe insertion of virtual lights. In the system of Loscos et al.[LDR00], it is possible to virtually modify the intensity of

real light sources, to insert virtual objects that can be dynam-ically moved and to insert virtual light sources. The prob-lem that comes with inserting new lights or increasing lightsource intensity is that the value of the factor computed be-tween the new radiosity value, divided by the original radios-ity, may be greater than one. In that case, multi-pass render-ing is used to enable the visualisation of brighter illumina-tion. This method allows interactivity and is fairly rapid inthe pre-processing computation. However, the obtained re-sults are inaccurate as the illumination of the real scene isnot fully estimated. Firstly, because lit areas are not alteredat all, and secondly, because it concentrates on the diffuse



Figure 14: Results for Boivin et al. [BG01]. The top left image illustrates the original scene. The top right image is a relightedsynthetic image. Diffuse and specular effects are simulated using an optimisation algorithm. The bottom left image illustratesthe possibility of changing the viewpoint by grouping objects with similar properties. The bottom right image illustrates therelighting of the original scene with a different illumination pattern. Courtesy of Boivin et al.

component only. An example of the results is shown in Fig-ure 3 using HDR images as an input.

Although it doesn’t seem feasible to estimate specularcomponents of the BRDF from one single image, Boivin etal. [BG01] present a technique that re-renders diffuse andspecular effects based on radiance information from one sin-gle image and a full geometric model of the scene, includ-ing the light source positioning and the camera properties.With a hierarchical and iterative technique they estimate thereflectance parameters in the scene. In this method, the re-flectance model of Ward [War92] is used, which presentsthe entire BRDF with either 3 (isotropic materials) or 5(anisotropic materials) different parameters. The BRDF esti-mation process starts by assuming that the BRDF values areall diffuse. A synthetic scene is rendered using the geome-try, the current BRDF estimate and global illumination tech-niques. If the difference between the real scene and the syn-

thetic scene is too large, the BRDF values are re-estimatedusing a more complex BRDF model. First specular effectsare added and a roughness factor is estimated using an time-consuming optimisation process. Later anisotropic effectsare introduced and the optimisation continues until a reason-able synthetic scene is acquired. This is very similar to theway parameters are estimated in [YDMH99]. However, inthis case, only one input image is used, and anisotropic pa-rameters are estimated as well. The method of Boivin et al.relies on one single image to capture all photometric infor-mation. The advantage of such an approach is that the imagecapturing is relatively easy; the disadvantage is that only par-tial geometric information is available: there is no informa-tion for those surfaces that are not visible in the image. Nev-ertheless,the proposed technique allows changing the view-point. If a sufficiently large portion of a certain object isvisible in the image, the reflectance properties of the miss-



ing parts of the object are calculated based on this portion.Grouping objects with similar reflectance properties makesthis process more robust. On the other hand, this requiresthat not only the geometry needs to be known, but also apartitioning of the scene into objects with similar reflectanceproperties, which greatly compromises the operatability ofthis technique. Although optimised, the rendering algorithmis computationally expensive and therefore only a non real-time solution can be obtained. In Figure 14 an illustration isgiven of the output results of the described method.

3.3. Model of real scene known, few images known

If more information about the radiance of the points in thescene is available, a better BRDF estimate can be acquired.The radiance perceived at a certain point depends on theviewing angle, on the angle of incident light and the BRDF.Hence, it is possible to gain more information about theBRDF of a certain point in the scene if radiance informationis available from images captured from a different viewingangle. Alternatively, if the viewpoint is kept the same but theposition of the light sources is changed, extra BRDF infor-mation is captured as well. In this section, the methods arediscussed that make use of this extra information.

Loscos et al. [LFD∗99] developed a system that allowsrelighting, as well as virtual light source insertion, dynamicvirtual objects inclusion and real object removal. They iden-tified that it is difficult to estimate reflectance values inshadow regions due to saturation and because this estimatedepends on the quality of the indirect light estimation. Thisis compensated for by adding extra photographs capturedunder different lighting. The geometry of the real scene ismodelled from photographs. This geometric model is tex-tured using one of the images, taken from the different view-points. A set of pictures is then taken from this chosen view-point while a light source is moved around the scene to mod-ify the illumination. These pictures can be HDR images asused in [Los99]. Loscos et al. decided to mix a ray-castingapproach to compute the local illumination and a radiosityapproach to compute the indirect lighting. Two sets of re-flectances are thus computed. First diffuse reflectance valuesare computed for each pixel of the viewing window. This isdone with a weighted average of the reflectance evaluatedwith each input image differently lit. The applied weight isbased on whether the 3D point associated to the pixel is inshadow relative to the light source position, and also whetherthe radiance value captured is saturated. The reflectance val-ues are then used to initialise a radiosity system similar tothose in [DRB97][LDR00]. This reflectance can be refinedby an iterative algorithm [LFD∗99]. With this reflectance,Loscos et al. are able to relight the scene using global il-lumination. Pixel values are updated by adding the local il-lumination value, computed by ray casting, to the indirectillumination value, computed by hierarchical radiosity usinga rough subdivision of the scene. Local modifications are

made after the insertion or moving of virtual objects by se-lecting the area of the window where local illumination willbe affected. Indirect illumination is modified by adapting thetechnique of [DS97]. Similarly, virtual light sources can beadded, and intensity of real light sources can be modified. Avery interesting application of this method is the removal ofreal objects. The unknown information previously maskedby the object is filled using automatic texture synthesis of asample of the image of the reflectance values of the previ-ously hidden object. The results show that the relighting andthe interaction with virtual objects can be achieved in an in-teractive time. Image examples of the results are shown inFigure 15. The produced results are good but could be im-proved by considering specular effects. Due to the nature ofthe image capture process, it would be very difficult to applythis technique on real outdoor scenes.

A different approach taken by Gibson et al. [GHH01] re-sults in another relighting method, in which the reflectanceof the material is roughly estimated based on a restrictedamount of geometry and radiance information of the scene.In theory, only geometry and radiance information is neededfor those parts of the scene that will be visible in the finalrelighted MR. In their approach a photometric reconstruc-tion algorithm is put forward, that is capable of estimatingreflectance and illumination for a scene if only incompleteinformation is available. To achieve this the direct illumi-nation is modeled as coming from unknown light sourcesusing virtual light sources, see Figure 16. The aim is not toproduce an accurate illumination model, but rather a modelthat produces a similar illumination as in the original scene.The model used is a spherical illumination surface: a set ofsmall area light sources that surrounds the known geometry.The parameters of this surface, the position and emission ofthe light sources, are estimated using an iterative minimiza-tion algorithm. Based on this model, the reflectance of thematerials in the scene are estimated. The MR scene is ren-dered using a ray tracing algorithm. User interaction is im-possible at real-time update rate but nevertheless the methodillustrates the possibility of getting fairly realistic mixed re-alities, without limiting input requirements. This method isoriginal, interesting and very practical to adapt to many situ-ations where information on a real scene is partially known.Imprecisions and ambiguities are compensated for, result-ing in a more accurate simulation of the existing illumina-tion. An example of a rendered scene and its comparablereal scene are given in Figure 17.

3.4. Model of real scene known, many images known

This category collects those techniques that require the mostinput information. Not only the geometry is known but alsoradiance information under many different geometric set-ups. Two significant methods could be identified that belongto this category of MR methods. They were selected froma broad set of techniques on inverse illumination because



Figure 15: Results for Loscos et al. [LFD∗99]. The left image is one of the input images of the real scene. The middle image isa relighted image of the real scene, using the calculated BRDF values. The left image illustrates the removal of an object (thedoor), the insertion of a new virtual object (the chair) and the insertion of a virtual light source. All manipulations are carriedout at interactive update rates. The illumination is updated locally with ray casting. The consistency of the indirect illuminationis kept using an adaptation of [DS97]. Courtesy of Loscos et al.

Figure 17: Results for Gibson et al. [GHH01]. The left images illustrates the reconstructed scene from a novel viewpoint. Theimage in the middle is a synthetic image illuminated with virtual light sources. The right image illustrates the addition of virtualobjects. Both specular and diffuse effects are simulated. Courtesy of Gibson et al.

they provide a solution for a large group of objects, whichis essential for MR. The first inverse illumination method[YDMH99] focuses on the BRDF estimation, using manyHDR images from different viewpoints. The second [YM98]allows to relight outdoor scenes. The remainder of this sec-tion briefly discusses these two techniques.

Yu et al. [YDMH99] use a low parametric reflectancemodel, which allows the diffuse reflectance to vary arbitrar-ily across the surface while non-diffuse characteristics re-main constant across a certain region. The input to their sys-tem is the geometry of the scene, a set of HDR images andthe position of the direct light sources. An inverse radiositymethod is applied to recover the diffuse albedo. The othertwo parameters in the reflectance model of Ward [War92],the roughness and the specular component, are estimated bya non-linear optimisation. For the estimation of the specularBRDF, it is assumed that many HDR images are availablefrom a different set of viewpoints. The estimation makes useof the position of the light sources and the possible high-lights they may produce on a surface due to specular effects.It is therefore helpful to capture images of the scene with avarious number of light sources, since this might increase thenumber of specular highlights. This precise estimate of the

BRDF values in the scene allows to remove all illuminationin the scene and a new illumination pattern can be applied.To render the scene they make use of Ward’s RADIANCE sys-tem [War94]. No further steps were taken to speed up therendering process. Figure 4 illustrates the results obtainedfor augmented images compared to photographs of the realscene. This technique is interesting for MR because it pro-vides an algorithm to estimate an accurate complex BRDF ofa complex real scene, resulting in an accurate representationof the illumination.

Yu and Malik [YM98] present a technique that allows re-lighting for outdoor scenes based on inverse illumination. Asit is impossible to retrieve the geometry of the entire scene,they separate the scene into four parts: the local model, thesun, the sky and the surrounding environment. The illumina-tion sources are the sun, the sky, and the surrounding envi-ronment. Luminance due to the sun and the sky are estimatedbased on a set of input images. At least two photographs persurface of the local model are captured, which should showtwo different lighting conditions (directly and not directly litby the sun). The local model is subdivided into small sur-faces. Based on these two photographs, two pseudo-BRDFvalues are estimated per surface. One relates to the illumina-



VirtualSource

x’

Figure 16: Technique Gibson et al. [GHH01]. The real il-lumination is approximated by a illumination surface. Thisillumination surface is covered by a set of virtual lightsources. The parameters of these virtual light sources areestimated such that its effect resembles the real illumination.Courtesy of Gibson et al.

tion from the sun, the other relates to the illumination fromthe integrated environment (sky plus surrounding environ-ment). A least square solution is then used to approximatethe specular term for each surface and for each lighting con-ditions (from the integrated environment and from the sun).This approach uses an approximation of the inverse illumi-nation equation. It illustrates the difficulty of setting up aparameterised MR system for outdoor scenes. At renderingtime, different positions of the sun are simulated. After ex-tracting the sun and the local model from the background,sky regions are identified and they are mapped on a meshsupported by a hemisphere. Three parameters control the skyintensity. A first scale factor is applied when simulating sun-rise and sunset; it is constant otherwise. The second para-meter adjusts the intensity of the sky depending on the posi-tion of the mesh on the dome. A last parameter controls thesky intensity depending on the sun’s position. Next, the ra-diance values and the pseudo-BRDFs are used to reproducethe global illumination on the local scene. This method is thefirst to present the possibility of relighting outdoor scenes.Results of these relighted scenes and a comparison imageare shown in Figure 18. Although it is difficult to evaluatethe quality of the relighting from the images provided by theauthors, the images resemble the real conditions, and thiscan satisfy most of the MR applications for outdoor environ-ments.

4. Discussion

In section 2.2 we pointed out that the assessment of the vari-ous illumination techniques for MR comes with a certain de-gree of subjectivity. Fortunately there are some aspects thatcan be evaluated in a rather objective way. Some of these

measures will be used in this section to assess the meth-ods from section 3. Section 4.1 discusses the amount of pre-processing required. In section 4.2 an evaluation of the de-gree of interactivity is given and in section 4.3, the methodswill be evaluated based on the quality of the results. Section4.4 explains which methods are suitable for outdoor scenes.Finally an overview of the discussed methods is given in sec-tion 4.5.

4.1. Pre-processing time

The term pre-processes refers to those steps, carried outonce, that are required by the method before the mergingof real and virtual objects takes place. The geometry recon-struction, image capturing and BRDF estimation, are con-sidered as pre-processing steps.

A few methods do not require a full geometric model ofthe real scene: Sato et al. [SSI99], Nakamae et al. [NHIN86]and Haller et al. [HDH03]. All other methods require a geo-metric model. Some of these methods do not explain howthis model can be constructed, others assume that it is con-structed using semi-manual 3D reconstruction software, ex-amples of such software were given in section 3. Usingreconstruction software usually results in a low resolutionmodel and is in general error prone, this is due to the factthat no automatic, accurate 3D reconstruction software is yetcommercially available. Scanning devices give a better res-olution, but these devices are expensive and while the scan-ning of a small object might be straightforward, the scanningof a larger scene is tedious. As a summary we can say thata perfect geometric model is difficult to acquire and that re-construction is always a tedious work.

Some methods require radiance information capturedfrom several viewpoints [YDMH99] [GHH01] or under dif-ferent types of illumination [LFD∗99] [YM98]. Taking sev-eral HDR images from different viewpoints and under dif-ferent illumination delays the image capture time.

Many methods calculate a BRDF estimate, some usea diffuse model, some allow a more complex model.Often the calculation of the BRDF needs to be carried outoff-line, due to timing issues and is therefore considered aspre-processing work. Methods that calculate a diffuse-onlyBRDF are: [Deb98][FGR93][DRB97][LDR00][LFD∗99],methods that allow specular components are:[GHH01][YDMH99][YM98][BG01].

4.2. Level of interactivity

Interactivity means:

• the possibility of navigating objects or viewpoints in thescene,

• the effort made to get an interactive rendering,• the possibility to modify reflectance properties of real ob-

jects in the scene,



Figure 18: Results for Yu et al. [YM98]. The top row images illustrates the original tower from different viewpoints. The bottomrow are synthetic images of the tower from approximately the same viewpoint. The real images were not used to generate thesynthetic images, nevertheless the synthetic and real images look very similar. Courtesy of Yu and Malik.

• the possibility to modify the illumination sources in thereal scene.

A few methods allow to navigate the virtual objects orthe viewpoints. These techniques have either enough BRDFinformation [BG01][YDMH99][FGR93], enough geometryand illumination information [SSI99][YM98] or use a dif-ferent approach [ALCS03][SHC∗94][JNP∗95].

Only a few of the methods operate in true real-time (RT)[ALCS03][SHC∗94][GCHH03], others are near real-time(near RT) [LDR00][LFD∗99][DRB97] but most of them arenon real-time (NRT). However, it should be noted that somemethods were developed years ago, when computer hard-ware and software were much slower than nowadays. Also,it should be pointed out that some methods did not made aspecial attempt in producing interactive systems. With a fewmodifications, it should be possible to speed up most of thedescribed systems.

Some methods that specifically tried to speed up the com-putations are worth mentioning. Agusanto et al. [ALCS03]exploited the idea of environment mapping while State et al.[SHC∗94] used shadow mapping and Haller et al. [HDH03]shadow volumes. Gibson et al. [GM00] developed a newtechnique to simulate soft shadows at interactive rates andDrettakis et al. [DRB97], Loscos et al. [LDR00] and Loscoset al. [LFD∗99] made use of a hierarchical radiosity algo-

rithm, that decreased the computation time to interactiverates as well. Gibson et al. [GCHH03] used shadow volumes.

Most methods that calculate the BRDF values are in prin-ciple capable of changing the BRDF values into somethingnew. This can be used to modify the appearances of real ob-jects in the scene. Relighting methods can use this BRDFinformation to relight a scene using a different illuminationpattern. Table 1 gives an overview of the various differenttypes of illumination the discussed methods allow.

4.3. Evaluation of the quality

Some of the described methods evaluated the quality of theirmethod using one or more of the following evaluation meth-ods:

• a comparison is made between a photograph reference ofthe real scene and a synthetic version of the same scene,

• the BRDF is measured using a device and these results arecompared with the calculated BRDF values.

Gibson et al. [GCHH03] compare their shadow renderingtechnique with a ray traced rendering and an image of thereal scene, see Figure 11. They are capable of producing re-alistic and similar shadows as in the real image and at a fastertime than the ray traced rendering. In [GM00] the presentedextended shadow mapping is compared with a ray traced ver-sion using the same input parameters, see Figure 9. There are



some differences between the two synthetic scenes, but thegenerated shadows look realistic.

Boivin et al. [BG01] extract a full BRDF model and com-pare their rendering with an original image of the real scene,see Figure 14. In [YM98] the diffuse and specular com-ponents are calculated; the resulting rendering is comparedwith an original image of the real scene. Likewise, [LDR00][LFD∗99] estimate the diffuse BRDF and compare a syn-thetic rendering with a original image of the real scene (seeFigures 3 and 15). In both methods, the rendering occurs atinteractive update rates.

Similarly, Gibson et al. [GHH01], see Figure 17, comparean original and synthetic image and find that the error be-tween the two images decreases drastically in the first threeiterations. Both diffuse and specular reflectances are mod-elled.

Yu et al. [YDMH99], see Figure 4, estimate diffuse andspecular BRDF values and compare these with measuredBRDF values of objects in the scene. The estimates and thetrue values are similar.

We can also compare methods that use both specular anddiffuse BRDF values for the rendering with those that havea more restrictive understanding of the BRDF. It is under-stood that systems based on a more complete BRDF modelresult in an MR of a higher quality than those based on dif-fuse BRDF values only or those that do not estimate BRDFvalues at all. For some methods, only a subjective user per-ceptive assessment can be made.

4.4. Usability on indoor and outdoor scenes

The reader may have noticed that most techniques weretested on indoor scenes. Outdoor scenes are more complexthan indoor scenes. Not only is the geometry more difficultto model, the illumination is difficult to extract as well. Out-door illumination is time and weather dependent and diffi-cult to model and simulate. Only three methods from sec-tion 3 explicitly used an outdoor scene to test their method[Deb98][GCHH03][SSI99][YM98] but this does not implythat the other methods are not suitable for outdoor scenes.For instance one might argue that all methods that use envi-ronment maps are capable of capturing the outdoor illumi-nation. But some caution is in place when interpreting thisstatement [JL04]. If HDR images are used to capture the en-vironment map, which is in general the case, one needs tobare two things in mind. Firstly, the intensity of the sun isin general too bright to be captured in a HDR image with-out saturation, even at very fast shutter speeds. Secondly, ifthe sky is clouded and the clouds drift in the sky, there willinevitable be some movement in the low dynamic imagesused to compile the HDR image, making them worthless. Itshould be clear, that the extension from indoor to outdoorscenery is not straightforward. The current state of the art ofMR shows no good solutions for the outdoor scenes.

4.5. Overview

Table 1 gives an overview of all methods discussed in section3. For each method, the overview discusses the followingaspects:

• Geometric model of the scene: whether or not themethod requires a geometric model of the scene.

• Number of different images: the number of different im-ages needed per point in the scene, to calculate the MR.

• Methodology: the methodology used to create the MR. Insection 2.3 three different approaches were discussed:

1. common illumination,2. relighting,3. inverse Illumination.

Further to this division, a distinction is made between lo-cal and global illumination techniques.

• Rendering: the rendering method used to compose theMR. Possible answers are: ray-casting, ray-tracing, ra-diosity, etc.

• Computation time: the update time of the method is real-time (RT), non real-time (NRT) or near real-time (nearRT).



Tabl

e1:

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wof

illu

min

atio

nm

etho

dsfo

rm

ixed

real

ity.

Geo

met

ric

mod

el�

Imag

esM

etho

dolo

gyR

ende

ring

Com

puta

tion

time

Sect

ion

[AL

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3]no

one

glob

alco

mm

onill

umin

atio

nen

viro

nmen

tm

aps,

mul

tipas

sre

nder

ing

RT

3.1

[NH

IN86

]no

one

loca

lcom

mon

illum

inat

ion

ray

cast

ing

NR

T3.

1

[SSI

99]

noon

egl

obal

com

mon

illum

inat

ion

ray

cast

ing

NR

T3.

1

[SH

C∗

94]

yes

one

loca

lcom

mon

illum

inat

ion

shad

owm

appi

ngR

T3.

2

[HD

H03

]ye

son

elo

calc

omm

onill

umin

atio

nsh

adow

volu

mes

RT

3.2

[JN

P∗95

]ye

son

elo

calc

omm

onill

umin

atio

nra

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acin

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RT

3.2

[GC

HH

03]

yes

one

glob

alco

mm

onill

umin

atio

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adow

map

ping

RT

3.2

[Deb

98]

yes

one

glob

alco

mm

onill

umin

atio

ndi

ffer

entia

lre

nder

ing

+ra

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acin

gN

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3.2

[GM

00]

yes

one

glob

alco

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onill

umin

atio

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tend

edsh

adow

map

ping

near

RT

3.2

[FG

R93

]ye

son

egl

obal

com

mon

illum

inat

ion

radi

osity

+ra

yca

stin

gN

RT

3.2

[DR

B97

]ye

son

ere

light

ing

usin

ggl

obal

illum

i-na

tion

hier

arch

ical

radi

osity

algo

rith

mne

arR

T3.

2

[LD

R00

]ye

son

ere

light

ing

usin

ggl

obal

illum

i-na

tion

hier

arch

ical

radi

osity

algo

rith

mne

arR

T3.

2

[BG

01]

yes

one

inve

rse

glob

alill

umin

atio

nra

ytr

acin

gN

RT

3.2

[LFD

∗99

]ye

sfe

wre

light

ing

usin

ggl

obal

illum

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tion

hier

arch

ical

radi

osity

algo

rith

m+

ray

cast

ing

near

RT

3.3

[GH

H01

]ye

sfe

wre

light

ing

usin

ggl

obal

illum

i-na

tion

ray

trac

ing

NR

T3.

3

[YD

MH

99]

yes

man

yin

vers

egl

obal

illum

inat

ion

ray

trac

ing

NR

T3.

4

[YM

98]

yes

man

yin

vers

egl

obal

illum

inat

ion

ray

trac

ing

NR

T3.

4



5. Conclusions and Future work

In the past few years research has been motivated to con-sider a new type of simulation: the simulation of a new real-ity called mixed reality which refers to the concept of mixinga real scene with virtual elements. Mixed reality has now be-come very important for various applications ranging fromentertainment with movie post-production and games, archi-tecture, cultural heritage, education and training, etc. Sev-eral problems arise when composing reality with virtual ele-ments. A first problem is how to automatically calibrate therelative position and the occlusion of virtual objects withvirtual ones. As mentioned in this report, this has been ad-dressed successfully in two different ways. One can use ascanning device or one can use real-time stereovision to ex-tract depth and shape information. A second problem is howto illuminate the virtual objects consistently with the originallight conditions in the real scene. Research papers appearedalready in the late eighties to answer this last need of the in-dustry, but it is only recently, within the last ten years, thatthe international community made a more significant effortto provide more automated solutions for computing the illu-mination in mixed reality.

Although it is tempting to compare techniques relativelyto the quality of the results achieved, this report classifiesthem depending on the context and the goal of the method.Firstly, it is of course easier to compute illumination formixed reality if a 3D model is available. Secondly, it maybe that only a few images of the real scene are availablefrom different viewpoints, and some available with differ-ent lighting conditions. The more images are available forthe illumination extraction, the easier the computation pro-cedure becomes. On the contrary, the fewer images are avail-able the more difficult it is to perform an accurate estimationand therefore simulation. Consequently it was decided that itwould be fairer and more interesting to compare techniquesusing similar types of data. Four different categories wereidentified based on the amount of geometric detail and ra-diance information available. Different manners to comparethe illumination techniques used for mixed reality were pre-sented as well. For example, the methods were comparedbased on the type of the illumination achieved: local orglobal, diffuse or complex illumination effects. It was alsopointed out if relighting was possible and if the user couldinteract with the scene.

An ideal conclusion of this report would state which tech-nique is the most perfect one. However it is impossible toassess the methods without knowing the application at hand.It is therefore very difficult to describe the ideal method. Itshould be a real-time and automatic method with no pre-processing requirements. It would allow any type of vir-tual interaction: modification of lighting, removal of realobjects, modification of material properties of real objectsand addition of virtual elements. And the rendering qualitywould perfectly match with the real one. Research is head-

ing towards this, and it is likely that this technology will be-come more accessible in future years. Progress in stereovi-sion techniques, in automatic calibration, registration and incomputer graphics will help in the progression in illumina-tion for mixed reality. More automatic reconstruction meth-ods of the geometry are needed, that will also model morecomplex details. Progress in augmented reality is heading to-wards systems being able to recognise shape and depth with-out markers. Computer graphics research needs to providemore precise description of reflection models and renderingsoftware needs to be adapted to these more complex materi-als. Little work has been done in modelling the behaviour oflight sources, which are often assumed diffuse. It will be im-portant for future work to consider more complex lighting inorder to find a better estimate for the illumination in mixedreality. Finally, most of the methods have been designed forindoor environments that are easier to control. Outdoor en-vironments present a real challenge, both in the capture andin the simulation. It is expected that more work for outdoorenvironments will appear in the near future.

6. Acknowledgements

We would like to thank Simon Gibson, Greg Ward, AnthonySteed, Mel Slater, Erik De Witte, Hila Ritter Widerfield andBernhard Spanlang for reviewing this paper.

This report was partly funded by CREATE (IST-2001-34231), a 3-year RTD project funded by the 5th FrameworkInformation Society Technologies (IST) Programme of theEuropean Union and a UCL graduate school research schol-arship.

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