volumetric zero-variance-based path guidingjirka/path-guiding-in...volumetric monte-carlo path...
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S. Herholz: A Unified Manifold Framework for Efficient BRDF Sampling โฆ
Sebastian Herholz1 Yangyang Zhao2 Oskar Elek3
Derek Nowrouzezahrai 2 Hendrik P. A. Lensch1 Jaroslav Kลivรกnek3
Volumetric Zero-Variance-Based
Path Guiding
1University of Tรผbingen 2McGill University Montreal 3Charles University Prague
MOTIVATION
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding2
MOTIVATION
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding3
MOTIVATION
โข A correct physically-based simulation of volumetric effects is crucial for rendering realistic scenes
โข In the recent years, brute-force path tracing these effects startedto become applicable in production environments ([Fong2017], [Novak2018])
โข Increased complexity of the light transport makes it still challenging
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding4
5
No guiding Guiding
(Our)
10 min10 min
VOLUMETRIC MONTE-CARLO PATH TRACING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding6
๐ ๐
p ๐
โข The variance is defined by how well we can generate
random paths proportional to the volumetric light transport:
๐2 = ๐๐(๐)
๐(๐)
๐ผ = เถฑ๐ ๐ ๐๐
VOLUMETRIC MONTE-CARLO PATH TRACING: ZERO-VARIANCE
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding7
๐ ๐
p๐ง๐ฃ ๐ (optimal)
๐ผ = เถฑ๐ ๐ ๐๐
โข If the PDF for all paths is proportional to the light transport function
we would get a perfect zero-variance estimator:
๐2 = ๐๐(๐)
๐๐ง๐ฃ(๐)= 0
We need to know the
shape of ๐ ๐ฟ !
THE 4 SAMPLING DECISIONS:
1. Scatter: ๐๐ ๐๐ , ๐๐
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding8
3. Direction: ๐๐ ๐๐+1|๐๐+1, ๐๐ 4. Termination: ๐๐ ๐ ๐๐ , ๐๐โ1
2. Distance: ๐๐ ๐๐+1|๐๐ , ๐๐
VOLUMETRIC RANDOM WALK - DECISIONS
๐ฅ0
๐0
๐ฅ๐
๐๐
๐ฅ๐+1
๐๐+1
๐ฅ๐โ1
๐๐โ1
๐ฅ๐+2
๐๐+2
โข Path PDF :
๐ ๐ฟ = เท
๐=1
๐โ1
๐๐ โฆ โ ๐๐ โฆ โ ๐๐ โฆ โ 1 โ ๐๐ ๐ โฆ
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding9
Source of variance
Path segment PDF
VOLUME RENDERING EQUATION
โข Incident radiance (volume):
โข In-scattered radiance:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding10
๐ฟ ๐ฅ, ๐ = ๐ โฆ โ ๐ฟ๐(โฆ ) + เถฑ๐ โฆ โ ๐๐ (โฆ ) โ ๐ฟ๐(โฆ )d๐
๐ฟ๐ โฆ = เถฑ๐ โฆ โ ๐ฟ(โฆ )d๐โฒ
Surface contribution Volume contribution
VOLUME RENDERING EQUATION
โข Incident radiance (volume):
โข In-scattered radiance:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding11
๐ฟ ๐ฅ, ๐ = ๐ โฆ โ ๐ฟ๐(โฆ ) + เถฑ๐ โฆ โ ๐๐ (โฆ ) โ ๐ฟ๐(โฆ )d๐
๐ฟ๐ โฆ = เถฑ๐ โฆ โ ๐ฟ(โฆ )d๐โฒ
Known Local
Quantities
Transmittance
Phase function
VOLUME RENDERING EQUATION
โข Incident radiance (volume):
โข In-scattered radiance:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding12
๐ฟ ๐ฅ, ๐ = ๐ โฆ โ ๐ฟ๐(โฆ ) + เถฑ๐ โฆ โ ๐๐ (โฆ ) โ ๐ฟ๐(โฆ )d๐
๐ฟ๐ โฆ = เถฑ๐ โฆ โ ๐ฟ(โฆ )d๐โฒ
Unknown Light
Transport Quantities
Incident radiance
In-scattered radiancesurface radiance
STANDARD SAMPLING
13
๐ฅ๐+1๐ฅ๐ ๐๐ ๐ฅ๐+1 ๐๐๐ฅ๐+1
๐๐+1
1+2 Scatter and Distance:
โข Based on the transmittance
3 Direction:
โข Based on the phase function
STANDARD SAMPLING
14
โข Based on local albedo or throughput
4 Termination:
๐ฅ๐
๐๐๐ฅ๐+1
CHALLENGES FOR VOLUME SAMPLINGWhy do we need volumetric path guiding?
15
LIGHT SHAFTS
โข Light shafts:
- We need to scatter inside the light shaft.
- We need to follow the direction of the light shaft.
- We need to scatter towards the light shaft.
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding16
LIGHT SHAFTS
โข Light shafts:
- We need to scatter inside the light shaft.
- We need to follow the direction of the light shaft.
- We need to scatter towards the light shaft.
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding17
LIGHT SHAFTS
โข Light shafts:
- We need to scatter inside the light shaft.
- We need to follow the direction of the light shaft.
- We need to scatter towards the light shaft.
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding18
No guiding (1024 spp) Our guiding (1024 spp)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding19
SUB-SURFACE-SCATTERING
๐ฅ
๐
โข Sub-Surface-Scattering:
- We โoftenโ need stay close to the surface
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding20
SUB-SURFACE-SCATTERING
๐ฅ
๐
โข Sub-Surface-Scattering:
- We โoftenโ need to stay close to the surface
- We need to leave the object with the right direction
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding21
No guiding (256 spp) Our guiding (256 spp)
22
DENSE MEDIA
โข Dense media (back illuminated):
- We may need to โavoidโ generating a scattering
event even if the transmittance is low
(e.g. strong light source behind the volume).
๐ฅ
๐
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding23
No guiding (256 spp) Our guiding (256 spp)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding24
NON-DENSE MEDIA
โข Non-dense media (no back illumination):
- We may need to โforceโ a scattering event
even if the transmittance is high.
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding25
No guiding (256 spp) Our guiding (256 spp)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding26
SPECIALIZED SOLUTIONS: SHORTCOMINGS
โข Many individual solutions:
โข Equiangular Sampling: [Kulla2012]
โข Joint-Importance Sampling: [Georgiev2012]
โข Zero-Variance Dwivedi Sampling: [Krivanek2014]
[Meng2016]
โข Directional (illumination-based) guiding: [Pegoraro2008][Bashford2012]
โข Only considering sub-sets or special cases:
โข Surface-bounded volumes
โข Homogenous or isotropic volumes
โข Single scattering
โข None of the current methods importance samples the full volumetric light transport!
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding27
SPECIALIZED SOLUTIONS: SHORTCOMINGS
โข Many individual solutions:
โข Equiangular Sampling: [Kulla2012]
โข Joint-Importance Sampling: [Georgiev2012]
โข Zero-Variance Dwivedi Sampling: [Krivanek2014]
[Meng2016]
โข Directional (illumination-based) guiding: [Pegoraro2008][Bashford2012]
โข Only considering sub-sets or special cases:
โข Surface-bounded volumes
โข Homogenous or isotropic volumes
โข Single scattering
โข None of the current methods importance samples the full volumetric light transport!
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding28
SPECIALIZED SOLUTIONS: SHORTCOMINGS
โข Many individual solutions:
โข Equiangular Sampling: [Kulla2012]
โข Joint-Importance Sampling: [Georgiev2012]
โข Zero-Variance Dwivedi Sampling: [Krivanek2014]
[Meng2016]
โข Directional (illumination-based) guiding: [Pegoraro2008][Bashford2012]
โข Only considering sub-sets or special cases:
โข Surface-bounded volumes
โข Homogenous or isotropic volumes
โข Single scattering
โข None of the current methods importance samples the full volumetric light transport!
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding29
ZERO-VARIANCE-BASEDVOLUMETRIC PATH GUIDING
30
TUE: 30TH JULY TIME: 9:00 AMROOM: 152
TECH TALK:
[Hoogenboom 2008]
ZV-BASED VOLUMETRIC PATH GUIDING: GOALS
โข Leverage recent success of local surface guiding methods:
โข Extend the concept to volumes
โข Consider the complete volumetric light transport:
โข No prior assumptions or special cases
โข Guide based on the optimal zero-variance decisions
โข Replace unknown quantities by estimates:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding31
๐ฟ ๐, ๐ = เทจ๐ฟ ๐, ๐ ๐ฟ๐ ๐,๐ = เทจ๐ฟ๐ ๐,๐
[Vorba2014],
[Herholz2016],
[Mueller2017]
ZV-BASED VOLUMETRIC PATH GUIDING: CONTRIBUTIONS
โข Guiding all local sampling decisions:
โข 1+2 Guided product distance sampling:
โข 3 Guided product directional sampling:
โข 4 Guided Russian roulette and Splitting:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding32
ZV-BASED VOLUMETRIC PATH GUIDING: CONTRIBUTIONS
โข Guiding all local sampling decisions:
โข 1+2 Guided product distance sampling:
โข 3 Guided product directional sampling:
โข 4 Guided Russian roulette and Splitting:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding33
ZV-BASED VOLUMETRIC PATH GUIDING: CONTRIBUTIONS
โข Guiding all local sampling decisions:
โข 1+2 Guided product distance sampling:
โข 3 Guided product directional sampling:
โข 4 Guided Russian roulette and Splitting:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding34
VOLUME RADIANCE ESTIMATES
35
VOLUME RADIANCE ESTIMATES
โข Spatial caches via BSP-tree: max. 2K photons per node:
โข Similar 3D structure as PPG [Mueller2017]
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding36
VOLUME RADIANCE ESTIMATES
โข Pre-processing step to fit estimates from photons (50M):
โข EM-fitting of von Mises-Fisher mixtures (similar to [Vorba2014]โs GMMs)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding37
VON MISES-FISHER MIXTURE MODELS
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding38
โข Spherical Distribution:
โข Features (closed-form):
- Sampling
- Convolution
- Product
๐ ๐|ฮ =
๐พ
๐๐๐ฃ(๐|๐๐ , ๐ ๐)
RADIANCE ESTIMATES
โข Incident Radiance Distribution โข In-Scattered Radiance Distribution
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INCIDENT RAD. TO IN-SCATTERED RAD. TRANSFORMATION
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding40
โข Convolution between incident radiance ๐ฟ and the phase function ๐
โ
INCIDENT RADIANCE ESTIMATES
Ground truth (2K spp) Our estimates (VMM)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding41
IN-SCATTERED RADIANCE ESTIMATES
Ground truth (2K spp) Our estimates (VMM)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding42
GUIDED SAMPLING DECISIONS
43
DISTANCE SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding44
2. Scatter distance
1. Volume or surface decision
DISTANCE SAMPLING
โข Standard distance PDF:
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding45
1+2. Event distance
๐๐๐ ๐ก๐ โฆ โ ๐ โฆ โ ๐๐ โฆ
GUIDED PRODUCT DISTANCE SAMPLING
โข Our guided PDF:
๐๐๐ง๐ฃ โฆ =
๐ โฆ โ ๐๐ โฆ โ เทจ๐ฟ๐(โฆ )
เทจ๐ฟ(โฆ )Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding46
1+2. Event distance
Our estimates
NAรVE TABULATED APPROACH
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding47
โข Naรฏve tabulated approach:
โข Step through the complete volume and build a tabulated PDF
โข Inefficient (large scenes dense media):
โข we always need to evaluated all bins first
OUR INCREMENTAL GUIDED PRODUCT DISTANCE SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding48
โข Incremental approach:
โข At each step make a local decision, if we scatter inside the bin
โข We only need to step until the scattering event happens
Full CDF (30min) Our incremental (30min)
49
Spp: 548
Avg. steps: 18
Spp: 1140
Avg. steps: 4
45 min
No guiding
Spp: 960
relMSE: 1.342
45 min
No guiding Distance guiding
Spp: 960
relMSE: 1.342Spp: 424
relMSE: 0.901
45 min
No guiding (256 spp) Distance guiding (256 spp)
53
โข Here, distance sampling is not the main cause of variance!!
DIRECTIONAL SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding54
3. Scatter direction
๐๐๐ฅ๐+1
โข Standard PDF:
๐๐๐ ๐ก๐ โฆ โ แ๐ โฆ
GUIDED PRODUCT DIRECTIONAL SAMPLING
โข Our guided PDF:
๐๐๐ง๐ฃ โฆ โ แ๐ โฆ โ เทจ๐ฟ(โฆ )
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding55
3. Scatter direction
๐๐๐ฅ๐+1 ๐๐+1
Our estimates
OUR GUIDED PRODUCT DIRECTIONAL SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding56
Incident radiance VMM
OUR GUIDED PRODUCT DIRECTIONAL SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding57
Incident radiance VMM Phase function VMM
OUR GUIDED PRODUCT DIRECTIONAL SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding58
Product sampling VMM
30 min
59
30 min No guiding
Spp: 2212
relMSE: 0.376
Directional guiding
Spp: 1756
relMSE: 0.048
30 min No guiding
Spp: 2212
relMSE: 0.376
Directional guiding Dist + Direct
Spp: 1756
relMSE: 0.048Spp: 1228
relMSE: 0.034
30 min No guiding
Spp: 2212
relMSE: 0.376
No Guiding
(256 spp)
Product Guiding
(256 spp)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding63
Illum Guiding
(256 spp)
IMPORTANCE OF THE PRODUCT FOR DENSE ANISOTROPIC MEDIA
GUIDED RUSSIAN ROULETTE AND SPLITTING
4a. Termination 4b. Splitting Distance
Directional
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding64
GUIDED RUSSIAN ROULETTE AND SPLITTING
โข Post-sampling compensation strategies:
โข Identify, if we did a sub-optimal sampling decision
โข Terminate: to increase performance
โข Split: bound/reduce sample variance
4b. Splitting
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding65
4a. Termination
GUIDED RUSSIAN ROULETTE AND SPLITTING
โข Path contribution: ๐ธ[๐]โข The expected contribution
if we continue the path
โข Reference solution: ๐ผโข the final pixel value
๐ =๐ธ ๐
๐ผ
Path contribution
Reference solution
survival prob /
splitting factor
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding66
GUIDED RUSSIAN ROULETTE AND SPLITTING
โข Path contribution: ๐ธ[๐]โข The expected contribution
if we continue the path
โข Reference solution: ๐ผโข the final pixel value
๐ =๐ธ ๐
๐ผ= 1
Path contribution
Reference solution
survival prob /
splitting factor
Zero-Variance
Estimator
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding67
GUIDED RUSSIAN ROULETTE AND SPLITTING
โข If ๐ โค 1: Russian Roulette
โข Terminates low contributing paths
โข Survival probability: ๐
โข If ๐ > 1: Splitting
โข Splits an under sampled paths with
a potential high contribution (๐ times)
๐ =๐ธ ๐
๐ผ
Path contribution
Reference solution
survival prob /
splitting factor
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding68
ESTIMATED PATH CONTRIBUTION
โข See course notes or paper for more details
เทจ๐ฟ๐
๐ฟ
๐ธ ๐ฟ = ๐โฒ(๐ฟ) โ เทจ๐ฟ๐ ๐ฅ๐ , ๐๐โ1
Path throughput: ๐(๐ฟ)/๐(๐ฟ) In-scattered radiance estimate
๐ฅ๐
๐๐โ1
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding69
GUIDED RUSSIAN ROULETTE AND SPLITTING: PIXEL ESTIMATE
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding71
โข Ray marched cache to integrate: ๐ โ ๐๐ โ เทจ๐ฟ๐
No RR
Spp: 468
relMSE: 0.454
45 min
No RR Guided RR
Spp: 468
relMSE: 0.454Spp: 1500
relMSE: 0.174
45 min
No RR Guided RR
Spp: 468
relMSE: 0.454Spp: 1500
relMSE: 0.174
45 min
+ Guided splitting
Spp: 1340
relMSE: 0.066
Guided RR + Guided splitting
Spp: 1500
relMSE: 0.174
Spp: 1340
relMSE: 0.06675
No guiding
Time: 60 min
Spp: 10644
relMSE: 11.58
Distance guiding
Time: 60 min
Spp: 4624
relMSE: 3.520
Distance + directional guiding
Time: 60 min
Spp: 4448
relMSE: 0.468
Distance + directional guiding + GRRS
Time: 60 min
Spp: 3796
relMSE: 0.321
OPEN PROBLEMS AND LIMITATIONSOpen Challenges to make it bullet proof
80
SPATIAL CACHE STRUCTURE
โข Naive approach to define the resolution:
โข Heuristic based on sample numbers
โข Takes time or many samples to model/separate fine features (e.g. thin shafts or caustics)(PPG by [Mueller2017] has the same problem)
โข Influences the performance of some sampling methods (e.g. distance)
โข Ideal structure should adjust to the light transport characteristics
81
INSUFFICIENT CACHE SIZES
โข Shared problem with other 3D caching based guiding approaches(e.g. [Vorba2014], [Mueller2017], โฆ)
โข By merging the samples of a spatial cache we blur the directional distribution
โข Can lead to incorrect estimates of ๐ฟ and ๐ฟ๐
82
Ground truth Our estimate Spatial avg. ground truth
PRODUCTION CHALLENGESHow can we get good guiding estimates?
83
VMM PHASE FUNCTION FITTING: PRE-PROCESSING STEP
โข Pre-processing step:โข Fitting a VMM for each phase function
โข Fitting up to K = 4 componentsโข Details in the course notes
โข Open Challenge:โข Procedural phase functions or
procedural mixtures?
โข How to deal with changing mean cosines (roughening/mollification)?
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding84
VMM PHASE FUNCTION FITTING: PRE-PROCESSING STEP
โข Pre-processing step:โข Fitting a VMM for each phase function
โข Fitting up to K = 4 componentsโข Details in the course notes
โข Open Challenge:โข Procedural phase functions or
procedural mixtures?
โข How to deal with changing mean cosines (roughening/mollification)?
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding85
FITTING/LEARNING THE INCIDENT RADIANCE MIXTURES
Pros:
โข Photons directly represents the light transport
โข Spatial distribution corresponds to important features (light shaft)
โข Number of traced photons can be fixed
โข No additional fitting during rendering
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding86
Photon-based pre-processing ([Herholz2019][Vorba2014])
FITTING/LEARNING THE INCIDENT RADIANCE MIXTURES
Cons:
โข Pre-processing step:
โข Long time to first render iteration
โข Complex scenes need bidirectional learning:
โข Ping-Pong style [Vorba2014]
โข It is not the ideal solution for artists in production
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding87
Photon-based pre-processing ([Herholz2019][Vorba2014])
FITTING/LEARNING THE INCIDENT RADIANCE MIXTURES
Pros:
โข First experiments show promising results
โข No pre-processing
โข Refines spatial and directional distributions in each iteration
โข Sample data gets more reliable
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding88
Progressive learning (PPG-style [Mueller2017])
FITTING/LEARNING THE INCIDENT RADIANCE MIXTURES
Cons (open challenges):
โข Sample count grows exponential:
โข Memory and fitting time increases
โข Shorter update rates ?
โข Online fitting for mixtures?
โข Spatial structure adapts slowly to LT:
โข Important for distance sampling
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding89
Progressive learning (PPG-style [Mueller2017])
CONCLUSION
โข Even approximate local sampling decisions lead to a good approximation of the globally optimal guiding distribution (and thus significantly reducing MC variance)
โข Converges to optimal ZV estimator in the hypothetical limit (i.e., if the approximations were perfect)
โข Solely based one guiding structure for alldecisions (incident radiance VMMs)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding90
THANK YOU
91
REFERENCES
โข [Fong2017]: โProduction volume renderingโ
โข [Novak2018]: โMonte Carlo methods for volumetric light transport simulationโ
โข [Kulla2012]: โImportance sampling techniques for path tracing in participating mediaโ
โข [Georgiev2012]: โimportance sampling of low-order volumetric scatteringโ
โข [Krivanek2014]: โA zero-variance-based sampling scheme for Monte Carlo subsurface scatteringโ
โข [Meng2016]: โImproving the Dwivedi sampling schemeโ
โข [Vorba2014]: โOnline learning of parametric mixture models for light transport simulationโ
โข [Vorba2016]: โAdjoint-driven Russian roulette and splitting in light transport simulationโ
โข [Herholz2016]: โProduct importance sampling for light transport path guidingโ
โข [Koerner2016]: โSubdivision next-event estimation for path-traced subsurface scatteringโ
โข [Mueller2017]: โPractical path guiding for efficient light-transport simulationโ
โข [Hoogenboom2008]: โZero-varianceMonte Carlo schemes revisitedโ
โข [Pegoraro2008]:โ Sequential Monte Carlo integration in low-anisotropy participating mediaโ
โข [Bashford2012]: โA significance cache for accelerating global illuminationโ
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding92
ADJOINT ESTIMATE ACCURACY
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding93
COMPARING AGAINST EQUIANGULAR SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding94
BUMPY SPHERE
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding95
INCREMENTAL GUIDED DISTANCE SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding96
INCREMENTAL GUIDED DISTANCE SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding97
INCREMENTAL GUIDED DISTANCE SAMPLING
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding98
VMM PHASE FUNCTION FITTING: PRE-PROCESSING STEP
โข Using up to K = 4 components
โข Optimization Problem:
arg mi๐ฮ๐
๐=1
๐
โlog(๐ ๐๐, โฆ , ๐(๐๐, ฮ๐))2
โlog(๐,๐) = log ๐ + ๐ โ log ๐ + ๐
๐ = (1๐ โ 4) โ max(๐1, โฆ , ๐๐)
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding99
VMM PHASE FUNCTION FITTING
โข Manifold representation of the VMM parameters for an HG phase function model for different mean cosines
Sebastian Herholz | Volumetric Zero-Variance-Based Path Guiding100