Automatic Generation of Subdivision Surface Head Models from PointCloud Data

Won-Ki Jeong Kolja Kahler Jorg Haber Hans-Peter Seidel

Max-Planck-Institut fur Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrucken, Germanyjeong,kaehler,haberj,hpseidel@mpi-sb.mpg.de

AbstractAn automatic procedure is presented to generate a mul-tiresolution head model from sampled surface data. Ageneric control mesh serves as the starting point for a fit-ting algorithm that approximates the points in an unstruc-tured set of surface samples, e.g. a point cloud obtaineddirectly from range scans of an individual. A hierarchicalrepresentation of the model is generated by repeated re-finement using subdivision rules and measuring displace-ments to the input data. Key features of our method arethe fully automated construction process, the ability todeal with noisy and incomplete input data, and no re-quirement for further processing of the scan data afterregistering the range images into a single point cloud.

Key words: range scans, subdivision surface, facial ani-mation, point cloud fitting

1 Introduction

In the task of modeling human heads from real individ-uals for facial animation we are usually confronted withtwo conflicting goals: one is the requirement for accuratereproduction of facial features, the other is the demandfor an efficient representation which can be animated eas-ily and quickly. Additional difficulties are brought in bylimitations of current range scanning technology: the datais often noisy and has “holes” due to shadowing effectsor bad reflection properties of the scanned surface. Somedata, like the part of the lips on the inside of the mouth,cannot be captured at all. To create a triangle mesh that issuitable for real-time animation, extensive manual post-processing of the scanned geometry is often necessary,followed by mesh simplification to reduce the complexityof the mesh. Unfortunately, mesh decimation techniquescannot exert enough control over the connectivity of themesh to obtain an optimal mesh for animation: the dis-tribution of vertices and alignment of edges should corre-spond to the basic symmetry of the face and the potentialdeformations of the mesh, which are not easily derivedfrom the static shape. With low-polygon models, a sin-gle misplaced edge can destroy the visual impression ofa smooth surface. Resorting to higher resolution meshes

is nonetheless undesirable due to the additional computa-tional load for the animation system.

We chose to use a subdivision surface representation inour facial animation environment. Subdivision surfaceshave become increasingly popular due to their ability tobridge the gap between polygon meshes and higher-ordersurfaces. Since they are constructed by repeated refine-ment of triangle meshes up to an arbitrarily close approx-imation to their smooth limit surface, they also providean effective means to control accuracy and efficiency ina systematic manner. By constructing the surface from acontrol mesh of known topology, we can also avoid theinstabilities that are incurred by animating an irregulartriangle mesh.

In this paper, we present our approach for generationof multiresolution head model geometry from sampledsurface data. The method takes as input an unstructuredpoint cloud that is obtained from range scans of an in-dividual. A fully automatic procedure is used to fit ahand-designed generic control mesh to this point cloud,taking special care to match facial features such as earsand mouth. A hierarchical structure of displaced subdivi-sion surfaces is then constructed, which approximates theinput geometry with increasing precision, up to the sam-pling resolution of the input data. Our method generatesuseful models from noisy and incomplete input data, withno requirement for further processing of the scan data ex-cept for registration into a single point cloud. Figure 1shows the main stages of our method.

Since we use an interpolating subdivision scheme, dis-placing a vertex of the subdivision control mesh corre-sponds directly to the local change of the surface. In ourphysics-based facial animation system, we interpret thevertices and edges of the control mesh as point massesand springs which are reacting to forces applied by vir-tual muscles. Animating this very coarse spring mesh iscomputationally efficient, while the level of detail for ren-dering the geometry is controlled separately. For a givenrefinement level, the support of a vertex in the controlmesh is known, and thus we can achieve efficient anima-tion by only locally updating the mesh structure.

Figure 1: The main stages of head model construction. From left to right: a) a dense set of surface samples obtaineddirectly from a range scanner (thinned in this image for visualization); b) generic mesh; c) deformed mesh used assubdivision control mesh; d) subdivision surface fitted to range data.

2 Previous Work

The literature on surface representations used in model-ing and animation is vast. Since we are interested in con-structing multiresolution models for real-time facial ani-mation, we focus here on triangle mesh-based structures,because of their conceptual simplicity and the availabilityof efficient graphics hardware for rendering.

Adaptive refinement of arbitrary triangle meshes is anactive topic in multiresolution editing [26, 11]. Whilethese methods provide powerful tools for mesh deforma-tions, the computational complexity is still considerablytoo high for real-time applications.

In physics-based animation, the vertices of a de-formable mesh surface are often interpreted as nodes of aspring mesh [13, 22]. Adaptively refining such a mass-spring system is non-trivial [7]. An efficient methodto smooth polygonal geometry proposed by VOLINO etal. [23] can be applied to the deformed geometry thatresults from a mass-spring simulation to improve visualquality. The technique uses on-the-fly refinement of poly-gons, where additional vertex positions are computedfrom the vertex normals of the original mesh. The result-ing surface has smoother appearance, but does not con-tain additional geometric detail.

Subdivision surfaces have been successfully used incomputer animation [3]. A wide range of subdivisionschemes exists today, basically structured by the typeof the control mesh (quadrilateral or triangular), the or-der of continuity they can achieve (usuallyC1 or C2)and whether they approximate or interpolate the con-trol mesh after refinement [24]. While most subdivisionschemes apply the subdivision operator uniformly to thesurface, some recent results demonstrate adaptive refine-ment [26, 10]. The algorithms become considerably morecomplex in these cases.

PIGHIN et al. [18] have used an approach based onradial basis functions to match a generic head mesh to

several photographs of a head simultaneously. Their ap-proach doesn’t need additional hardware besides a low-cost still camera, but requires the manual specification offacial features in all of the views. Animation is limited,because each expression needs to be captured in advance.An optimization process proposed by BLANZ et al. [2]generates close approximations to even only a single pho-tograph. This technique draws from a large database ofseveral hundred scanned faces. The resulting model hasthe same resolution as the scanned faces and cannot bereadily animated.

In the context of medical imaging, SZELISKI et al. [21]minimize the distance between two surfaces obtainedfrom volume scans of human heads by applying local andglobal deformations in a hierarchical manner. The defor-mations are modelled by a combination of global polyno-mial deformations and local free-form deformations [20].The method does not require specification of correspond-ing features on the geometries.

The goal in the method presented by LEE et al. [13]is the automated construction of animatable head mod-els from range scans. They adapt a generic face meshwith embedded muscle vectors to range scans of humanheads. This process is largely automated, but relies onthe inherent automatic registration of the texture to therange data. The model created from the scan data is fullyanimatable. The generated mesh approximates the inputgeometry well on a rather coarse detail level.

MARSCHNERet al. [17] match a subdivision surface togeometry measured by a range scanner. They use Loopsubdivision rules [16] and a fitting algorithm based onthe work of HOPPE et al. [5]. A continuous optimiza-tion process alters vertex positions to minimize an energyfunctional. For rendering, the surface is subdivided to thedesired level. Due to the approximating nature of Loopsubdivision, the coarser levels of the subdivision hierar-chy do not resemble the scanned geometry everywhere.

Motion of the face is specified by varying positions ofsample points on the surface and computing the corre-sponding control vertex displacements.

3 Overview

In our approach, facial geometry is acquired from real hu-mans using a range scanner. The individuals are capturedwith a closed mouth and neutral expression. No trian-gulation or further post-processing such as hole-filling isperformed on the scan data. The result of the acquisitionstage is an unstructured, dense point cloud, possibly withinfrequent large holes due to missing or bad data.

Given the generic head model as shown in Figure 1 b),we deform this mesh to approximate the point cloud ina three-step procedure, which runs automatically withoutuser intervention:

1. Initial alignment: This step automatically computesan affine transformation (rotation, translation andnon-uniform scaling) that minimizes the differencebetween the silhouette of the generic head modeland the outer hull of the point cloud. This proce-dure uses an iterative optimization technique, andwe exploit graphics hardware for evaluating the cur-rent match to achieve fast convergence.

2. Local fitting: Due to individual differences in facialproportions, the global affine transformation doesusually not result in good registration of the promi-nent features of the face. Thus, we apply anotheroptimization to the regions containing the ears, nose,and mouth, which are marked in the prototype mesh.Here, a local rigid transformation is found that min-imizes the distance from the point samples to themesh surface. The transformation is applied directlyto the mesh regions and blended into the surround-ing parts of the mesh to achieve smooth transitions.

3. Global fitting: The deformed prototype mesh is nowwell-aligned to the facial features of the sampledata. The final fitting step reduces the distancefrom the point cloud to the mesh by global energyminimization. The employed energy functional isessentially the same as used by HOPPE et al. [6]and MARSCHNER et al. [17]. In addition to min-imization of the distance between point cloud andmesh, the function accounts for smoothness andconstraints defined on the generic mesh.

All three steps of this fitting procedure are explainedin detail in Section 4. Provided the deformed genericmesh, we proceed with the construction of the subdivi-sion hierarchy, using the interpolating Modified Butterfly

scheme [25]. On the base level and on each level of re-finement, the vertices are displaced along triangle normaldirection to lie on the surface sampled by the point cloud.In this manner, a hierarchy of surfaces is generated withlocally encoded details, similar to normal meshes [4].The construction process is detailed in Section 5. For an-imation, we rebuild the surface in the changed areas, suchthat the local detail will follow the deformation properly,see Section 6.

4 Fitting the Control Mesh

For the following discussion we need some notation. Wedefine a triangle meshM as a tuple(VM, EM, TM), de-noting the vertices, edges and triangles of the mesh, re-spectively. We refer to the initial generic mesh asG. Thismesh will be deformed over the three fitting stages byupdating its vertex positions, but leaving the connectivityunchanged. The sample data is given as a set of pointsP. All points and mesh vertex positions are given as 3Dcoordinates and will be written in bold face:p ∈ R3. Forconvenience, for a vertexv ∈ VM, v will denote its po-sition. We writestar(v) for the set of vertices directlyconnected tov via an edge, andvalence(v) for the num-ber of these adjacent vertices.

4.1 Initial alignment

In the initial step of the subdivision surface fitting pro-cess, we approximately align the generic head modelG to the point cloud using an affine transformationT .Throughout this section,G will mean the transformedversion of the generic mesh using the currentT , which isused – after convergence – as the input for the next stepdescribed in Section 4.2. The parameters forT are de-termined fully automatically by exploiting graphics hard-ware to perform a silhouette-based geometry fitting. Ourapproach thus extends the idea of the 2D silhouette-basedtexture mapping technique presented in [14, 15] to three-dimensional geometry.

To evaluate the currentT , we render bothG andPinto a common frame buffer for one of the three canon-ical viewing directions along the coordinate axes. Theframe buffer is initialized to black. Next, we render thepoint cloud with a white color, an identity modelviewmatrix, and no further lighting or depth test. We thenset the OpenGL logical fragment operation to XOR andrender the generic head model with the modelview ma-trix set toT and identical rendering parameters. Nowthe frame buffer contains those pixels in white that arecovered by only one of the two geometric objectsG andP. The frame buffer image can thus be interpreted as thesilhouette-based difference betweenG andP for the cho-

sen viewing direction1. Finally, the number of white pix-els in the frame buffer is evaluated using theglGetH-istogram function. It is a measure of how well the ob-jectsG andP are aligned in their image space projection.This process is repeated for all three different viewing di-rections in turn and their difference measures are summedup. The resultingtotal differenceD is used to control aniterative optimization process to determineT .

We initialize the scaling and translation parameters ofT such that the bounding boxes of the point cloud andthe generic head model have the same size and centerpoint. Since we know from our range scanner that thepoint cloud is roughly oriented in such a way that theface looks along thez-axis and the up-vector coincideswith the y-axis, we set the initial rotation parameters ofT accordingly. For the optimization process, we applyPowell’s method [19, Sec. 10.5] to the set of parametersof T . The function to be minimized is given by the to-tal differenceD. Figure 2 shows three silhouette-baseddifference images (according to three orthogonal view-ing directions) both after the initialization step and afterconvergence of the optimization process.

In addition, we have to take into account that the partof the point cloudP representing the neck of the headmight be longer or shorter than the corresponding part ofthe generic head modelG. To avoid artificial “differencepixels” due to these non-corresponding parts ofP andG,we introduce a clipping plane in the world coordinate sys-tem (i.e. the location of the clipping plane is independentof T ) to cut away those unwanted parts ofP andG. Also,the back of the head can often not be captured appro-priately due to difficulties with structured light scannersin hair-covered head regions, so we add another clippingplane that removes this part inP andG as well. We pro-vide a generic position and orientation for each of theseplanes based on the initialT , which may have to be mod-ified by the user before the fitting process is started, ac-cording to the specifics of the range scan data.

Further optimization of the process can be achieved byinitially rendering the point cloud once for each viewingdirection and storing the resulting frame buffer images inthree textures. During the optimization process, we thenonly need to render one textured quad for each viewingdirection instead of rendering the full point cloud.

4.2 Adaptive Local AlignmentThe initial alignment step gives an optimal fit for thegeneric mesh using an affine transform. Since individ-ual faces are of different proportions, the main facial fea-tures like ears, nose and mouth are generally not regis-

1If the point cloud does not contain enough data points to result ina fully covered silhouette during rendering, we repeat this step withglPointsize set to a slightly higher value.

Figure 2: Silhouette-based geometry fitting: white pix-els indicate the difference between the silhouettes of thegeneric head model and the point cloud. Top row: ini-tial difference images for three orthogonal viewing direc-tions. Bottom row: difference images after optimizationprocess.

tered well in the transformed generic mesh and the pointcloud, which prohibits a direct execution of the globaldistance minimization procedure (section 4.3). Hence,we apply local deformations to the mesh in four areasof the generic model (one for each ear, the nose and themouth).

For this purpose, a set of bounding boxesB enclosingeach feature is predefined for the generic mesh, as shownin Figure 4. The bounding boxes are chosen large enoughto ensure that after the initial alignment the sample pointsbelonging to the respective feature on the point cloud arealso included in the box. In the following, we writeGb forthe part of the generic meshG that is enclosed in bound-ing box b ∈ B. Similarly,Pb is the portion of the pointcloud enclosed in boxb.

For each bounding box, we now minimize the energyfunctionalElocal = Edist + Estretch by optimizing theposition of the mesh vertices included in the box.Edistis minimized as the distance from every point in the pointcloud to the mesh becomes smaller:

Edist(Gb) =∑

p∈Pb(‖Π(Gb,p)− p‖2),

whereΠ(Gb,p) is the projection of pointp onto the near-est surface point on the meshGb.Estretch penalizes changes in length of edges in the

generic mesh after transformation, and is defined as

Estretch(Gb) =∑e∈EGb

12k|le − re|2,

wherek is a spring constant,le is the current length, andre the rest length of edgee. Including this term prohibitslarge changes in the position and orientation of the fea-ture, and thus keeps the optimization from converging toa solution too far from the initial configuration.

To find an affine transformation that minimizes thenon-linear functionElocal, we employ Powell’s algo-rithm, as in Section 4.1. Since the optimization is per-formed only locally over the mesh regionGb, it can becarried out quickly.

After the energy minimization procedure has con-verged, we apply the transformation found for eachbounding box to the contained geometry and performa gradual blend with the surrounding area, similar tothe method used in [1]. For blending, we use a setL = l1, . . . , ln of n landmarks defined on the unde-formed generic mesh, which are contained in the abovementioned boxes. In practice, we use three landmarksfor each ear, and four for the nose and the mouth, seeFigure 4. The transformation found for each box is alsoapplied to the contained landmarks, resulting in the trans-formed landmark setL = l1, . . . , ln. The displace-ment vectors for all the landmarks are used to update thesubsetVb := VG \VGbb∈B of vertices ofVG that are notcontained in any box. The displacements are weighted byan exponential fall-off function according to the distancebetween landmark and mesh vertex:

∀v ∈ Vb : v← v +∑ni=1 exp(− 1

k‖v − li‖)(li − li)

We initialize the constant valuek to 1/30 of the diagonallength of the bounding box of the given point set. Thisparameter controls the size of the region influenced bythe blending.

4.3 Global Control Mesh FittingGiven the generic meshG with locally aligned facial fea-tures, we can now perform straightforward global opti-mization by iteratively minimizing the distance from thepoints of the sample data set to the mesh surface. We per-form least squares minimization of the energy functional

Eglobal = Edist + λEsmooth + µEbinding + νEconstraint.

Optimization stops, when the difference of the previousand currentEglobal drops below a user-specified errorthreshold. Edist is just the same functional as used inSection 4.2, but this time applied to all vertices inG. Theuser-specified weightsλ, µ, andν balance the additionalterms againstEdist. To enforce local flatness of the mesh,Esmooth measures the deviation of mesh vertices to thecentroid of their respective one-neighborhood:

Esmooth(G) =∑v∈VG

∥∥∥∥∥∑w∈star(v) w

valence(v)− v

∥∥∥∥∥2

,

Figure 3: Improving definition of facial features in the fit-ted control mesh with imperfect scan data. Left: withoutusing binding energy, the upper area behind the ear is flat-tened due to lack of data in the input sample set. Right:by use of binding edges the shape of the ear is improved.

Because the numerical value ofEdist increases with thelocal density of the points in the scan data set,Esmoothhas only a comparatively small influence in the regionswhere data is present. In regions of the scan data setwhere there is no data, the smoothing term leads to ashrinking effect, since here the distance minimizationdoes not act as a counter-force. We thus introduce addi-tional constraint termsEbinding andEconstraint into theenergy function.Ebinding is used to minimize the length of a set of

edges, which we callbinding edges. This constraint helpsto keep features in the face from flattening out due to lackof data, as is frequently the case behind the ears: our tri-angulation scanner cannot measure data in these regionsdue to shadowing between light source and projector.Since there are no data samples that the surface could ap-proximate, the smoothing term eventually removes con-cavities. If we define binding edges in these regions, theflattening of that area is effectively prevented:

Ebinding(G) =∑e∈Eb

l2e ,

whereEb is the set of binding edges andle is the lengthof edgee. These edges are for the most part defined bya subset of edges fromEG . Additionally, some verticesof G that are not actually connected by edges inEG arebound together inEb (see Figure 4). These additionaledges are used to keep corresponding vertices of the up-per and lower lips together: unconstrained, the shrinkingeffect of the smoothing term leads to the introduction ofa gap between the lips, which should remain closed as inthe generic modelG. Figure 3 demonstrates the effect ofthe binding energy term.

Finally, we constrain vertices to their original positionsbyEconstraint. This constraint helps to keep the shape of

the inner part of the lips of the mesh model, which wouldotherwise be flattened onto the outside in the process ofminimizing the distance to the point cloud (see Figure 4).

Econstraint(G) =∑v∈VcG

‖v − v‖2,

whereVcG is the set of constrained vertices defined onG,andv denotes the original position of vertexv before theoptimization.

As described in [17], a sparse linear system can be builtexpressing the functionEglobal, which can be solved us-ing the conjugate gradient method [19]. To be able to setup a linear system,Edist has to be linearized, which canbe done as shown in [5, 17].

5 Generation of the Multiresolution Model

We employ the Modified Butterfly subdivision scheme[25] to construct the subdivision hierarchy on top of thebase mesh resulting from the fitting process described inthe previous section. This scheme guaranteesC1 con-tinuity everywhere and has the advantage of interpolat-ing the vertices of the previous refinement levels, so thatcoarser levels of refinement serve as an approximation tothe head geometry, which is not necessarily the case withapproximating subdivision schemes [17].

After fitting, the surface of the deformed generic meshapproximates the point cloud in a least squares sense,i.e. the distance between the points and the surface is min-imized. The control mesh vertices arenot necessarily ly-ing on the point cloud. Before refining the mesh usingthe Butterfly subdivision rules, we measure the distancefrom each vertex along normal direction to the nearestpoint on the point cloud and store this value as an addi-tional displacement. The displacements are then appliedto the vertices and the updated mesh is refined. On eachlevel of the resulting hierarchy, we thus obtain a trianglemesh with vertices interpolating the original point cloudafter the respective displacements have been applied. Inareas of the point cloud with no data we cannot measuredisplacements, but the subdivision operator generates asmooth surface in these regions. This construction tech-nique is similar tonormal meshes[4], but we sample dis-placements to a set of sample points instead of to anothermesh. By storing only one scalar displacement value pervertex introduced on each level, we achieve a storage-efficient hierarchical mesh structure [4, 12].

6 Animating the Surface

During animation, the control mesh vertices of the sub-division surface are displaced via simulated muscle con-traction [9]. Since the subdivision hierarchy is built usingan interpolating scheme, each refinement level including

the control mesh can serve as an approximation to thelimit surface for rendering. Depending on the availablecomputation time per frame and quality requirements, anappropriate refinement level can be picked for display.Since the mesh topology is completely determined by thetopology of the base mesh and the subdivision scheme,the area of change to the refined mesh induced by move-ment of a control mesh vertex is known a priori and isdetermined by the support of that vertex [8, 26]. In theButterfly scheme, the support includes at most the three-neighborhood of a control mesh vertex. When a controlmesh vertex is animated, we apply the subdivision rulesand displacements only to this area. Thus, we can achievefast updates of the refined geometry, without having to in-clude the detailed geometry into the simulation task of thephysics-based animation engine. Figure 5 shows snap-shots from an animation of the head geometry.

7 Results

We have applied our surface generation method to scansof male and female individuals, see figures 1 and 6. Withour structured light scanner, the scans show defects inlarge regions due to shadowing effects and bad reflectiveproperties of the surface, especially on hair. Nonethe-less, our algorithm generates subdivision models consis-tent with the range data, complementing it in a plausi-ble manner in areas with no data. User intervention wasnot necessary, the only initial requirement being that bothscan data and generic head model are looking roughlydown the same axis in world coordinates.

The silhouette-based geometry fitting approach con-verges quite quickly in 8–14 iterations of Powell’s op-timization method. However, each iteration performsabout 250–300 evaluations of the “function” to be min-imized, i.e. counting the number of white pixels us-ing glGetHistogram calls. For each of these calls,we have to read back and draw the framebuffer us-ing glCopyPixels to retrieve the results of the his-togram. Unfortunately, such framebuffer read-backs arestill quite expensive on current PC graphics boards: usinga 256×256 framebuffer, the optimization process takesabout 6–10 min on a 1.7 GHz PC with a GeForce3 graph-ics board while completing within 90–150 sec on ansgiOctane with a 300 MHz R12k processor. Increasingthe resolution of the framebuffer to 512×512 results ina slightly better alignment and a (relative) convergencespeed-up of 1–2 iterations. Due to the larger amount ofdata that is read from and drawn into the framebuffer, thewhole process takes about 20–30 min on the PC and 5–8 min on the Octane in this case.

In the current implementation, we have to reduce theinput complexity for the local and global fitting steps to

handle large data sets. On the PC, with a dataset of 50kpoints subsampled from the initial 300k points, the lo-cal fitting process runs for approx. 5 minutes, performingabout 35 iterations per bounding box. The global fittingprocess performs 100 iterations in approx. 40 minutes un-til convergence. The multiresolution mesh is then builtusing the complete set of point samples with no subsam-pling. Even though the processing takes up considerabletime even on a fast PC, this does not impair usability toa large extent due to the full automation. Not countingtimes for the simulation and rendering parts in our fa-cial animation system, updating the animated mesh onthe second refinement level requires about 40–50ms onthe PC, corresponding to a rate of 20–25 fps.

For the models shown in Figure 6, the following tableshows the development of the mean and maximum dis-tances from the point cloud to the current control meshafter each of the three steps of the algorithm. The lastcolumn shows the distance to the final subdivision surfacewith displacements applied. The values are normalized to“percent of the point cloud bounding box diameter”. Themaximum distance to the final surface reflects the “noisi-ness” of the input data: outliers in overlapping regions ofthe range scans are not interpolated.

initial local global subdiv.alignment fitting fitting surface

male / mean 1.51 1.42 0.11 0.04male / max. 13.13 13.13 1.28 1.30female / mean 1.09 0.91 0.12 0.08female / max. 11.35 10.26 1.55 1.55

8 Future Work

Apart from geometric similarities, we would like to em-ploy texture information to improve the accuracy of fea-ture matching. Also, instead of simply generating asmooth surface in areas with no data, it would be interest-ing to generate artificial surface detail to make the surfacematch the surrounding areas. For the animation system,we are planning the automatic insertion of separate com-ponents representing eyes, teeth, and tongue.

References[1] T. Akimoto, Y. Suenaga, and R. S. Wallace. Automatic

creation of 3d facial models.IEEE Computer Graphics &Applications, 13(5):16–22, September 1993.

[2] V. Blanz and T. Vetter. A Morphable Model for the Syn-thesis of 3D Faces. InComputer Graphics (SIGGRAPH’99 Conf. Proc.), pages 187–194, 1999.

[3] T. DeRose, M. Kass, and T. Truong. Subdivision Surfacesin Character Animation. InComputer Graphics (SIG-GRAPH ’98 Conf. Proc.), pages 85–94, 1998.

[4] I. Guskov, K. Vidimce, W. Sweldens, and P. Schroder.Normal Meshes. InComputer Graphics (SIGGRAPH ’00Conf. Proc.), pages 95–102, 2000.

[5] H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin,J. McDonald, J. Schweitzer, and W. Stuetzle. PiecewiseSmooth Surface Reconstruction. InComputer Graphics(SIGGRAPH ’94 Conf. Proc.), pages 295–302, 1994.

[6] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, andW. Stuetzle. Mesh Optimization. InComputer Graphics(SIGGRAPH ’93 Conf. Proc.), pages 19–26, 1993.

[7] D. Hutchinson, M. Preston, and T. Hewitt. Adaptive Re-finement for Mass-Spring Simulation. In7th EG Work-shop on Animation and Simulation, pages 31–45, 1996.

[8] I. P. Ivrissimtzis and M.A. Sabin. On the support of recur-sive subdivision.submitted for publication, 2001.

[9] K. K ahler, J. Haber, and H.-P. Seidel. Geometry-basedmuscle modeling for facial animation. InGraphics Inter-face2001 Conf. Proc., pages 37 – 46, 2001.

[10] L. Kobbelt.√

3-Subdivision. InComputer Graphics (SIG-GRAPH ’00 Conf. Proc.), pages 103–112, 2000.

[11] L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Sei-del. Interactive Multi-Resolution Modeling on ArbitraryMeshes. InComputer Graphics (SIGGRAPH ’98 Conf.Proc.), pages 105–114, 1998.

[12] A. Lee, H. Moreton, and H. Hoppe. Displaced SubdivisionSurfaces. InComputer Graphics (SIGGRAPH ’00 Conf.Proc.), pages 85–94, 2000.

[13] Y. Lee, D. Terzopoulos, and K. Waters. Realistic Model-ing for Facial Animations. InComputer Graphics (SIG-GRAPH ’95 Conf. Proc.), pages 55–62, 1995.

[14] H. P. A. Lensch, W. Heidrich, and H.-P. Seidel. AutomatedTexture Registration and Stitching for Real World Models.In Proc. Pacific Graphics 2000, pages 317–326, 2000.

[15] H. P. A. Lensch, W. Heidrich, and H.-P. Seidel. ASilhouette-based Algorithm for Texture Registration andStitching.Graphical Models, 2001. (to appear).

[16] C. T. Loop. Smooth Subdivision Surfaces Based on Trian-gles. Master’s thesis, University of Utah, Department ofMathematics, 1987.

[17] S. Marschner, B. Guenter, and S. Raghupathy. Modelingand Rendering for Realistic Facial Animation. InRender-ing Techniques 2000 (Proc. 11th EG Workshop on Ren-dering), pages 231–242, 2000.

[18] F. Pighin, J. Hecker, D. Lischinski, R. Szeliski, and D. H.Salesin. Synthesizing Realistic Facial Expressions fromPhotographs. InComputer Graphics (SIGGRAPH ’98Conf. Proc.), pages 75–84, 1998.

[19] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P.Flannery. Numerical Recipes in C: The Art of Scien-tific Computing. Cambridge University Press, Cambridge,MA, 2nd edition, 1992.

[20] T. W. Sederberg and S. R. Parry. Free-Form Deformationof Solid Geometric Models. InComputer Graphics (SIG-GRAPH ’86 Conf. Proc.), pages 151–160, 1986.

[21] R. Szeliski and S. Lavallee. Matching 3-D Anatomi-cal Surfaces with Non-Rigid Deformations using Octree-Splines. International Journal of Computer Vision,18(2):171–186, 1996.

[22] A. Van Gelder. Approximate Simulation of Elastic Mem-branes by Triangulated Spring Meshes.Journal of Graph-ics Tools, 3(2):21–41, 1998.

[23] P. Volino and N. Magnenat-Thalmann. The SPHERIGON:A Simple Polygon Patch for Smoothing Quickly yourPolygonal Meshes. InProc. Computer Animation ’98,pages 72–79, 1998.

[24] D. Zorin and P. Schroder. Subdivision for Modeling andAnimation. Computer Graphics (SIGGRAPH ’00 CourseNotes), 2000.

[25] D. Zorin, P. Schroder, and W. Sweldens. Interpolating sub-division for meshes with arbitrary topology. InComputerGraphics (SIGGRAPH ’96 Conf. Proc.), pages 189–192,1996.

[26] D. Zorin, P. Schroder, and W. Sweldens. Interactive Mul-tiresolution Mesh Editing. InComputer Graphics (SIG-GRAPH ’97 Conf. Proc.), pages 259–268, 1997.

Figure 4: Extra information stored with the generichead model: Left and center: four bounding boxes (red)around ears, nose and mouth; edges to which binding en-ergy constraint is applied (green lines); landmarks on theboxed features (yellow dots). Right: cross-section of themouth region. The binding energy term is applied to vir-tual edges connecting upper and lower lip vertices (greenline and dots). The inner part of the lips is kept in shapeby constraining vertices to their positions (red dots).

Figure 5: Displaced subdivision surface head modelshowing different expressions.

Figure 6: Two more point sample sets and the head mod-els generated from them, shown at 2 levels of refinementof the base mesh. Left: female scanned with a bathingcap to enable our scanner to capture data on the back ofthe head. Right: scan of a male, exhibiting lack of sampledata in the hair-covered region.