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64
SCAPE: shape completion and animation of people
 ACM Trans. Graph
, 2005
"... Figure 1: Animation of a motion capture sequence taken for a subject, of whom we have a single body scan. The muscle deformations are synthesized automatically from the space of pose and body shape deformations. We introduce the SCAPE method (Shape Completion and Animation for PEople) — a datadriv ..."
Abstract

Cited by 173 (4 self)
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Figure 1: Animation of a motion capture sequence taken for a subject, of whom we have a single body scan. The muscle deformations are synthesized automatically from the space of pose and body shape deformations. We introduce the SCAPE method (Shape Completion and Animation for PEople) — a datadriven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and nonrigid deformations. We learn a pose deformation model that derives the nonrigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion — generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a highquality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan and a marker motion capture sequence of the person.
ExampleBased 3D Scan Completion
 EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING
, 2005
"... Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete sur ..."
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Cited by 58 (19 self)
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Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete surface scans, using a database of 3D shapes to provide geometric priors for regions of missing data. Our method retrieves suitable context models from the database, warps the retrieved models to conform with the input data, and consistently blends the warped models to obtain the final consolidated 3D shape. We define a shape matching penalty function and corresponding optimization scheme for computing the nonrigid alignment of the context models with the input data. This allows a quantitative evaluation and comparison of the quality of the shape extrapolation provided by each model. Our algorithms are explicitly designed to accommodate uncertain data and can thus be applied directly to raw scanner output. We show on a variety of real data sets how consistent models can be obtained from highly incomplete input. The information gained during the shape completion process can be utilized for future scans, thus continuously simplifying the creation of complex 3D models.
Möbius voting for surface correspondence
 ACM TRANS. GRAPH. (PROC. SIGGRAPH
, 2009
"... The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has lowdimensionality ..."
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Cited by 58 (5 self)
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The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has lowdimensionality – six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closedform after a midedge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportationtype distance between corresponding points in that plane. Motivated by these observations, we have developed a Möbius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Möbius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces “votes” for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.
Articulated Shape Matching Using Laplacian Eigenfunctions and Unsupervised Point Registration
"... Matching articulated shapes represented by voxelsets reduces to maximal subgraph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invarian ..."
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Cited by 46 (11 self)
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Matching articulated shapes represented by voxelsets reduces to maximal subgraph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invariance to change of pose. Classical graph isomorphism schemes relying on the ordering of the eigenvalues to align the eigenspaces fail when handling large datasets or noisy data. We derive a new formulation that finds the best alignment between two congruent Kdimensional sets of points by selecting the best subset of eigenfunctions of the Laplacian matrix. The selection is done by matching eigenfunction signatures built with histograms, and the retained set provides a smart initialization for the alignment problem with a considerable impact on the overall performance. Dense shape matching casted into graph matching reduces then, to point registration of embeddings under orthogonal transformations; the registration is solved using the framework of unsupervised clustering and the EM algorithm. Maximal subset matching of non identical shapes is handled by defining an appropriate outlier class. Experimental results on challenging examples show how the algorithm naturally treats changes of topology, shape variations and different sampling densities. 1.
Using combinatorial optimization within maxproduct belief propagation
 Advances in Neural Information Processing Systems (NIPS
, 2007
"... In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: cert ..."
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Cited by 39 (6 self)
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In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as subnetworks, but also other noncomplying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for subnetworks within the context of a maxproduct belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact maxmarginals for an entire subnetwork; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing maxmarginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higherscoring assignments. 1
A Survey on Shape Correspondence
, 2011
"... We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, an ..."
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Cited by 28 (6 self)
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We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in spacetime registration, where one seeks a correspondence between nonrigid and timevarying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult since it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function, and solution approach. We conclude the survey by discussing open problems and future perspectives.
Reconstruction of Deforming Geometry from TimeVarying Point Clouds
, 2007
"... In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent realtime range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondenc ..."
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Cited by 28 (7 self)
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In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent realtime range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondences, holes due to occlusion are filled in from other frames. Our reconstruction technique is based on a statistical framework: The reconstruction should both match the measured data points and maximize prior probability densities that prefer smoothness, rigid deformation and smooth movements over time. The optimization procedure consists of an inner loop that optimizes the 4D shape using continuous numerical optimization and an outer loop that infers the discrete 4D topology of the data set using an iterative model assembly algorithm. We apply the technique to a variety of data sets, demonstrating that the new approach is capable of robustly retrieving animated models with correspondences from data sets suffering from significant noise, outliers and acquisition holes.
Temporal Surface Tracking using Mesh Evolution
"... Abstract. In this paper, we address the problem of surface tracking in multiple camera environments and over time sequences. In order to fully track a surface undergoing significant deformations, we cast the problem as a mesh evolution over time. Such an evolution is driven by 3D displacement fields ..."
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Cited by 26 (8 self)
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Abstract. In this paper, we address the problem of surface tracking in multiple camera environments and over time sequences. In order to fully track a surface undergoing significant deformations, we cast the problem as a mesh evolution over time. Such an evolution is driven by 3D displacement fields estimated between meshes recovered independently at different time frames. Geometric and photometric information is used to identify a robust set of matching vertices. This provides a sparse displacement field that is densified over the mesh by Laplacian diffusion. In contrast to existing approaches that evolve meshes, we do not assume a known model or a fixed topology. The contribution is a novel mesh evolution based framework that allows to fully track, over long sequences, an unknown surface encountering deformations, including topological changes. Results on very challenging and publicly available image based 3D mesh sequences demonstrate the ability of our framework to efficiently recover surface motions. 1
Generalized Surface Flows for Mesh Processing
, 2007
"... Geometric flows are ubiquitous in mesh processing. Curve and surface evolutions based on functional minimization have been used in the context of surface diffusion, denoising, shape optimization, minimal surfaces, and geodesic paths to mention a few. Such gradient flows are nearly always, yet often ..."
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Cited by 25 (1 self)
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Geometric flows are ubiquitous in mesh processing. Curve and surface evolutions based on functional minimization have been used in the context of surface diffusion, denoising, shape optimization, minimal surfaces, and geodesic paths to mention a few. Such gradient flows are nearly always, yet often implicitly, based on the canonical L 2 inner product of vector fields. In this paper, we point out that changing this inner product provides a simple, powerful, and untapped approach to extend current flows. We demonstrate the value of such a norm alteration for regularization and volumepreservation purposes and in the context of shape matching, where deformation priors (ranging from rigid motion to articulated motion) can be incorporated into a gradient flow to drastically improve results. Implementation details, including a differentiable approximation of the Hausdorff distance between irregular meshes, are presented.