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Scape: Shape completion and animation of people
 ACM Trans. Graph
, 2005
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Cited by 286 (4 self)
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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions
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 115 (10 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.
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 87 (24 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.
A Survey on Shape Correspondence
, 2010
"... We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in ..."
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Cited by 78 (10 self)
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We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in the field such as those requiring the correspondence of nonrigid or timevarying surfaces and a recent trend towards semantic shape analysis, of which shape correspondence is one of the central tasks. Establishing a meaningful shape correspondence is a difficult problem since it typically relies on an understanding of the structure of the shapes in question at both a local and global level, and sometimes also the shapes ’ functionality. However, despite its inherent complexity, shape correspondence is a recurrent problem and an essential component in numerous geometry processing applications. In this report, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria which can be used by the reader to objectively compare the methods. We finalize the report by discussing open problems and future perspectives.
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 77 (12 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.
Dense Nonrigid Surface Registration Using HighOrder Graph Matching
"... In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper incl ..."
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Cited by 49 (11 self)
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In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper includes: 1) casting 3D surface registration into a graph matching problem that combines both geometric and appearance similarities and intrinsic embedding information, 2) the first implementation of highorder graph matching algorithm that solves a nonconvex optimization problem, and 3) an efficient twostage optimization approach to constrain the search space for dense surface registration. Our method is validated through a series of experiments demonstrating its accuracy and efficiency, notably in challenging cases of large and/or nonisometric deformations, or meshes that are partially occluded. 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 49 (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
Joint shape segmentation with linear programming
 ACM Trans. on Graphics (Proc. SIGGRAPH Asia
, 2011
"... We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of t ..."
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Cited by 47 (7 self)
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We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms singleshape segmentation techniques.
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 47 (12 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.