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81
ShapeGoogle: geometric words and expressions for invariant shape retrieval
, 2010
"... The computer vision and pattern recognition communities have recently witnessed a surge of featurebased methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words ” and treat them using text search approaches following the ..."
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Cited by 38 (5 self)
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The computer vision and pattern recognition communities have recently witnessed a surge of featurebased methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words ” and treat them using text search approaches following the “bag of features ” paradigm. In this paper, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words”, we construct compact and informative shape descriptors by means of the “bag of features ” approach. We also show that considering pairs of “geometric words ” (“geometric expressions”) allows creating spatiallysensitive bags of features with better discriminativity. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves stateoftheart results on the SHREC 2010 largescale shape retrieval benchmark.
Mesh Parameterization: Theory and Practice
 SIGGRAPH ASIA 2008 COURSE NOTES
, 2008
"... Mesh parameterization is a powerful geometry processing tool with numerous computer graphics applications, from texture mapping to animation transfer. This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools ..."
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Cited by 37 (2 self)
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Mesh parameterization is a powerful geometry processing tool with numerous computer graphics applications, from texture mapping to animation transfer. This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools like global parameterization and intersurface mapping, and demonstrates a variety of parameterization applications.
Dense correspondence finding for parametrizationfree animation reconstruction from video
 IN PROC. IEEE CONF. ON COMPUTER VISION AND PATTERN RECOGNITION
"... We present a dense 3D correspondence finding method that enables spatiotemporally coherent reconstruction of surface animations from multiview video data. Given as input a sequence of shapefromsilhouette volumes of a moving subject that were reconstructed for each time frame individually, our me ..."
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Cited by 26 (3 self)
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We present a dense 3D correspondence finding method that enables spatiotemporally coherent reconstruction of surface animations from multiview video data. Given as input a sequence of shapefromsilhouette volumes of a moving subject that were reconstructed for each time frame individually, our method establishes dense surface correspondences between subsequent shapes independently of surface discretization. This is achieved in two steps: first, we obtain sparse correspondences from robust optical features between adjacent frames. Second, we generate dense correspondences which serve as map between respective surfaces. By applying this procedure subsequently to all pairs of time steps we can trivially align one shape with all others. Thus, the original input can be reconstructed as a sequence of meshes with constant connectivity and small tangential distortion. We exemplify the performance and accuracy of our method using several synthetic and captured realworld sequences.
Constructing Laplace Operator from Point Clouds in R^d
, 2009
"... We present an algorithm for approximating the LaplaceBeltrami operator from an arbitrary point cloud obtained from a kdimensional manifold embedded in the ddimensional space. We show that this PCD Laplace (PointCloud Data Laplace) operator converges to the LaplaceBeltrami operator on the underl ..."
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Cited by 25 (3 self)
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We present an algorithm for approximating the LaplaceBeltrami operator from an arbitrary point cloud obtained from a kdimensional manifold embedded in the ddimensional space. We show that this PCD Laplace (PointCloud Data Laplace) operator converges to the LaplaceBeltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that the data samples are independent identically distributed from a probability distribution and do not require a global mesh. The resulting algorithm is easy to implement. We present experimental results indicating that even for point sets sampled from a uniform distribution, PCD Laplace converges faster than the weighted graph Laplacian. We also show that using our PCD Laplacian we can directly estimate certain geometric invariants, such as manifold area.
TopologyInvariant Similarity of Nonrigid Shapes
, 2009
"... This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their ..."
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Cited by 21 (3 self)
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This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topologyinvariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a setvalued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail.
Spectral GromovWasserstein Distances for Shape Matching
"... We introduce a spectral notion of distance between shapes and study its theoretical properties. We show that our distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if they are isometric. Our constr ..."
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Cited by 16 (1 self)
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We introduce a spectral notion of distance between shapes and study its theoretical properties. We show that our distance satisfies the properties of a metric on the class of isometric shapes, which means, in particular, that two shapes are at 0 distance if and only if they are isometric. Our construction is similar to the recently proposed GromovWasserstein distance, but rather than viewing shapes merely as metric spaces, we define our distance via the comparison of heat kernels. This allows us to relate our distance to previously proposed spectral invariants used for shape comparison, such as the spectrum of the LaplaceBeltrami operator. In addition, the heat kernel provides a natural notion of scale, which is useful for multiscale shape comparison. We also prove a hierarchy of lower bounds for our distance, which provide increasing discriminative power at the cost of increase in computational complexity. 1.
SpectralDriven IsometryInvariant Matching of 3D Shapes
, 2009
"... This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on pointbased statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eige ..."
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Cited by 15 (1 self)
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This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on pointbased statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the LaplaceBeltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a pointbased statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L1distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix
Global medical shape analysis using the LaplaceBeltrami spectrum
 in Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI
, 2007
"... Abstract. This paper proposes to use the LaplaceBeltrami spectrum (LBS) as a global shape descriptor for medical shape analysis, allowing for shape comparisons using minimal shape preprocessing: no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on ..."
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Cited by 15 (3 self)
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Abstract. This paper proposes to use the LaplaceBeltrami spectrum (LBS) as a global shape descriptor for medical shape analysis, allowing for shape comparisons using minimal shape preprocessing: no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on a population of female caudate shapes of normal control subjects and of subjects with schizotypal personality disorder. 1