Hierarchical Matching of Non-rigid Shapes

Raviv, Dan; Dubrovina, Anastasia; Kimmel, Ron

doi:10.1007/978-3-642-24785-9_51

Cited by 16 publications

(10 citation statements)

References 33 publications

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“…However, to extend their correspondences to a complete map, some up‐sampling procedure is required. Thus, several multiresolution approaches [SY11, RDK12] were suggested to alleviate this issue, producing dense point‐to‐point maps. Our approach can be also interpreted as a variant of QAP, but, as opposed to other techniques, we completely avoid the potentially problematic multiresolution methodology.…”

Section: Related Workmentioning

confidence: 99%

Consistent Shape Matching via Coupled Optimization

Azencot

Dubrovina

Guibas

2019

Computer Graphics Forum

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We propose a new method for computing accurate point‐to‐point mappings between a pair of triangle meshes given imperfect initial correspondences. Unlike the majority of existing techniques, we optimize for a map while leveraging information from the inverse map, yielding results which are highly consistent with respect to composition of mappings. Remarkably, our method considers only a linear number of candidate points on the target shape, allowing us to work directly with high resolution meshes, and to avoid a delicate and possibly error‐prone up‐sampling procedure. Key to this dimensionality reduction is a novel candidate selection process, where the mapped points drift over the target shape, finalizing their location based on intrinsic distortion measures. Overall, we arrive at an iterative scheme where at each step we optimize for the map and its inverse by solving two relaxed Quadratic Assignment Problems using off‐the‐shelf optimization tools. We provide quantitative and qualitative comparison of our method with several existing techniques, and show that it provides a powerful matching tool when accurate and consistent correspondences are required.

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Section: Related Workmentioning

confidence: 99%

Consistent Shape Matching via Coupled Optimization

Azencot

Dubrovina

Guibas

2019

Computer Graphics Forum

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“…The simplest way to choose these points is by using the Farthest Point Sampling technique [11], and the sampling density will determine the accuracy of the matching. In order to overcome these limitations we use the hierarchical matching technique introduced in [29]. It exploits the shapes' geometric structures to reduce the number of potential correspondences, and thus is able to find a denser matching, Fig.…”

Section: Hierarchical Matchingmentioning

confidence: 99%

Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures

Dubrovina

Raviv

Kimmel

2012

Mathematics and Visualization

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Finding a correspondence between two non-rigid shapes is one of the cornerstone problems in the field of three-dimensional shape processing. We describe a framework for marker-less non-rigid shape correspondence, based on matching intrinsic invariant surface descriptors, and the metric structures of the shapes. The matching task is formulated as a quadratic optimization problem that can be used with any type of descriptors and metric. We minimize it using a hierarchical matching algorithm, to obtain a set of accurate correspondences. Further, we present the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. We show that when using isometry invariant surface descriptors based on eigendecomposition of the Laplace-Beltrami operator, it is possible to construct distinctive sets of surface descriptors for different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore a number of possible correspondences between two given shapes.

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“…For instance, the eigenvalues of the Laplace-Beltrami operator on the surfaces are computed to measure the shape distances [38, 46, 29, 13]. Researchers in [45] use the Gromov-Hausdorff distance for non-rigid almost isometric shapes. In addition, the mass transport distance and the LDDMM metric have also been used [39, 40, 3].…”

Section: Introductionmentioning

confidence: 99%

Statistical shape analysis using 3D Poisson equation—A quantitatively validated approach

Gao

Bouix

2016

Medical Image Analysis

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Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures.

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Hierarchical Matching of Non-rigid Shapes

Cited by 16 publications

References 33 publications

Consistent Shape Matching via Coupled Optimization

Consistent Shape Matching via Coupled Optimization

Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures

Statistical shape analysis using 3D Poisson equation—A quantitatively validated approach

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