Volume 6, Issue 1
Partial Shape Matching Without Point-Wise Correspondence

Jonathan Pokrass, Alexander M. Bronstein & Michael M. Bronstein

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 223-244.

Published online: 2013-06

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  • Abstract

Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method.

  • Keywords

Deformable shapes, partial matching, partial correspondence, partial similarity, diffusion geometry, Laplace-Beltrami operator, shape descriptors, heat kernel signature, Mumford-Shah regularization.

  • AMS Subject Headings

65D18, 68U05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-223, author = {}, title = {Partial Shape Matching Without Point-Wise Correspondence}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {223--244}, abstract = {

Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm12}, url = {http://global-sci.org/intro/article_detail/nmtma/5901.html} }
TY - JOUR T1 - Partial Shape Matching Without Point-Wise Correspondence JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 223 EP - 244 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm12 UR - https://global-sci.org/intro/article_detail/nmtma/5901.html KW - Deformable shapes, partial matching, partial correspondence, partial similarity, diffusion geometry, Laplace-Beltrami operator, shape descriptors, heat kernel signature, Mumford-Shah regularization. AB -

Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method.

Jonathan Pokrass, Alexander M. Bronstein & Michael M. Bronstein. (2020). Partial Shape Matching Without Point-Wise Correspondence. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 223-244. doi:10.4208/nmtma.2013.mssvm12
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