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Partial Shape Matching Without Point-Wise Correspondence

Published online by Cambridge University Press:  28 May 2015

Jonathan Pokrass ,
Alexander M. Bronstein  and
Michael M. Bronstein
Jonathan Pokrass*
Affiliation:
School of Electrical Engineering, Tel Aviv University, Israel
Alexander M. Bronstein*
Affiliation:
School of Electrical Engineering, Tel Aviv University, Israel
Michael M. Bronstein*
Affiliation:
Institute of Computational Science, Faculty of Informatics, Università della Svizzera Italiana (USI), Lugano, Switzerland
*
Corresponding author.Email address:evgenyfo@post.tau.ac.il
Corresponding author.Email address:bron@eng.tau.ac.il
Corresponding author.Email address:michael.bronstein@usi.eh
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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

65D1868U05Deformable shapespartial matchingpartial correspondencepartial similaritydiffusion geometry Laplace-Beltrami operatorshape descriptorsheat kernel signatureMumford-Shah regularization
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 223 - 244
Copyright
Copyright © Global Science Press Limited 2013

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