Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.mssvm12
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 1 : pp. 223–244
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Deformable shapes partial matching partial correspondence partial similarity diffusion geometry Laplace-Beltrami operator shape descriptors heat kernel signature Mumford-Shah regularization.