Volume 6, Issue 1
Hierarchical Framework for Shape Correspondence

Dan Raviv, Anastasia Dubrovina & Ron Kimmel

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 245-261.

Published online: 2013-06

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  • Abstract

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment is not easily parameterized. Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds. Here we model the shapes using both local and global structures, employ these to construct a quadratic dissimilarity measure, and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding points. These correspondences may serve as an initialization for dense linear correspondence search.

  • Keywords

Shape correspondence, Laplace-Beltrami, diffusion geometry, local signatures

  • AMS Subject Headings

65M50, 65M60, 68T45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-245, author = {}, title = {Hierarchical Framework for Shape Correspondence}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {245--261}, abstract = {

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment is not easily parameterized. Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds. Here we model the shapes using both local and global structures, employ these to construct a quadratic dissimilarity measure, and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding points. These correspondences may serve as an initialization for dense linear correspondence search.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm13}, url = {http://global-sci.org/intro/article_detail/nmtma/5902.html} }
TY - JOUR T1 - Hierarchical Framework for Shape Correspondence JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 245 EP - 261 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm13 UR - https://global-sci.org/intro/article_detail/nmtma/5902.html KW - Shape correspondence, Laplace-Beltrami, diffusion geometry, local signatures AB -

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. In order to measure the similarity the shapes must first be aligned. As opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment is not easily parameterized. Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds. Here we model the shapes using both local and global structures, employ these to construct a quadratic dissimilarity measure, and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding points. These correspondences may serve as an initialization for dense linear correspondence search.

Dan Raviv, Anastasia Dubrovina & Ron Kimmel. (2020). Hierarchical Framework for Shape Correspondence. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 245-261. doi:10.4208/nmtma.2013.mssvm13
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