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Hierarchical Framework for Shape Correspondence

Published online by Cambridge University Press:  28 May 2015

Dan Raviv ,
Anastasia Dubrovina  and
Ron Kimmel
Dan Raviv*
Affiliation:
Technion, Israel Institute of Technology, Technion City, Haifa 32000, Israel
Anastasia Dubrovina*
Affiliation:
Technion, Israel Institute of Technology, Technion City, Haifa 32000, Israel
Ron Kimmel*
Affiliation:
Technion, Israel Institute of Technology, Technion City, Haifa 32000, Israel
*
Corresponding author.Email address:darav@cs.technion.ac.il
Corresponding author.Email address:nastyad@tx.technion.ac.il
Corresponding author.Email address:ron@cs.technion.ac.il
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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

65M5065M6068T45Shape correspondenceLaplace-Beltramidiffusion geometry local signatures
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 245 - 261
Copyright
Copyright © Global Science Press Limited 2013

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