TY - GEN
T1 - A correspondence-less approach to matching of deformable shapes
AU - Pokrass, Jonathan
AU - Bronstein, Alexander M.
AU - Bronstein, Michael M.
N1 - Funding Information:
This research has been supported in part by NSF grant DMI0093142. Opinions expressed in this paper are those of authors and do not necessarily reflect opinion of the sponsors.
PY - 2012
Y1 - 2012
N2 - Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric 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 meshes. Experiments demonstrating the success of the proposed method are presented.
AB - Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric 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 meshes. Experiments demonstrating the success of the proposed method are presented.
KW - Laplace-Beltrami operator
KW - Mumford-Shah regularization
KW - deformable shapes
KW - diffusion geometry
KW - heat kernel signature
KW - partial correspondence
KW - partial matching
KW - partial similarity
KW - shape descriptors
UR - http://www.scopus.com/inward/record.url?scp=84855679610&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-24785-9_50
DO - 10.1007/978-3-642-24785-9_50
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AN - SCOPUS:84855679610
SN - 9783642247842
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 592
EP - 603
BT - Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
T2 - 3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Y2 - 29 May 2011 through 2 June 2011
ER -