Sparse models for intrinsic shape correspondence

Jonathan Pokrass, Alexander M. Bronstein*, Michael M. Bronstein, Pablo Sprechmann, Guillermo Sapiro

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor do we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.

Original languageEnglish
Title of host publicationMathematics and Visualization
PublisherSpringer Heidelberg
Pages211-230
Number of pages20
Edition9783319247243
ISBN (Electronic)9783319247267
ISBN (Print)9783319247243, 9783319912738, 9783540250326, 9783540250760, 9783540332749, 9783540886051, 9783642150135, 9783642216077, 9783642231742, 9783642273421, 9783642341403, 9783642543005
DOIs
StatePublished - 2016
Externally publishedYes

Publication series

NameMathematics and Visualization
Number9783319247243
Volume0
ISSN (Print)1612-3786
ISSN (Electronic)2197-666X

Funding

FundersFunder number
European Research Council335491, 307047
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation
Israel Science Foundation

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