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Issue No. 12 - December (2010 vol. 32)
ISSN: 0162-8828
pp: 2205-2215
Michael Chertok , Bar-Ilan University, Ramat Gan
Yosi Keller , Bar-Ilan University, Ramat Gan
We present a computational approach to high-order matching of data sets in {{\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}}^{d}. Those are matchings based on data affinity measures that score the matching of more than two pairs of points at a time. High-order affinities are represented by tensors and the matching is then given by a rank-one approximation of the affinity tensor and a corresponding discretization. Our approach is rigorously justified by extending Zass and Shashua's hypergraph matching [CHECK END OF SENTENCE] to high-order spectral matching. This paves the way for a computationally efficient dual-marginalization spectral matching scheme. We also show that, based on the spectral properties of random matrices, affinity tensors can be randomly sparsified while retaining the matching accuracy. Our contributions are experimentally validated by applying them to synthetic as well as real data sets.
High-order assignment, probabilistic matching, spectral relaxation.

M. Chertok and Y. Keller, "Efficient High Order Matching," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 2205-2215, 2010.
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