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A Tensor-Based Algorithm for High-Order Graph Matching
December 2011 (vol. 33 no. 12)
pp. 2383-2395
Olivier Duchenne, École Normale Supérieure de Paris and the Willow project team (CNRS/ENS/INRIA UMR 8548)
Francis Bach, INRIA and the Sierra team, Laboratoire d'Informatique de École Normale Supe´rieure de Paris (CNRS/ENS/INRIA UMR 8548)
In-So Kweon, KAIST, Daejeon
Jean Ponce, École Normale Supérieure de Paris and the Willow project team (CNRS/ENS/INRIA UMR 8548)
This paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods. Concretely, the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features. This function is defined by a tensor representing the affinity between feature tuples. It is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix. The proposed approach has been implemented, and it is compared to state-of-the-art algorithms on both synthetic and real data.

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Index Terms:
Hypergraphs, graph matching, image feature matching.
Citation:
Olivier Duchenne, Francis Bach, In-So Kweon, Jean Ponce, "A Tensor-Based Algorithm for High-Order Graph Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 12, pp. 2383-2395, Dec. 2011, doi:10.1109/TPAMI.2011.110
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