A Tensor-Based Algorithm for High-Order Graph Matching

Olivier Duchenne 1 Francis Bach 1 Kweon In-So 2 Jean Ponce 1
1 WILLOW - Models of visual object recognition and scene understanding
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : 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 multi-dimensional 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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Olivier Duchenne, Francis Bach, Kweon In-So, Jean Ponce. A Tensor-Based Algorithm for High-Order Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2011, 33 (12), pp.2383 - 2395. ⟨10.1109/TPAMI.2011.110⟩. ⟨hal-01063322⟩

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