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arXiv · 1511.02667

An Efficient Multilinear Optimization Framework for Hypergraph Matching

Quynh Nguyen·Francesco Tudisco·Antoine Gautier·Matthias Hein
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Abstract

Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order optimization problem subject to the assignment constraints which turns out to be NP-hard. In recent work, we have proposed an algorithm for hypergraph matching which first lifts the third-order problem to a fourth-order problem and then solves the fourth-order problem via optimization of the corresponding multilinear form. This leads to a tensor block coordinate ascent scheme which has the guarantee of providing monotonic ascent in the original matching score function and leads to state-of-the-art performance both in terms of achieved matching score and accuracy. In this paper we show that the lifting step to a fourth-order problem can be avoided yielding a third-order scheme with the same guarantees and performance but being two times faster. Moreover, we introduce a homotopy type method which further improves the performance.

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Quynh Nguyen, Francesco Tudisco, Antoine Gautier, Matthias Hein. 2015-11-09. An Efficient Multilinear Optimization Framework for Hypergraph Matching. https://doi.org/10.1109/tpami.2016.2574706

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