title: An Efficient Multilinear Optimization Framework for Hypergraph Matching.
abstract: Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows the use of higher-order geometric information. Hypergraph matching can be formulated as a third-order optimization problem subject to 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.
authors.forename: Quynh
authors.initials: Q
authors.lastname: Nguyen
authors.forename: Francesco
authors.initials: F
authors.lastname: Tudisco
authors.forename: Antoine
authors.initials: A
authors.lastname: Gautier
authors.forename: Matthias
authors.initials: M
authors.lastname: Hein