An Efficient Multilinear Optimization Framework for Hypergraph Matching

TL;DR

This paper presents a faster third-order multilinear optimization framework for hypergraph matching in computer vision, improving efficiency while maintaining state-of-the-art accuracy through a novel homotopy method.

Contribution

It introduces a third-order scheme that avoids lifting to fourth-order, doubling speed, and incorporates a homotopy method for further performance enhancement.

Findings

Achieves state-of-the-art matching accuracy

Doubles the speed compared to previous methods

Provides a monotonic ascent guarantee in optimization

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.