A Low-Rank Matrix Approximation Approach to Multiway Matching with Applications in Multi-Sensory Data Association

Abstract

Consider the case of multiple visual sensors perceiving the same scene from different viewpoints. In order to achieve consistent visual perception, the problem of data association, in this case establishing correspondences between observed features, must be first solved. In this work, we consider multiway matching which is a specific instance of multi-sensory data association. Multiway matching refers to the problem of establishing correspondences among a set of images from noisy pairwise correspondences, typically by exploiting cycle- consistency. We propose a novel optimization-based formulation of multiway matching problem as a nonconvex low-rank matrix approximation problem. We propose two novel algorithms for numerically solving the problem at hand. The first one is an algorithm based on the Alternating Direction Method of Multipliers (ADMM). The second one is a Riemannian trust- region method on the multinomial manifold, the manifold of strictly positive stochastic matrices, equipped with the Fisher information metric. Experimental results demonstrate that the proposed methods have the state of the art performance in multiway matching while reducing the computational complexity compared to the state of the art.