Consistent multiple graph matching with multi-layer random walks synchronization

Abstract

We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified framework. The main contribution of this paper is twofold. First, we formulate the global correspondence search problem of multi-attributed graphs by utilizing a set of multi-layer structures. The proposed formulation describes each pair of graphs as a multi-layer structure, and jointly considers whole matching pairs. Second, we propose a robust multiple graph matching method based on the multi-layer random walks framework. The proposed framework synchronizes movements of random walkers, and leads them to consistent matching candidates. In our extensive experiments, the proposed method exhibits robust and accurate performance over the state-of-the-art multiple graph matching algorithms.

Probabilistic Permutation Synchronization Using the Riemannian Structure of the Birkhoff Polytope

“…Bernard et al [7] used an NMF-based approach to generate a cycle-consistent synchronization. Park and Yoon [65] used multi-layer random walks framework to address the global correspondence search problem of multiattributed graphs. Starting from a multi-layer random-walks initialization, the authors proposed a robust solver by iterative reweighting.…”

A Convex Relaxation for Multi-Graph Matching

“…The work [38] proposes a smooth nonconvex rankconstrained formulation of the multi-matching problem and utilize block coordinate descent on the resulting problem. Other approaches include extensions of random walk based methods [29], factorized graph matching [49] or matrix factorization [45]. The authors of [43] propose to alternatingly use existing graph matching solvers such that ultimately cycle consistency is achieved.…”

HiPPI: Higher-Order Projected Power Iterations for Scalable Multi-Matching

“…In order to reduce computational costs due to the lifting of the permutation matrices, the authors in [6] propose a lifting-free SDP relaxation for multi-graph matching. In [37], the authors propose a random walk technique for multi-layered multi-graph matching. While there is a wide range of algorithmic approaches for multi-graph matching, the aforementioned approaches have in common that they are computationally expensive and are only applicable to small-scale problems, where the total number of points does not significantly exceed a thousand (e.g.…”