Finding Matches in a Haystack: A Max-Pooling Strategy for Graph Matching in the Presence of Outliers

Abstract

A major challenge in real-world feature matching problems is to tolerate the numerous outliers arising in typical visual tasks. Variations in object appearance, shape, and structure within the same object class make it harder to distinguish inliers from outliers due to clutters. In this paper, we propose a max-pooling approach to graph matching, which is not only resilient to deformations but also remarkably tolerant to outliers. The proposed algorithm evaluates each candidate match using its most promising neighbors, and gradually propagates the corresponding scores to update the neighbors. As final output, it assigns a reliable score to each match together with its supporting neighbors, thus providing contextual information for further verification. We demonstrate the robustness and utility of our method with synthetic and real image experiments.

A flexible tensor block coordinate ascent scheme for hypergraph matching

“…In particular, we use the following third order approaches: Tensor Matching (TM) [10], Hypergraph Matching via Reweighted Random Walks (RRWHM) [16], Hypergraph Matching (HGM) [26]. For second order approaches, Max Pooling Matching (MPM) [8], Reweighted Random Walks for Graph Matching (RRWM) [6], Integer Projected Fixed Point (IPFP) [19], and Spectral Matching (SM) [17] are used. We denote our tensor block coordinate ascent methods as BCAGM from Algorithm 1 which uses the Hungarian algorithm as subroutine, and BCAGM+MP and BCAGM+IPFP from Algorithm 2 which uses MPM [8] and IPFP [19] respectively as subroutine.…”

“…For second order approaches, Max Pooling Matching (MPM) [8], Reweighted Random Walks for Graph Matching (RRWM) [6], Integer Projected Fixed Point (IPFP) [19], and Spectral Matching (SM) [17] are used. We denote our tensor block coordinate ascent methods as BCAGM from Algorithm 1 which uses the Hungarian algorithm as subroutine, and BCAGM+MP and BCAGM+IPFP from Algorithm 2 which uses MPM [8] and IPFP [19] respectively as subroutine. MPM has recently outperformed other second order methods in the presence of a large number of outliers without deformation.…”

“…We follow the approach in [8] for the creation of the point sets. That is, for P we sample n in inlier points from a Gaussian distribution N (0, 1).…”

“…Lee et al [15] tackle the graph matching problem using stochastic sampling, whereas Cho et al [6] propose a reweighted random walk (RRWM) where the reweighting jumps are aiming at enforcing the matching constraints. Recently, Cho et al [8] proposed a novel max pooling matching (MPM), where they tweak the power method to better cope with noise in the affinities. Although the algorithm comes without theoretical guarantees, it turns out to perform very well in practice, in particular, when one has a large number of outliers.…”

Graduated Consistency-Regularized Optimization for Multi-graph Matching

“…Optimization Methods: Most approaches first formulate an objective function, and then employ certain optimization methods to derive optimal solutions [21,29,42], which vary among a wide spectrum of optimization strategies [11]. Some recent work first relax the objective function to convex-concave formulation [52,49].…”