Second- and High-Order Graph Matching for Correspondence Problems

Abstract

Correspondence problems are challenging due to the complexity of real-world scenes. One way to solve this problem is to improve the graph matching (GM) process, which is flexible for matching non-rigid objects. GM can be classified into three categories that correspond with the variety of object functions: first-order, second-order, and high-order matching. Graph and hypergraph matching have been proposed separately in previous works. The former is equivalent to the second-order GM, and the latter is equivalent to high-order GM, but we use the terms second- and high-order GM to unify the terminology in this paper. Second- and high-order GM fit well with different types of problems; the key goal for these processes is to find better-optimized algorithms. Because the optimal problems for second- and high-order GM are different, we propose two novel optimized algorithms for them in this paper. (1) For the second-order GM, we first introduce a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -nearest-neighbor-pooling matching method that integrates feature pooling into GM and reduces the complexity. Meanwhile, we evaluate each matching candidate using discriminative weights on its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbors by taking locality as well as sparsity into consideration. (2) High-order GM introduces numerous outliers, because precision is rarely considered in related methods. Therefore, we propose a sub-pattern structure to construct a robust high-order GM method that better integrates geometric information. To narrow the search space and solve the optimization problem, a new prior strategy and a cell-algorithm-based Markov Chain Monte Carlo framework are proposed. In addition, experiments demonstrate the robustness and improvements of these algorithms with respect to matching accuracy compared with other state-of-the-art algorithms.