Sub-hypergraph matching based on adjacency tensor

Abstract

Point correspondence problem is an important problem in pattern recognition and computer vision, which can be solved by graph matching. Recently, high order graph matching methods have attracted much attention due to their robustness to geometric transformations. Since high order graph matching usually suffers from high complexity, we previously proposed an adjacency tensor based algorithm, which effectively reduced the complexity of high order graph matching, especially high storage complexity. However, this method can only be applied to equal sized hypergraphs, and it cannot be directly extended to hypergraphs with outliers which are common in real world tasks. Aiming at this problem, in this paper we propose a third order subgraph matching method by extending our previous method to deal with partial point correspondence problem with outliers. Specifically, first a novel objective function focusing on the outlier problem is proposed, by encoding the attributes in a hypergraph with an adjacency tensor, and representing vertex assignments with a partial permutation matrix. Then the objective function is transformed and relaxed to a tractable matrix form and solved by a gradient based optimization algorithm. Consequently, the proposed algorithm can not only tackle the outlier vertices in the hypergraphs, but also involve the same low computational and storage complexities with our previous algorithm. Both synthetic data and real image comparisons with the state-of-the-art methods validate the effectiveness of the proposed method.