Graph matching based on fast normalized cut and multiplicative update mapping

• Published in: Pattern recognition Vol. 122; p. 108228
• Main Authors: Yang, Jing, Yang, Xu, Zhou, Zhang-Bing, Liu, Zhi-Yong
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2022; Elsevier
• Subjects: Computer Science; Discrete constraint; Fast normalized cut; Graph matching; Multiplicative update; Discrete constraint; Multiplicative update; Fast normalized cut; Graph matching; Optimizing; NP Complete; Computer vision; Data mining; Algorithm
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2021.108228

•A graph matching method based on fast normalized cut and multiplicative update mapping is proposed.•The discrete constraint is incorporated into the optimization step and the multiplicative update algorithm is utilized in the mapping process.•Both synthetic points and real-world images comparisons with the state-of-the-art methods validate the effectiveness of the proposed method. Point correspondence is a fundamental problem in pattern recognition and computer vision, which can be tackled by graph matching. Since graph matching is basically an NP-complete problem, some approximate methods are proposed to solve it. Continuous relaxation offers an effective approximate method for graph matching problem. However, the discrete constraint is not taken into consideration in the optimization step. In this paper, a fast normalized cut based graph matching method is proposed, where the discrete constraint is introduced into the optimization step. Specifically, first a semidefinite positive affinity matrix based form objective function is constructed by introducing a regularization term which is related to the discrete constraint. Then the fast normalized cut algorithm is utilized to find the continuous solution. Last, the discrete solution of graph matching is obtained by a multiplicative update algorithm. Experiments on both synthetic points and real-world images validate the effectiveness of the proposed method by comparing it with the state-of-the-art methods.