Abstract
Graph matching has long been a fundamental problem in artificial intelligence and computer science. Because of the NP-complete nature, approximate methods are necessary for graph matching. As a type of approximate method, the continuous method is widely used in computer-vision-related graph matching tasks, which typically first relaxes the original discrete optimization problem to a continuous one and then projects the continuation solution back to the discrete domain. The continuation scheme usually provides a superior performance in finding a good continuous local solution within reasonable time, but it is limited to only the continuous optimization problem and therefore cannot be directly applied to graph matching. In this paper we propose a continuation scheme based algorithm directly targeting at the graph matching problem. Specifically, we first construct an unconstrained continuous optimization problem of which the objective function incorporates both the original objective function and the discrete constraints, and then the Gaussian smooth based continuation is applied to this problem. Experiments witness the effectiveness of the proposed method.
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Notes
- 1.
It uses convex envelope in the reference, which is the same in principle.
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Acknowledgment
This work is supported partly by the National Natural Science Foundation (NSFC) of China (grants 61503383, 61633009, U1613213, 61627808, 61502494, and U1713201), partly by the National Key Research and Development Plan of China (grant 2016YFC0300801 and 2017YFB1300202), and partly by the Development of Science and Technology of Guangdong Province Special Fund project (grant 2016B090910001).
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Yang, X., Liu, ZY., Qiao, H. (2018). A Continuous Method for Graph Matching Based on Continuation. In: Peng, Y., Yu, K., Lu, J., Jiang, X. (eds) Intelligence Science and Big Data Engineering. IScIDE 2018. Lecture Notes in Computer Science(), vol 11266. Springer, Cham. https://doi.org/10.1007/978-3-030-02698-1_9
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