基于渐非凸渐凹化过程的子图匹配算法

如何实现外点存在情况下的鲁棒高效匹配是图匹配领域的关键问题之一.针对此问题,提出将渐非凸渐凹化过程(GNCCP)用于子图匹配,即将外点存在情况下的图匹配问题建模为一个基于相似矩阵的二次组合优化问题,然后通过扩展GNCCP来近似优化,是一种新的采用二阶约束图匹配算法.相较于现有算法,提出的算法优势在于可以泛化目标函数定义方式,有效处理外点存在的情况的图匹配问题,且能同时实现有向图匹配和无向图匹配.人工数据与真实数据上的实验证实了算法的有效性. 

Subgraph matching algorithm based on graduated nonconvexity and concavity procedure

To achieve robust and efficient matching with outliers is a fundamental problem in the field of graph matching. To tackle this problem, a novel subgraph matching algorithm was proposed, which was based on the recently proposed graduated nonconvexity and concavity procedure (GNCCP). Specifically speaking, the graph matching problem in the existence of outliers was firstly formulated as a quadratic combinatorial optimization problem based on the affinity matrix, which was then optimized by extending the GNCCP. This is a new second-order constraint graph matching algorithm. Compared with the existing algorithms, there are mainly three benefits for the proposed algorithm, which are as follows. Firstly, it has a flexible objective function formulation; secondly, it is effective in graph matching problems with outliers; thirdly, it is applicable on both directed graphs and undirected graphs. Simulations on both synthetic and real world datasets validate the effectiveness of the proposed method.