Graph matching aims at establishing correspondences between graph elements, and is widely used in many computer vision tasks. Among recently proposed graph matching algorithms, those utilizing the path following strategy have attracted special research attentions due to their exhibition of state-of-the-art performances. However, the paths computed in these algorithms often contain singular points, which could hurt the matching performance if not dealt properly. To deal with this issue, we propose a novel path following strategy, named branching path following (BPF), to improve graph matching accuracy. In particular, we first propose a singular point detector by solving a KKT system, and then design a branch switching method to seek for better paths at singular points. Moreover, to reduce the computational burden of the BPF strategy, an adaptive path estimation (APE) strategy is integrated into BPF to accelerate the convergence of searching along each path. A new graph matching algorithm named ABPF-G is developed by applying APE and BPF to a recently proposed path following algorithm named GNCCP (Liu & Qiao 2014). Experimental results reveal how our approach consistently outperforms state-of-the-art algorithms for graph matching on five public benchmark datasets.

中文翻译：

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具有自适应和分支路径跟踪的图匹配


图匹配旨在建立图元素之间的对应关系，广泛应用于许多计算机视觉任务中。在最近提出的图匹配算法中，那些利用路径跟踪策略的算法由于其表现出最先进的性能而引起了特别的研究关注。然而，这些算法计算的路径通常包含奇异点，如果处理不当，可能会损害匹配性能。为了解决这个问题，我们提出了一种新颖的路径跟踪策略，称为分支路径跟踪（BPF），以提高图匹配的准确性。特别是，我们首先通过求解 KKT 系统提出了一种奇异点检测器，然后设计了一种分支切换方法以在奇异点处寻找更好的路径。此外，为了减少BPF策略的计算负担，将自适应路径估计（APE）策略集成到BPF中以加速沿每条路径的搜索收敛。通过将 APE 和 BPF 应用于最近提出的名为 GNCCP 的路径跟踪算法（Liu & Qiao 2014），开发了一种名为 ABPF-G 的新图匹配算法。实验结果揭示了我们的方法如何在五个公共基准数据集上始终优于最先进的图形匹配算法。