IEEE Trans Cybern. 2018 Feb;48(2):765-779. doi: 10.1109/TCYB.2017.2655538. Epub 2017 Feb 17.
This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.
本文针对使用高阶亲和力信息的超图匹配问题提出了一种求解器。该求解器通过线性分配逼近在离散域中迭代更新解。所提出的方法保证收敛到一个稳定的离散解，并且避免了几个先前方法所需的退火过程和特殊的后二值化步骤。具体来说，我们从一个简单的迭代离散梯度分配求解器开始。在中等条件下，这个求解器可能会陷入一个 -循环序列中，其中是图匹配问题的阶数。然后，我们设计了一个自适应松弛机制来跳出这种退化情况，并证明得到的新路径将收敛到离散域中的固定解。我们的方法在合成和真实基准上进行了测试。实验结果证实了我们方法的有效性。
