In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the Laplacian family signature (LFS) on the nodes, and the pairwise heat kernel map on the edges. In this paper, without assuming an explicit form of parametric dependence nor a distance metric between node signatures, we formulate an optimization problem which incorporates the knowledge of anchor nodes. Solving this problem gives us an optimized proximity measure specific to the graphs under consideration. Using this as a first order compatibility term, we then set up an integer quadratic program (IQP) to solve for a near optimal graph matching. Our experiments demonstrate the superior performance of our approach on randomly generated graphs and on two widely-used image sequences, when compared with other existing signature and adjacency matrix based graph matching methods.

使用基于图拉普拉斯的节点签名以及边的点对热核映射来构建一种在锚节点已知的情况下，用于权重图匹配的距离度量方法，并使用整数二次规划法确定最优匹配。实验结果表明，该方法在随机生成的图和两个广泛使用的图像序列上具有优异的性能。

使用锚节点的图匹配：一种学习方法