  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.
