Tight Relaxation of Quadratic Matching

Establishing point correspondences between shapes is extremely challenging as it involves both finding sets of semantically persistent feature points, as well as their combinatorial matching. We focus on the latter and consider the Quadratic Assignment Matching QAM model. We suggest a novel convex relaxation for this NP-hard problem that builds upon a rank-one reformulation of the problem in a higher dimension, followed by relaxation into a semidefinite program SDP. Our method is shown to be a certain hybrid of the popular spectral and doubly-stochastic relaxations of QAM and in particular we prove that it is tighter than both.