Alpha divergences based mass transport models for image matching problems

Abstract

Registration methods could be roughly divided into two groups:area-based methods and feature-based methods. In the literature, theMonge-Kantorovich (MK) mass transport problem has been applied toimage registration as an area-based method. In this paper, wepropose to use Monge-Kantorovich (MK) mass transportmodel as a feature-based method. This novel image matchingmodel is a coupling of the MK problem withthe well-known alpha divergence from the probability theory.The optimal matching scheme is the one which minimizes theweighted alpha divergence between two images. A primal-dualapproach is employed to analyze the existence anduniqueness/non-uniqueness of the optimal matching scheme. A blockcoordinate method, analogous to the Sinkhorn matrix balancingmethod, can be used to compute the optimal matching scheme.We also derive a distance function for image morphing.Similar to elastic distances proposed by Younes, thegeodesic under this distance function has an explicit expression.