Alpha divergences based mass transport models for image matching problems

摘要

Registration methods could be roughly divided into two groups: Area-based methods and feature-based methods. In the literature, the Monge- Kantorovich (MK) mass transport problem has been applied to image registration as an area-based method. In this paper, we propose to use Monge- Kantorovich (MK) mass transport model as a feature-based method. This novel image matching model is a coupling of the MK problem with the wellknown alpha divergence from the probability theory. The optimal matching scheme is the one which minimizes the weighted alpha divergence between two images. A primal-dual approach is employed to analyze the existence and uniquenesson-uniqueness of the optimal matching scheme. A block coordinate method, analogous to the Sinkhorn matrix balancing method, 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, the geodesic under this distance function has an explicit expression.