Mass transport problem and its application in imaging registration

Abstract

The quadratic Wasserstein distance is an important distance and it amazingly arises in various applications. In this talk, we will study its application in? imaging registration. In this talk, we present a new registration method for solving point set matching problems based on mass transport, i.e., minimizing quadratic Wasserstein distance.Roughly speaking, the method utilizes a global affine transform and a local curl-free transform. The affine transform is estimated by the first two moments of point sets, which is equivalent to the asymptotic transform in the kernel correlation method as the kernel scale approaches infinity. The curl-free transform is achieved by optimizing some kernel correlation function weighted by a square root of a pair of correspondence matrices.The use of the square root structure is motivated by one pioneering work of L. Younes (SIAM 1998). In application, we employ this method to match two sets of pulmonary vascular tree branch points whose displacement is caused by the lung volume changes of the same human subject. Nearly perfect match performances on six human subjects verdict the effectiveness of this model.This is a joint work with Ching-Long Lin and I-Liang Chern.