On the computation of optimal transport maps using gradient flows and multiresolution analysis

Abstract

The optimal mass transport methodology has numerous applications in econometrics, fluid dynamics, automatic control, statistical physics, shape optimization, expert systems, and meteorology. Further, it leads to some beautiful mathematical problems. Motivated by certain issues in image registration, visual tracking and medical image visualization, we outline in this note a straightforward gradient descent approach for computing the optimal L 2 optimal transport mapping which may be easily implemented using a multiresolution scheme. We discuss the well-posedness of our scheme, and indicate how the optimal transport map may be computed on the sphere. © 2008 Springer London.