An efficient numerical method for the solution of the L₂optimal mass transfer problem

Abstract

In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L₂mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.