An efficient numerical method for the solution of the \(L_2\) optimal mass transfer problem. (English) Zbl 1428.49034

Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen

SIAM J. Sci. Comput. 32, No. 1, 197-211 (2010).

Summary: In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal \(L_2\) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent et al., SIAM J. Math. Anal. 35, No. 1, 61–97 (2003; Zbl 1042.49040)], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.

MSC:

49M37	Numerical methods based on nonlinear programming
90C20	Quadratic programming

Keywords:

optimal mass transport; sequential quadratic programming; variational formulation

Citations:

Zbl 1042.49040