Mathematics, Computation and Geometry of Data
Volume 1 (2021)
A geometric variational framework for computing optimal transportation maps, I
Pages: 207 – 253
Optimal transportation (OT) maps play fundamental roles in many engineering and medical fields. The computation of optimal transportation maps can be reduced to solve highly non-linear Monge–Ampère equations. In this work, we summarize the geometric variational framework to solve optimal transportation maps in Euclidean spaces.We generalize the method to solve worst transportation maps and discuss about the symmetry between the optimal and the worst transportation maps. Many algorithms from computational geometry are incorporated into the method to improve the efficiency, the accuracy and the robustness of computing optimal transportation.
Received 5 March 2021
Published 2 August 2022