A geometric variational framework for computing optimal transportation maps. I (Q2171720)

To solve the semi-discrete optimal transportation (OT) problem the geometric variational method was proposed in [\textit{Z. Su}, ``Optimal mass transport for shape matching and comparison'', IEEE Trans. Pattern Anal. Mach. Intell. 37, 2246--2259 (2015; \url{doi:10.1109/TPAMI.2015.2408346})]. The authors improve the computational efficiency of this algorithm by incorporating several ideas from computational geometry. Moreover, within the same framework, the authors study the worst transportation (WT) problem as well and discover the intrinsic symmetry between the OT and WT map. The authors illustrate their results with numerical experiments.