This paper introduces a new class of algorithms for optimization problems involving optimal
transportation over geometric domains. Our main contribution is to show that optimal …

Surfaces serve as a natural parametrization to 3D shapes. Learning surfaces using
convolutional neural networks (CNNs) is a challenging task. Current paradigms to tackle this …

Optimal transport is a long‐standing theory that has been studied in depth from both
theoretical and numerical point of views. Starting from the 50s this theory has also found a …

We review the computation of 3D geometric data mapping, which establishes one-to-one
correspondence between or among spatial/spatiotemporal objects. Effective mapping …

Surface based 3D shape analysis plays a fundamental role in computer vision and medical
imaging. This work proposes to use optimal mass transport map for shape matching and …

In this paper, we develop several related finite dimensional variational principles for discrete
optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge …

Surface parameterization is of fundamental importance for many tasks in computer vision
and imaging. In recent years, computational quasi-conformal geometry has become an …

This article presents a new method to optimally partition a geometric domain with capacity
constraints on the partitioned regions. It is an important problem in many fields, ranging from …

We show that the discrete Sinkhorn algorithm—as applied in the setting of Optimal Transport
on a compact manifold—converges to the solution of a fully non-linear parabolic PDE of …

Surface parameterizations have been widely used in computer graphics and geometry
processing. In particular, as simply-connected open surfaces are conformally equivalent to …