This paper studies the universal approximation property of deep neural networks for
representing probability distributions. Given a target distribution $\pi $ and a source …

Scene segmentation is widely used in autonomous driving for environmental perception.
Semantic scene segmentation (3S) has gained considerable attention owing to its rich …

This work introduces an optimal transportation (OT) view of generative adversarial networks
(GANs). Natural datasets have intrinsic patterns, which can be summarized as the manifold …

Optimal mass transport (OMT) theory, the goal of which is to move any irregular 3D object
(ie, the brain) without causing significant distortion, is used to preprocess brain tumor …

In this work, we give a geometric interpretation to the Generative Adversarial Networks
(GANs). The geometric view is based on the intrinsic relation between Optimal Mass …

This paper introduces a numerical algorithm to compute the L2 optimal transport map
between two measures μ and ν, where μ derives from a density ρ defined as a piecewise …

We introduce a novel method for computing the earth mover's distance (EMD) between
probability distributions on a discrete surface. Rather than using a large linear program with …

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 …

This article gives an introduction to optimal transport, a mathematical theory that makes it
possible to measure distances between functions (or distances between more general …

This chapter describes techniques for the numerical resolution of optimal transport
problems. We will consider several discretizations of these problems, and we will put a …