Skip to main content
eScholarship
Open Access Publications from the University of California

Vector-valued optimal mass transport

  • Author(s): Chen, Y
  • Georgiou, TT
  • Tannenbaum, A
  • et al.
Abstract

© 2018 Society for Industrial and Applied Mathematics. We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may ow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to define an appropriate notion of optimal transport on a graph. The corresponding distance between distributions is readily computable via convex optimization and provides a suitable generalization of Wasserstein-type metrics. Building on this, we define Wasserstein-type metrics on vector-valued distributions supported on continuous spaces as well as graphs. Motivation for developing vector-valued mass transport is provided by applications such as color image processing, multimodality imaging, polarimetric radar, as well as network problems where resources may be vectorial.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View