Vector-valued optimal mass transport
- Author(s): Chen, Y
- Georgiou, TT
- Tannenbaum, A
- et al.
Published Web Locationhttps://doi.org/10.1137/17M1130897
© 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.