Optimal transport for manifold-valued images

Abstract

We introduce optimal transport-type distances for manifold valued images. To do so we lift the initial data to measures on the product space of image domain and signal space, where they can then be compared by optimal transport with a transport cost that combines spatial distance and signal discrepancy. Applying recently introduced ‘unbalanced’ optimal transport models leads to more natural results. We illustrate the benefit of the lifting with numerical examples for interpolation of color images and classification of handwritten digits.