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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 are compared using a transport cost that combines spatial distance and signal discrepancy. Applying recent ‘unbalanced’ optimal transport models leads to more natural results. We illustrate the benefit of the lifting with examples for interpolation of color images and classification of handwritten digits.
This presentation is part of Minisymposium “MS35 - Optimal Transport and Patch based Methods for Color Image Editing”
organized by: Nicolas Papadakis (CNRS, Institut de Mathématiques de Bordeaux) , Rabin Julien (CNRS, Normandie Univ.) .