Optimal Transport on the Lie Group of Roto-translations

arXiv:2402.15322v1 Announce Type: new
Abstract: The roto-translation group SE2 has been of active interest in image analysis due to methods that lift the image data to multi-orientation representations defined on this Lie group. This has led to impactful applications of crossing-preserving flows for image de-noising, geodesic tracking, and roto-translation equivariant deep learning. In this paper, we develop a computational framework for optimal transportation over Lie groups, with a special focus on SE2. We make several theoretical contributions (generalizable to matrix …

abstract analysis applications arxiv cs.cv data deep learning image image data math.dg math.oc tracking translation transport type