Topological Optimal Transport for Matching Persistent Homology Cycles Across Point Clouds

The core message of this paper is to develop a mathematical framework for optimal transport-based matchings of topological features, by combining topological data analysis and optimal transport theory. The proposed Topological Optimal Transport (TpOT) framework provides a transport model on point clouds that minimises topological distortion while simultaneously yielding a geometrically informed matching between persistent homology cycles.