TPAMI! We Made It!

Jie Shi, Yalin Wang

Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence

This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces.