Date: 12 February 2025
Time: 12.45 Hours
Room: RA1501
Speaker: Dr Gautam Pai (MDS/MCS-MIA)
Title: "Computational Optimal Transport on Geometric Domains"
Abstract:
Optimal Transport (OT) provides a principled and versatile framework to compare, interpolate and transform probability measures defined on very general spaces including Riemannian manifolds. In recent years, the development of efficient numerical approaches has enabled many diverse applications of OT notably in image processing, computer graphics, and machine learning. In this talk, I will outline two geometric setups: spectral embeddings of 3D shapes and the Lie-group SE(2). We apply the Entropic regularized formulation of OT and leverage efficient local approximations of geodesic distances and kernels on the underlying manifold. We demonstrate the efficiency and effectiveness of OT in challenging problems like non-rigid 3D shape correspondence and roto-translation equivariant interpolation of contours in images. Beyond these applications, I will highlight some strong connections with geometric deep learning leading to promising directions combining OT for generative modelling on geometric domains.