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Explore the latest advancements in computational optimal transport through this 56-minute lecture by Jean Feydy at Institut Henri Poincaré. Delve into the fundamental tool for handling discrete and continuous point distributions, understanding it as a generalization of sorting to higher dimensions or as a nearest neighbor projection with incompressibility constraints. Discover how recent numerical innovations have dramatically accelerated transport-related computations, enabling millisecond-level Earth Mover's Distance and Wasserstein barycenter calculations for 3D volumes and surfaces. Learn about mature libraries and software tools available as of 2022, examine new applications in 3D shape analysis focusing on population analysis and shape registration, and identify open problems awaiting expert solutions. Gain valuable insights into the current state-of-the-art and potential future directions in geometric data analysis, machine learning, and computer graphics.
