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Explore the Extended Persistent Homology Transform (XPHT) for manifolds with boundary in this 59-minute conference talk by Vanessa Robins. Delve into the evolution of topological transforms, from the Persistent Homology Transform (PHT) to the XPHT, and understand their applications in shape analysis. Learn how the XPHT overcomes limitations of the PHT by providing finite distances between shapes with different Betti numbers. Discover the computational efficiency of deriving XPHT from PHT for compact manifolds with boundary. Gain insights into the implementation of these algorithms for 2-dimensional binary images and their potential applications in shape clustering. Follow the presentation's structure, covering the background, motivation, persistence modules for relative homology, extended persistence modules, Wasserstein distance for extended persistence, and practical examples using letter shape variations.
