Skeletonization Algorithms With Theoretical Guarantees for Point Clouds

Explore skeletonization algorithms with theoretical guarantees for point clouds in this comprehensive lecture. Delve into the problem of approximating unorganized point clouds in Euclidean or metric spaces using 1-dimensional graphs or skeletons. Learn about three recent algorithms: the 1-dimensional Mapper, alpha-Reeb graphs, and Homologically Persistent Skeleton. Understand their theoretical guarantees and see them applied to simple examples. Compare these algorithms experimentally using synthetic data, including random point samples around planar graphs and edge pixel sets from the Berkeley Segmentation Database BSD500. Evaluate the algorithms based on running time and homotopy type of reconstructed graphs. Gain insights from the joint work of Vitaliy Kurlin and PhD student Phil Smith in this hour-long presentation from the Applied Algebraic Topology Network.