Reconstructing Manifolds by Weighted L_1-Norm Minimization
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
Explore a novel approach to shape reconstruction in this 51-minute lecture from the Applied Algebraic Topology Network. Delve into the challenge of constructing triangulations for shapes known only through finite data points, with a focus on orientable smooth d-manifolds embedded in RN. Learn how the problem of finding a triangulation can be reformulated as a convex minimization problem using a weighted l1-norm. Discover the conditions under which this minimization solution yields a valid triangulation of the manifold, coinciding with a variant of the tangential Delaunay complex. Gain insights into the collaborative research of Dominique Attali and André Lieutier, including their work presented at the 38th International Symposium on Computational Geometry (SoCG'22).
Syllabus
Dominique Attali (7/21/23): Reconstructing manifolds by weighted l_1-norm minimization
Taught by
Applied Algebraic Topology Network
Related Courses
From Reinforcement Learning to Spin Glasses - The Many Surprises in Quantum State PreparationAPS Physics via YouTube Mathematical Frameworks for Signal and Image Analysis - Diffusion Methods in Manifold and Fibre Bundle Learning
Joint Mathematics Meetings via YouTube Quantifying the Topology of Coma
Institute for Pure & Applied Mathematics (IPAM) via YouTube Demystifying Latschev's Theorem for Manifold Reconstruction
Applied Algebraic Topology Network via YouTube Low Distortion Embeddings With Bottom-up Manifold Learning
IEEE Signal Processing Society via YouTube