Reconstructing Manifolds by Weighted L_1-Norm Minimization

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).