Extracting Manifold Information from Point Clouds

arXiv:2404.00427v1 Announce Type: new
Abstract: A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and include bounded smooth manifolds of any codimension. The interpolation and analysis of point clouds are the main application. Two extreme cases in terms of regularity are considered, where the data set is interpolated by an analytic surface, at the …

abstract analysis and analysis arxiv construction cs.cg cs.cv cs.na functions information kernel manifold math.na subsets type