Manifolds defined by points: Parameterizing and boundary detection (extended abstract)

Abstract

We are given a set of noisy points in n-dimensional (nD) Euclidean space (the native space) which lie on a finite dD manifold. We assume that it can be smoothly mapped to a dD Euclidean space without holes, and would like to create a dD parameterization of the manifold. We also want to identify points that are close to the manifold boundary. Parameterizing the manifold is important for a number of follow-on tasks. Our objective is to develop a method that can be used as the basis for a robust code that requires no human intervention.