Manifold Reconstruction From Unorganized Points

D. Freedman

Asilomar Conference on Signals, Systems, and Computers, 2000

A new algorithm for manifold reconstruction is presented. The goal is to take samples drawn from a finite-dimensional manifold, and to reconstruct a manifold, based only on the samples, which is a good approximation to the true manifold; nothing of the true manifold’s geometry or topology is known a priori. The algorithm constructs a simplicial complex based on approximating tangent hyperplanes to the manifold, and does so efficiently. Successful examples are presented for curve reconstruction in the plane, curve reconstruction in space, and surface reconstruction in space.