@InProceedings{freedman:ssc00,
author = {D.\ Freedman},
title = {Manifold reconstruction from unorganized points},
booktitle = {Signals, Systems and Computers, 2000. Conference
Record of the Thirty-Fourth Asilomar Conference on},
year = 2000,
volume = 2,
pages = {1744--1748},
keywords = {approximation theory, image reconstruction, set
theory, algorithm, curve reconstruction, edge set,
finite dimensional manifold, image processing,
manifold approximation, manifold geometry, manifold
reconstruction, manifold topology, samples, surface
reconstruction, tangent hyperplanes approximation,
unorganized points},
abstract = {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},
annote = {}
}