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Abstract: A new algorithm for manifold learning is presented. Given only samples of a finite-dimensional differentiable manifold, and no a priori knowledge of the manifold's geometry or topology except for its dimension, the goal is to find a description of the manifold. The learned manifold must approximate the true manifold well, both geometrically and topologically, when the sampling density is sufficiently high. The proposed algorithm constructs a simplicial complex based on approximations to the... (Update)
Context of citations to this paper: More
...of the signed distance function to the surface. The zero set of this distance function is extracted using the marching cubes algorithm [11]. Other algorithms [8, 9, 13] use a greedy approach. The ball pivoting algorithm [9] rolls a ball over the sample points; it...
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BibTeX entry: (Update)
D. Freedman. Efficient simplicial reconstruction of manifolds from their samples. IEEE Transaction on Pattern Analysis and Machine Intelligence 24(10):1349--1357, 2002. http://citeseer.ist.psu.edu/article/freedman02efficient.html More
@misc{ freedman02efficient,
author = "D. Freedman",
title = "Efficient simplicial reconstruction of manifolds from their samples",
text = "D. Freedman. Efficient simplicial reconstruction of manifolds from their
samples. IEEE Transaction on Pattern Analysis and Machine Intelligence 24(10):1349--1357,
2002.",
year = "2002",
url = "citeseer.ist.psu.edu/article/freedman02efficient.html" }
Citations (may not include all citations):1386 Snakes: active contour models (context) - Kass, Witkin et al. - 1987
364 Condensation - conditional density propagation for visual tr.. - Blake, Isard - 1998
102 Icondensation: unifying low-level and high-level tracking in.. - Isard, Blake - 1998 DBLP
55 Surface reconstruction by voronoi filtering - Amenta, Bern ACM DBLP
8 Provably fast algorithms for contour tracking - Freedman, Brandstein - 2000 DBLP
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