Approximating Loops in a Shortest Homology Basis from Point Data

@inproceedings{Dey2010ApproximatingLI,
  title={Approximating Loops in a Shortest Homology Basis from Point Data},
  author={Tamal K. Dey and Jian Sun and Yusu Wang},
  booktitle={Symposium on Computational Geometry},
  year={2010}
}
Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper we present an algorithm to compute a set of loops from a point data that presumably sample a smooth manifold <i>M</i> ⊂ <b>R</b><sup><i>d</i></sup>. These loops approximate a <i>shortest</i> basis of the one dimensional homology group H<sub>1</sub>(<i>M</i>) over coefficients in finite field <b>Z</b… CONTINUE READING
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