Inferring Local Homology from Sampled Stratified Spaces

Providence, Rhode Island October 21-October 23

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http://doi.ieeecomputersociety.org/10.1109/FOCS.2007.45

48th Annual IEEE Symposium on Foundat ...

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	ASCII Text	x
	Paul Bendich, David Cohen-Steiner, Herbert Edelsbrunner, John Harer, Dmitriy Morozov, "Inferring Local Homology from Sampled Stratified Spaces," Foundations of Computer Science, Annual IEEE Symposium on, pp. 536-546, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), 2007.

	BibTex	x
	@article{ 10.1109/FOCS.2007.45, author = {Paul Bendich and David Cohen-Steiner and Herbert Edelsbrunner and John Harer and Dmitriy Morozov}, title = {Inferring Local Homology from Sampled Stratified Spaces}, journal ={Foundations of Computer Science, Annual IEEE Symposium on}, volume = {0}, year = {2007}, issn = {0272-5428}, pages = {536-546}, doi = {http://doi.ieeecomputersociety.org/10.1109/FOCS.2007.45}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Foundations of Computer Science, Annual IEEE Symposium on TI - Inferring Local Homology from Sampled Stratified Spaces SN - 0272-5428 SP536 EP546 A1 - Paul Bendich, A1 - David Cohen-Steiner, A1 - Herbert Edelsbrunner, A1 - John Harer, A1 - Dmitriy Morozov, PY - 2007 KW - Topological data analysis KW - local homology KW - persistence KW - stratified spaces KW - simplicial complexes KW - power diagrams KW - Delaunay triangulations KW - algorithms. VL - 0 JA - Foundations of Computer Science, Annual IEEE Symposium on ER -

We study the reconstruction of a stratified space from a possibly noisy point sample. Specifically, we use the vineyard of the distance function restricted to a 1-parameter family of neighborhoods of a point to assess the local homology of the stratified space at that point. We prove the correctness of this assessment under the assumption of a sufficiently dense sample. We also give an algorithm that constructs the vineyard and makes the local assessment in time at most cubic in the size of the Delaunay triangulation of the point sample.

Index Terms:

Topological data analysis, local homology, persistence, stratified spaces, simplicial complexes, power diagrams, Delaunay triangulations, algorithms.

Citation:

Paul Bendich, David Cohen-Steiner, Herbert Edelsbrunner, John Harer, Dmitriy Morozov, "Inferring Local Homology from Sampled Stratified Spaces," focs, pp.536-546, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), 2007

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