Inferring local homology from sampled stratified spaces

P. Bendich, D. Cohen Steiner, H. Edelsbrunner, J. Harer, D. Morozov, in:, IEEE, 2007, pp. 536–546.

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Abstract
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 I-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.
Publishing Year
Date Published
2007-01-01
Page
536 - 546
Conference
FOCS: Foundations of Computer Science
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Bendich P, Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. Inferring local homology from sampled stratified spaces. In: IEEE; 2007:536-546. doi:10.1109/FOCS.2007.33
Bendich, P., Cohen Steiner, D., Edelsbrunner, H., Harer, J., & Morozov, D. (2007). Inferring local homology from sampled stratified spaces (pp. 536–546). Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/FOCS.2007.33
Bendich, Paul, David Cohen Steiner, Herbert Edelsbrunner, John Harer, and Dmitriy Morozov. “Inferring Local Homology from Sampled Stratified Spaces,” 536–46. IEEE, 2007. https://doi.org/10.1109/FOCS.2007.33.
P. Bendich, D. Cohen Steiner, H. Edelsbrunner, J. Harer, and D. Morozov, “Inferring local homology from sampled stratified spaces,” presented at the FOCS: Foundations of Computer Science, 2007, pp. 536–546.
Bendich P, Cohen Steiner D, Edelsbrunner H, Harer J, Morozov D. 2007. Inferring local homology from sampled stratified spaces. FOCS: Foundations of Computer Science 536–546.
Bendich, Paul, et al. Inferring Local Homology from Sampled Stratified Spaces. IEEE, 2007, pp. 536–46, doi:10.1109/FOCS.2007.33.

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