Earlier Version

Homology and robustness of level and interlevel sets

P. Bendich, D. Morozov, A. Patel, H. Edelsbrunner, Homology and Robustness of Level and Interlevel Sets, ArXiv, 2011.

Report | Published | English
Department
Abstract
Given a function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the ex- tended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups. After characterizing these groups, we show how to read their ranks from the same extended persistence diagram. The special case X = R3 has ramifications in the fields of medical imaging and scientific visualization.
Publishing Year
Date Published
2011-02-16
Volume
abs/1102.3389
IST-REx-ID

Cite this

Bendich P, Morozov D, Patel A, Edelsbrunner H. Homology and Robustness of Level and Interlevel Sets. Vol abs/1102.3389. ArXiv; 2011.
Bendich, P., Morozov, D., Patel, A., & Edelsbrunner, H. (2011). Homology and robustness of level and interlevel sets (Vol. abs/1102.3389). ArXiv.
Bendich, Paul, Dmitriy Morozov, Amit Patel, and Herbert Edelsbrunner. Homology and Robustness of Level and Interlevel Sets. Vol. abs/1102.3389. ArXiv, 2011.
P. Bendich, D. Morozov, A. Patel, and H. Edelsbrunner, Homology and robustness of level and interlevel sets, vol. abs/1102.3389. ArXiv, 2011.
Bendich P, Morozov D, Patel A, Edelsbrunner H. 2011. Homology and robustness of level and interlevel sets, ArXiv,p.
Bendich, Paul, et al. Homology and Robustness of Level and Interlevel Sets. Vol. abs/1102.3389, ArXiv, 2011.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1102.3389

Search this title in

Google Scholar