The robustness of level sets
Publication
, Journal Article
Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A
Published in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
November 19, 2010
We define the robustness of a level set homology class of a function f : double-struck X → ℝ as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case double-struck X = ℝ3 has ramifications in medical imaging and scientific visualization. © 2010 Springer-Verlag.
Duke Scholars
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
November 19, 2010
Volume
6346 LNCS
Issue
PART 1
Start / End Page
1 / 10
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences
Citation
APA
Chicago
ICMJE
MLA
NLM
Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2010). The robustness of level sets. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6346 LNCS(PART 1), 1–10. https://doi.org/10.1007/978-3-642-15775-2_1
Bendich, P., H. Edelsbrunner, D. Morozov, and A. Patel. “The robustness of level sets.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 6346 LNCS, no. PART 1 (November 19, 2010): 1–10. https://doi.org/10.1007/978-3-642-15775-2_1.
Bendich P, Edelsbrunner H, Morozov D, Patel A. The robustness of level sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2010 Nov 19;6346 LNCS(PART 1):1–10.
Bendich, P., et al. “The robustness of level sets.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6346 LNCS, no. PART 1, Nov. 2010, pp. 1–10. Scopus, doi:10.1007/978-3-642-15775-2_1.
Bendich P, Edelsbrunner H, Morozov D, Patel A. The robustness of level sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2010 Nov 19;6346 LNCS(PART 1):1–10.
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
November 19, 2010
Volume
6346 LNCS
Issue
PART 1
Start / End Page
1 / 10
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences