--- _id: '3849' abstract: - lang: eng text: Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain. alternative_title: - LNCS author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. Persistent homology under non-uniform error. In: Vol 6281. Springer; 2010:12-23. doi:10.1007/978-3-642-15155-2_2' apa: 'Bendich, P., Edelsbrunner, H., Kerber, M., & Patel, A. (2010). Persistent homology under non-uniform error (Vol. 6281, pp. 12–23). Presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic: Springer. https://doi.org/10.1007/978-3-642-15155-2_2' chicago: Bendich, Paul, Herbert Edelsbrunner, Michael Kerber, and Amit Patel. “Persistent Homology under Non-Uniform Error,” 6281:12–23. Springer, 2010. https://doi.org/10.1007/978-3-642-15155-2_2. ieee: 'P. Bendich, H. Edelsbrunner, M. Kerber, and A. Patel, “Persistent homology under non-uniform error,” presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic, 2010, vol. 6281, pp. 12–23.' ista: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. 2010. Persistent homology under non-uniform error. MFCS: Mathematical Foundations of Computer Science, LNCS, vol. 6281, 12–23.' mla: Bendich, Paul, et al. Persistent Homology under Non-Uniform Error. Vol. 6281, Springer, 2010, pp. 12–23, doi:10.1007/978-3-642-15155-2_2. short: P. Bendich, H. Edelsbrunner, M. Kerber, A. Patel, in:, Springer, 2010, pp. 12–23. conference: end_date: 2010-08-27 location: Brno, Czech Republic name: 'MFCS: Mathematical Foundations of Computer Science' start_date: 2010-08-23 date_created: 2018-12-11T12:05:30Z date_published: 2010-08-10T00:00:00Z date_updated: 2021-01-12T07:52:38Z day: '10' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-15155-2_2 file: - access_level: open_access checksum: af61e1c2bb42f3d556179d4692caeb1b content_type: application/pdf creator: system date_created: 2018-12-12T10:13:13Z date_updated: 2020-07-14T12:46:17Z file_id: '4994' file_name: IST-2016-537-v1+1_2010-P-05-NonuniformError.pdf file_size: 142357 relation: main_file file_date_updated: 2020-07-14T12:46:17Z has_accepted_license: '1' intvolume: ' 6281' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 12 - 23 publication_status: published publisher: Springer publist_id: '2333' pubrep_id: '537' quality_controlled: '1' scopus_import: 1 status: public title: Persistent homology under non-uniform error type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6281 year: '2010' ...