--- res: bibo_abstract: - Given a continuous 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 extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Paul foaf_name: Bendich, Paul foaf_surname: Bendich foaf_workInfoHomepage: http://www.librecat.org/personId=43F6EC54-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Dmitriy foaf_name: Morozov, Dmitriy foaf_surname: Morozov - foaf_Person: foaf_givenName: Amit foaf_name: Patel, Amit foaf_surname: Patel foaf_workInfoHomepage: http://www.librecat.org/personId=34A254A0-F248-11E8-B48F-1D18A9856A87 bibo_doi: 10.4310/HHA.2013.v15.n1.a3 bibo_issue: '1' bibo_volume: 15 dct_date: 2013^xs_gYear dct_language: eng dct_publisher: International Press@ dct_title: Homology and robustness of level and interlevel sets@ ...