--- _id: '3795' abstract: - lang: eng text: 'The (apparent) contour of a smooth mapping from a 2-manifold to the plane, f: M → R2 , is the set of critical values, that is, the image of the points at which the gradients of the two component functions are linearly dependent. Assuming M is compact and orientable and measuring difference with the erosion distance, we prove that the contour is stable.' acknowledgement: This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057. alternative_title: - Mathematics and Visualization author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: 'Edelsbrunner H, Morozov D, Patel A. The stability of the apparent contour of an orientable 2-manifold. In: Topological Data Analysis and Visualization: Theory, Algorithms and Applications. Springer; 2010:27-42. doi:10.1007/978-3-642-15014-2_3' apa: 'Edelsbrunner, H., Morozov, D., & Patel, A. (2010). The stability of the apparent contour of an orientable 2-manifold. In Topological Data Analysis and Visualization: Theory, Algorithms and Applications (pp. 27–42). Springer. https://doi.org/10.1007/978-3-642-15014-2_3' chicago: 'Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” In Topological Data Analysis and Visualization: Theory, Algorithms and Applications, 27–42. Springer, 2010. https://doi.org/10.1007/978-3-642-15014-2_3.' ieee: 'H. Edelsbrunner, D. Morozov, and A. Patel, “The stability of the apparent contour of an orientable 2-manifold,” in Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42.' ista: 'Edelsbrunner H, Morozov D, Patel A. 2010.The stability of the apparent contour of an orientable 2-manifold. In: Topological Data Analysis and Visualization: Theory, Algorithms and Applications. Mathematics and Visualization, , 27–42.' mla: 'Edelsbrunner, Herbert, et al. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42, doi:10.1007/978-3-642-15014-2_3.' short: 'H. Edelsbrunner, D. Morozov, A. Patel, in:, Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42.' date_created: 2018-12-11T12:05:13Z date_published: 2010-12-22T00:00:00Z date_updated: 2021-01-12T07:52:15Z day: '22' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-15014-2_3 file: - access_level: open_access checksum: f03a44c3d1c3e2d4fedb3b94404f3fd5 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:40Z date_updated: 2020-07-14T12:46:16Z file_id: '4896' file_name: IST-2016-538-v1+1_2011-B-02-ApparentContour.pdf file_size: 210710 relation: main_file file_date_updated: 2020-07-14T12:46:16Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Submitted Version page: 27 - 42 publication: 'Topological Data Analysis and Visualization: Theory, Algorithms and Applications' publication_status: published publisher: Springer publist_id: '2428' pubrep_id: '538' quality_controlled: '1' scopus_import: 1 status: public title: The stability of the apparent contour of an orientable 2-manifold type: book_chapter user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2010' ...