{"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.","quality_controlled":"1","day":"22","abstract":[{"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.","lang":"eng"}],"status":"public","date_updated":"2021-01-12T07:52:15Z","has_accepted_license":"1","pubrep_id":"538","department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"27 - 42","author":[{"first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"},{"id":"34A254A0-F248-11E8-B48F-1D18A9856A87","last_name":"Patel","full_name":"Patel, Amit","first_name":"Amit"}],"publist_id":"2428","file_date_updated":"2020-07-14T12:46:16Z","language":[{"iso":"eng"}],"date_published":"2010-12-22T00:00:00Z","ddc":["000"],"year":"2010","file":[{"checksum":"f03a44c3d1c3e2d4fedb3b94404f3fd5","creator":"system","access_level":"open_access","file_id":"4896","relation":"main_file","date_updated":"2020-07-14T12:46:16Z","content_type":"application/pdf","file_name":"IST-2016-538-v1+1_2011-B-02-ApparentContour.pdf","date_created":"2018-12-12T10:11:40Z","file_size":210710}],"date_created":"2018-12-11T12:05:13Z","publication":"Topological Data Analysis and Visualization: Theory, Algorithms and Applications","alternative_title":["Mathematics and Visualization"],"type":"book_chapter","citation":{"mla":"Edelsbrunner, Herbert, et al. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” <i>Topological Data Analysis and Visualization: Theory, Algorithms and Applications</i>, Springer, 2010, pp. 27–42, doi:<a href=\"https://doi.org/10.1007/978-3-642-15014-2_3\">10.1007/978-3-642-15014-2_3</a>.","chicago":"Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” In <i>Topological Data Analysis and Visualization: Theory, Algorithms and Applications</i>, 27–42. Springer, 2010. <a href=\"https://doi.org/10.1007/978-3-642-15014-2_3\">https://doi.org/10.1007/978-3-642-15014-2_3</a>.","ieee":"H. Edelsbrunner, D. Morozov, and A. Patel, “The stability of the apparent contour of an orientable 2-manifold,” in <i>Topological Data Analysis and Visualization: Theory, Algorithms and Applications</i>, 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.","ama":"Edelsbrunner H, Morozov D, Patel A. The stability of the apparent contour of an orientable 2-manifold. In: <i>Topological Data Analysis and Visualization: Theory, Algorithms and Applications</i>. Springer; 2010:27-42. doi:<a href=\"https://doi.org/10.1007/978-3-642-15014-2_3\">10.1007/978-3-642-15014-2_3</a>","apa":"Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2010). The stability of the apparent contour of an orientable 2-manifold. In <i>Topological Data Analysis and Visualization: Theory, Algorithms and Applications</i> (pp. 27–42). Springer. <a href=\"https://doi.org/10.1007/978-3-642-15014-2_3\">https://doi.org/10.1007/978-3-642-15014-2_3</a>","short":"H. Edelsbrunner, D. Morozov, A. Patel, in:, Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42."},"oa_version":"Submitted Version","month":"12","title":"The stability of the apparent contour of an orientable 2-manifold","_id":"3795","doi":"10.1007/978-3-642-15014-2_3","publication_status":"published","publisher":"Springer","scopus_import":1,"oa":1}