---
_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'
...