The stability of the apparent contour of an orientable 2-manifold

Edelsbrunner, Herbert; Morozov, Dmitriy; Patel, Amit

The stability of the apparent contour of an orientable 2-manifold

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.

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IST-2016-538-v1+1_2011-B-02-ApparentContour.pdf 210.71 KB [Submitted Version]

DOI

10.1007/978-3-642-15014-2_3

Book Chapter | Published | English

Scopus indexed

Author

Edelsbrunner, Herbert^ISTA ; Morozov, Dmitriy; Patel, Amit^ISTA

Department

Edelsbrunner Group

Series Title

Mathematics and Visualization

Abstract

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.

Publishing Year

2010

Date Published

2010-12-22

Book Title

Topological Data Analysis and Visualization: Theory, Algorithms and Applications

Publisher

Springer

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.

Page

27 - 42

IST-REx-ID

3795

Cite this

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

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

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.

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.

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.

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