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The Stability of the Apparent Contour of an Orientable 2-Manifold

  • Herbert Edelsbrunner
  • Dmitriy Morozov
  • Amit Patel
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

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.

Keywords

Distance Function Branch Point Triple Point Homology Group Double Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Herbert Edelsbrunner
    • 1
    • 2
    • 3
  • Dmitriy Morozov
    • 4
  • Amit Patel
    • 1
    • 2
  1. 1.Dept. Comput. Sci.Duke Univ.North CarolinaUSA
  2. 2.IST Austria (Institute of Science and Technology Austria)KlosterneuburgAustria
  3. 3.GeomagicRaleighUSA
  4. 4.Dept. Comput. Sci. and MathStanford Univ.StanfordUSA

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