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

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


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.


Distance Function Branch Point Triple Point Homology Group Double Point 
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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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