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Discrete Mean Curvature Flow

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Scale-Space Theories in Computer Vision (Scale-Space 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1682))

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Abstract

In this paper, we introduce the linear scale-space theory for functions on finite graphs. This theory permits us to derive a discrete version of the mean curvature flow. This discrete version yields a defor- mation procedure for polyhedrons. The adjacent matrix and the degree matrix of a polyhedral graph describe the system equation of this poly- hedral deformation. The spectral thepry of graphs derive the stability condition of the polyhedral deformation.

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Author information

Authors and Affiliations

  1. Dept. of Information and Image Sciences, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Atsushi Imiya

  2. Dept. of Applied Mathematics, University of Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Ulrich Eckhardt

Authors
  1. Atsushi Imiya
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  2. Ulrich Eckhardt
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Editor information

Editors and Affiliations

  1. The IT University in Copenhagen, Glentevej 67, DK-2400, Copenhagen NV, Denmark

    Mads Nielsen

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen OE, Denmark

    Peter Johansen  & Ole Fogh Olsen  & 

  3. Department of Mathematics and Computer Science, University of Mannheim, D-68131, Mannheim, Germany

    Joachim Weickert

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© 1999 Springer-Verlag Berlin Heidelberg

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Imiya, A., Eckhardt, U. (1999). Discrete Mean Curvature Flow. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_46

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  • DOI: https://doi.org/10.1007/3-540-48236-9_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66498-7

  • Online ISBN: 978-3-540-48236-9

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