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Γ-Convergence Approximation to Piecewise Constant Mumford-Shah Segmentation

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Advanced Concepts for Intelligent Vision Systems (ACIVS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3708))

Abstract

Piecewise constant Mumford-Shah segmentation[17] has been rediscovered by Chan and Vese [6] in the context of region based active contours. The work of Chan and Vese demonstrated many practical applications thanks to their clever numerical implementation using the level-set technology of Osher and Sethian [18]. The current work proposes a Γ-convergence formulation to the piecewise constant Mumford-Shah model, and demonstrates its simple implementation by the iterated integration of a linear Poisson equation. The new formulation makes unnecessary some intermediate tasks like normal data extension and level-set reinitialization, and thus lowers the computational complexity.

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Author information

Authors and Affiliations

  1. University of Minnesota, Minneapolis, MN, 55455, USA

    Jianhong Shen

Authors
  1. Jianhong Shen
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Editor information

Editors and Affiliations

  1. DGA/D4S/MRIS, 94114, Arcueil, France

    Jacques Blanc-Talon

  2. Ghent University, 9000, Gent, Belgium

    Wilfried Philips

  3. Wireless Technologies Lab, CSIRO ICT Centre, NSW 2122, Marsfield, Australia

    Dan Popescu

  4. University of Antwerp, 2610, Wilrijk, Belgium

    Paul Scheunders

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© 2005 Springer-Verlag Berlin Heidelberg

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Shen, J. (2005). Γ-Convergence Approximation to Piecewise Constant Mumford-Shah Segmentation. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2005. Lecture Notes in Computer Science, vol 3708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558484_63

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  • DOI: https://doi.org/10.1007/11558484_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29032-2

  • Online ISBN: 978-3-540-32046-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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