Ambrosio-Tortorelli Segmentation of Stochastic Images

  • Torben Pätz
  • Tobias Preusser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6315)


We present an extension of the classical Ambrosio-Tortorelli approximation of the Mumford-Shah approach for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows to quantify the robustness of edges in noisy images and under gray value uncertainty. We develop an ansatz space for such images by identifying gray values with random variables. The use of these stochastic images in the minimization of energies of Ambrosio-Tortorelli type leads to stochastic partial differential equations for the stochastic smoothed image and a stochastic phase field for the edge set. For their discretization we utilize the generalized polynomial chaos expansion and the generalized spectral decomposition (GSD) method. We demonstrate the performance of the method on artificial data as well as real medical ultrasound data.


Polynomial Chaos Polynomial Chaos Expansion Stochastic Collocation Street Scene Stochastic Phase 
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-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Torben Pätz
    • 1
    • 2
  • Tobias Preusser
    • 1
    • 2
  1. 1.School of Engineering and ScienceUniversity BremenJacobs
  2. 2.Fraunhofer MEVISBremenGermany

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