An Active Contour Approach for a Mumford-Shah Model in X-Ray Tomography

  • Elena Hoetzl
  • Wolfgang Ring
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5876)


This paper presents an active contour approach for the simultaneous inversion and segmentation of X-ray tomography data from its Radon Transform. The optimality system is found as the necessary optimality condition for a Mumford-Shah like functional over the space of piecewise smooth densities, which may be discontinuous across the contour. In our approach the functional variable is eliminated by solving a classical variational problem for each fixed geometry. The solution is then inserted in the Mumford-Shah cost functional leading to a geometrical optimization problem for the singularity set. The resulting shape optimization problem is solved using shape sensitivity calculus and propagation of shape variables in the level-set form.

As a special feature of this paper, a new, second order accurate, finite difference method based approach for the solution of the optimality system is introduced and numerical experiments are presented.


Intersection Point Optimality System Active Contour Taylor Series Expansion Descent Direction 
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 2009

Authors and Affiliations

  • Elena Hoetzl
    • 1
  • Wolfgang Ring
    • 1
  1. 1.Institute of Mathematics and Scientific ComputingUniversity of Graz 

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