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

Authors:
Elena Hoetzl;Wolfgang Ring
Affiliations:
Institute of Mathematics and Scientific Computing, University of Graz,;Institute of Mathematics and Scientific Computing, University of Graz,
Venue:
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Year:
2009

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Abstract

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.