A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz (Austria)
- Institut fuer Mathematik, Universitaet Graz, Heinrichstrasse 36, A-8010 Graz (Austria)
A level-set based approach for the determination of a piecewise constant density function from data of its Radon transform is presented. Simultaneously, a segmentation of the reconstructed density is obtained. The segmenting contour and the corresponding density are found as minimizers of a Mumford-Shah like functional over the set of admissible contours and - for a fixed contour - over the space of piecewise constant densities which may be discontinuous across the contour. Shape sensitivity analysis is used to find a descent direction for the cost functional which leads to an update formula for the contour in the level-set framework. The descent direction can be chosen with respect to different metrics. The use of an L {sup 2}-type and an H {sup 1}-type metric is proposed and the corresponding steepest descent flow equations are derived. A heuristic approach for the insertion of additional components of the density is presented. The method is tested for several data sets including synthetic as well as real-world data. It is shown that the method works especially well for large data noise ({approx}10% noise). The choice of the H {sup 1}-metric for the determination of the descent direction is found to have positive effect on the number of level-set steps necessary for finding the optimal contours and densities.
- OSTI ID:
- 20991557
- Journal Information:
- Journal of Computational Physics, Vol. 221, Issue 2; Other Information: DOI: 10.1016/j.jcp.2006.06.041; PII: S0021-9991(06)00302-0; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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