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A Mumford–Shah level-set approach for the inversion and segmentation of X-ray tomography data
- Source :
-
Journal of Computational Physics . Feb2007, Vol. 221 Issue 2, p539-557. 19p. - Publication Year :
- 2007
-
Abstract
- Abstract: 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 2-type and an H 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 (∼10% noise). The choice of the H 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. [Copyright &y& Elsevier]
- Subjects :
- *LEVEL set methods
*RADON transforms
*DENSITY functionals
*GEOMETRIC tomography
Subjects
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 221
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 23813189
- Full Text :
- https://doi.org/10.1016/j.jcp.2006.06.041