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Title: A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data

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 {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 onmore » the number of level-set steps necessary for finding the optimal contours and densities.« less

Authors:
 [1];  [2]
  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz (Austria). E-mail: ronny.ramlau@oeaw.ac.at
  2. Institut fuer Mathematik, Universitaet Graz, Heinrichstrasse 36, A-8010 Graz (Austria). E-mail: wolfgang.ring@uni-graz.at
Publication Date:
OSTI Identifier:
20991557
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 221; Journal 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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY FUNCTIONAL METHOD; EQUATIONS; MATHEMATICAL SPACE; METRICS; OPTIMIZATION; PROBABILITY DENSITY FUNCTIONS; RADON; SENSITIVITY ANALYSIS; TOMOGRAPHY; X RADIATION

Citation Formats

Ramlau, Ronny, and Ring, Wolfgang. A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data. United States: N. p., 2007. Web. doi:10.1016/j.jcp.2006.06.041.
Ramlau, Ronny, & Ring, Wolfgang. A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data. United States. doi:10.1016/j.jcp.2006.06.041.
Ramlau, Ronny, and Ring, Wolfgang. Sat . "A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data". United States. doi:10.1016/j.jcp.2006.06.041.
@article{osti_20991557,
title = {A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data},
author = {Ramlau, Ronny and Ring, Wolfgang},
abstractNote = {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.},
doi = {10.1016/j.jcp.2006.06.041},
journal = {Journal of Computational Physics},
number = 2,
volume = 221,
place = {United States},
year = {Sat Feb 10 00:00:00 EST 2007},
month = {Sat Feb 10 00:00:00 EST 2007}
}