title: Polygonal and polyhedral contour reconstruction in computed tomography.
abstract: This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3-D image. It is based on the construction and optimization of a regularized criterion that accounts for surface smoothness. We investigate original deterministic local algorithms, based on the exact computation of the line projections, their update, and their derivatives with respect to the vertice coordinates. Results are first derived in the two-dimensional (2-D) case, which consists of reconstructing a 2-D object of deformable polygonal contour from its tomographic data. Then, we investigate the 3-D extension that requires technical adaptations. Simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time.
authors.affiliation: Laboratoire des Signaux et Systèmes, Centre National de la Recherche Scientifique, Supélec, Gif-sur-Yvette, France. charles.soussen@limsi.fr
authors.forename: Charles
authors.initials: C
authors.lastname: Soussen
authors.forename: Ali
authors.initials: A
authors.lastname: Mohammad-Djafari
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014057:Tomography, X-Ray Computed / Q000379:methods*