Polygonal and Polyhedral Contour Reconstruction in Computed Tomography

Abstract

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.Index Terms-Block relaxation algorithms, closed contour and surface reconstruction, deformable template, global and local iterative descent algorithms, polygonal and polyhedral modeling, two-dimensional and three-dimensional binary image reconstruction from projections, X-ray tomography.

Model-based Tomographic Reconstruction Literature Search

“…Ye, Bresler, and Moulin used this approach to estimate object shape [17,18,19] for both radar imaging and tomography. Mohammed-Djafari and Soussen reconstructed general polyhedral objects by estimating the vertices directly from projections using both ML and MAP approaches [20,21,22,23]. Finally, Feng, et al [24], used a level-set approach to estimating the contours of objects.…”

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Sampling Schemes for Multidimensional Signals With Finite Rate of Innovation

“…[19], [30], [31]). In particular, the approach of [30] considers estimation of polygonal and polyhedral corner points in Bayesian framework, where as the focus of [31] is on information-theoretic issues in nonparametric boundary estimation.…”