Soussen Charles, Mohammad-Djafari Ali
Laboratoire des Signaux et Systèmes, Centre National de la Recherche Scientifique, Supélec, Gif-sur-Yvette, France.
IEEE Trans Image Process. 2004 Nov;13(11):1507-23. doi: 10.1109/tip.2004.836159.
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.
本文是关于从X射线断层扫描数据对二值图像进行三维（3-D）重建的研究。我们研究了一个完全包含在均匀背景中的紧凑均匀多面体的特殊情况，并直接进行多面体表面估计。我们使用贝叶斯框架将此问题表述为一个非线性逆问题。顶点估计不使用三维图像的体素近似。它基于一个考虑表面平滑性的正则化准则的构建和优化。我们研究了基于线投影的精确计算、其更新以及关于顶点坐标的导数的原始确定性局部算法。首先在二维（2-D）情况下得出结果，即从其断层扫描数据重建具有可变形多边形轮廓的二维物体。然后，我们研究需要技术调整的三维扩展。模拟结果从质量和计算时间方面说明了多边形和多面体重建算法的性能。
