直线与三维固定网格的交线长度与索引公式计算

Formulas of the Length and Index for the Intersection of a Line and a Fixed Grid in Three-Dimensional Space

本文首先介绍了数字图像重建中最典型的计算机断层成像技术(X-ray Computerized Tomography)的成像原理,并考虑将重建问题转化成线性方程组Ax = b的求解,重点讨论了系数矩阵A的生成。以三维实际重建问题为例,本文给出了计算直线与三维固定网格的交线长度与索引公式。最后利用MATLAB实现这一计算过程,并分析算法运行的效率。

In this paper, we introduce the principle of imaging for X-ray CT and try to convert the reconstruction problem to a linear system Ax=b. We emphasize on the construction of A. Using a reconstruction example, we provide formulas of length and index of the intersection of a line and a fixed grid in three-dimensional space. Finally, we try to verify the formulas with MATLAB programming.