Sitek Arkadiusz, Huesman Ronald H, Gullberg Grant T
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
IEEE Trans Med Imaging. 2006 Sep;25(9):1172-9. doi: 10.1109/tmi.2006.879319.
Medical images in nuclear medicine are commonly represented in three dimensions as a stack of two-dimensional images that are reconstructed from tomographic projections. Although natural and straightforward, this may not be an optimal visual representation for performing various diagnostic tasks. A method for three-dimensional (3-D) tomographic reconstruction is developed using a point cloud image representation. A point cloud is a set of points (nodes) in space, where each node of the point cloud is characterized by its position and intensity. The density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution. The reconstructed volume, which in general could be of any resolution, size, shape, and topology, is represented by a set of nonoverlapping tetrahedra defined by the nodes. The intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron. This approach creates a continuous piecewise linear intensity over the reconstruction domain. The reconstruction provides a distinct multiresolution representation, which is designed to accurately and efficiently represent the 3-D image. The method is applicable to the acquisition of any tomographic geometry, such as parallel-, fan-, and cone-beam; and the reconstruction procedure can also model the physics of the image detection process. An efficient method for evaluating the system projection matrix is presented. The system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud. Examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a Jaszczak cardiac torso phantom are presented. This work creates a framework for voxel-less multiresolution representation of images in nuclear medicine.
核医学中的医学图像通常以三维形式呈现为一堆从断层投影重建而来的二维图像。尽管这种方式自然且直接，但对于执行各种诊断任务而言，它可能并非最优的视觉呈现方式。一种使用点云图像表示法的三维（3-D）断层重建方法被开发出来。点云是空间中的一组点（节点），其中点云的每个节点由其位置和强度来表征。节点的密度决定了局部分辨率，从而能够以不同分辨率对图像的不同部分进行建模。重建后的体积，通常可以具有任何分辨率、大小、形状和拓扑结构，由节点定义的一组不重叠四面体表示。体积内任何一点的强度通过在一个四面体内从定义该四面体的四个节点的值进行线性插值来确定。这种方法在重建域上创建了一个连续的分段线性强度。该重建提供了一种独特的多分辨率表示，旨在准确且高效地表示三维图像。该方法适用于任何断层几何结构的采集，如平行束、扇形束和锥形束；并且重建过程还可以对图像检测过程的物理原理进行建模。提出了一种评估系统投影矩阵的有效方法。系统矩阵用于迭代算法中，以重建点云中点分布的强度和位置。给出了由计算机模拟生成的投影数据以及使用Jaszczak心脏躯干模型实验获取的投影数据的重建示例。这项工作为核医学中无体素的多分辨率图像表示创建了一个框架。
