A fast ray-tracing technique for TCT and ECT studies

In transmission computed tomography (TCT) and emission computed tomography (ECT) studies, a common geometric problem is to trace those voxels along a certain projection ray. It is a time consuming task due to enormous number of voxels on each ray and enormous number of rays involved for the tomographic studies. A straight-forward ray-tracing technique would require computing time that scales with the array size N ³. Siddon (1986) proposed a fast method to trace the rays whose computing time scales with 3N. In this study, a refinement to Siddon´s algorithm is investigated. In Siddon´s algorithm, the index of each voxel along a ray and the intersecting length of that ray within that voxel are computed by four multiplications, which consumes 53% of the total computing time for a typical tomographic study involving an array of 21³ points. By the authors´ new algorithm described in this article, three multiplications of Siddon´s method for computing the voxel indices are replaced by an increment or decrement operation. The fourth multiplication for computing the voxel intersecting lengths is eliminated by carefully selecting a factor to parameterize the rays. Simulation studies on randomly generated projection rays in a N³ . voxel array of N=21, 64, 128, 256, 384 and 512 showed a decrease of approximately 2/3 in total computing time in tracing the rays