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/sup 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 21/sup 3/ 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 N/sup 3/. 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.