High performance volume ray casting: A branchless generalized Joseph projector

A concise and highly performant branchless formulation of a Joseph-type interpolating ray-casting algorithm for the computation of X-ray projections is presented. It efficiently utilizes the hardware resources of modern graphics processing units at the scale of their theoretic maximum performance reaching access rates of 600 GB/s within read-and-write memory, and is further shown to do so without compromising on image quality. The computation of X-ray projections from discrete voxel grids is an ubiquitous task in many problems related to volume image processing, including tomographic reconstruction and visualization. Although its central role has given rise to numerous publications discussing the optimal modeling of ray-volume intersections, a unique benchmark in this respect does not exist. Here, a 3D Shepp-Logan phantom is used, which allows the computation of analytic reference projections that can further serve as input to iterative reconstructions without committing the inverse crime. The proposed algorithm (GJP) is compared to the competing and widely adopted digital differential analyzer (DDA), which computes exact line-box intersections. It is thereby found to outperform the DDA on recent graphics processors in all respects: Despite accessing twice as much memory, the GJP is still able to calculate projections twice as fast. It further exhibits considerably less discretization artifacts, and neither oversampling of the DDA nor a smooth interpolation kernel within the GJP are able to improve on these results in any respect.