Ray tracing through a grid of blobs

In this paper we describe two ray tracing algorithms for images represented using spherically symmetric basis functions (blobs) on regular grids. The method presented here allows more realistic modeling of the forward projection by considering tube shaped kernels, rather than simple lines. Each kernel is a function of the radial distance r from its center and can vary with the position l along the projection line. The forward projections are computed by convolutions of the kernel with the blob line integrals. Both ray tracing procedures presented incrementally compute the square distance r² for each visited blob enabling the appropriate resolution kernel to be used. The second variant also computes the l coordinate along the line of response axis allowing for longitudinal variations of the resolution kernel to be considered as well as time-of-flight (TOF) modeling.