A Stochastic Approach for Rendering Multiple Irregular Volumes

In this paper, we propose a technique for rendering multiple irregular volumes using a stochastic approach. In this approach, we extend our stochastic projected tetrahedral (SPT) algorithm to treat irregular volumes. The SPT algorithm is a sorting-free volume rendering algorithm that projects a tetrahedral cell onto an image plane and controls the particle rendering using the opacity as the probability in the rasterization process. In the rasterization process, the particle depth is determined as that of a pre-defined location, which may be the front, back or middle point on a ray segment in the SPT algorithm. This determination causes a prominent artifact when treating multiple volumes, although it does not cause any problem when treating a single volume. The artifact occurs because the SPT algorithm controls the particle stochastically in the image plane but not in the depth direction. In the volume rendering process, it is assumed that the number of particles follows a Poisson distribution along the segment of the viewing ray that intersects the tetrahedral cell. The particle spacing follows the exponential distribution. In this case, we construct a cumulative distribution function of the particle spacing and develop a technique for calculating the nearest particle along the interval. We apply this technique to multiple volumes to confirm its effectiveness.