Probabilistic Visibility Evaluation for Direct Illumination

The efficient evaluation of visibility in a three-dimensional scene is a longstanding problem in computer graphics. Visibility evaluations come in many different forms: figuring out what object is visible in a pixel; determining whether a point is visible to a light source; or evaluating the mutual visibility between 2 surface points. This paper provides a new, experimental view on visibility, based on a probabilistic evaluation of the visibility function. Instead of checking the visibility against all possible intervening geometry, the visibility between 2 points is now evaluated by testing only a random subset of objects. The result is not a Boolean value that is either 0 or 1, but a numerical value that can even be negative. Because we use the visibility evaluation as part of the integrand in illumination computations, the probabilistic evaluation of visibility becomes part of the Monte Carlo procedure of estimating the illumination integral, and results in an unbiased computation of illumination values in the scene. Moreover, the number of intersections tests for any given ray is decreased, since only a random selection of geometric primitives is tested. Although probabilistic visibility is an experimental and new idea, we present a practical algorithm for direct illumination that uses the probabilistic nature of visibility evaluations.