Adaptive density estimation using an orthogonal series for global illumination

In Monte-Carlo photon-tracing methods energy-carrying particles are traced in an environment to generate hit points on object surfaces for simulating global illumination. The surface illumination can be reconstructed from particle hit points by solving a density estimation problem using an orthogonal series. The appropriate number of terms of an orthogonal series used for approximating surface illumination depends on the numbers of hit points (i.e. the number of samples) as well as illumination discontinuity (i.e. shadow boundaries) on a surface. Existing photon-tracing methods based on orthogonal series density estimation use a pre-specified or fixed number m of terms of an orthogonal series; this results in undesirable visual artifacts, i.e. either near-constant shading across a surface which conceals the true illumination variation when m is very small or excessive illumination oscillation when m is very large. On the other hand, interactive user specification of the number of terms for different surface patches is inefficient and inaccurate, and thus is not a practical solution. In this paper an algorithm is presented for automatically determining on the fly the optimal number of terms to be used in an orthogonal series in order to reconstruct surface illumination from surface hit points. When the optimal number of terms required is too high due to illumination discontinuity of a surface, a heuristic scheme is used to subdivide the surface along the discontinuity boundary into some smaller patches, called sub-patches, so as to allow a smaller number of terms in the orthogonal series to optimally represent illumination on these subpatches. Experimental results are presented to show that the new method improves upon other existing orthogonal series-based density estimation methods used for global illumination in both running time and memory requirements. r 2005 Elsevier Ltd. All rights reserved.