Bounds and error estimates for radiosity

We present a method for determining a posteriori bounds and estimates for local and total errors in radiosity solutions. The ability to obtain bounds and estimates for the total error is crucial fro reliably judging the acceptability of a solution. Realistic estimates of the local error improve the efficiency of adaptive radiosity algorithms, such as hierarchical radiosity, by indicating where adaptive refinement is necessary. First, we describe a hierarchical radiosity algorithm that computes conservative lower and upper bounds on the exact radiosity function, as well as on the approximate solution. These bounds account for the propagation of errors due to interreflections, and provide a conservative upper bound on the error. We also describe a non-conservative version of the same algorithm that is capable of computing tighter bounds, from which more realistic error estimates can be obtained. Finally, we derive an expression for the effect of a particular interaction on the total error. This yields a new error-driven refinement strategy for hierarchical radiosity, which is shown to be superior to brightness-weighted refinement.