Refinement criteria for global illumination using convex funcions
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In several computer graphics areas, a refinement criterion is often needed to decide whether to go
on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that
they represent the signal fairly well and we do not need further refinement, otherwise more samples are
required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very
sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the
f-divergences, meeting this requirement. These convex functions have been well studied and successfully
applied to image processing and several areas of engineering. Two applications to global illumination
are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We
obtain significantly better results than with classic criteria, showing that f-divergences are worth further
investigation in computer graphics. Also a discrimination measure based on entropy of the samples for
refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural
method to deal with the adaptive subdivision of the sampling region
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