Structured sampling and reconstruction of illumination for image synthesis

An important goal of image synthesis is to achieve accurate, efficient and consistent sampling and reconstruction of illumination varying over surfaces in an environment. A new approach is introduced for the treatment of diffuse polyhedral environments lit by area light sources, based on the identification of important properties of illumination structure. The properties of unimodality and curvature of illumination in unoccluded environments are used to develop a high quality sampling algorithm which includes error bounds. An efficient algorithm is presented to partition the scene polygons into a mesh of cells, in which the visible part of the source has the same topology. A fast incremental algorithm is presented to calculate the backprojection, which is an abstract representation of this topology. The behaviour of illumination in the penumbral regions is carefully studied, and is shown to be monotonic and well behaved within most of the mesh cells. An algorithm to reduce the mesh size, and an algorithm which selects between linear and quadratic interpolants are presented. The results show that the mesh size and the degrees of the interpolants can be reduced without significant degradation of image quality. The preceding algorithms are combined into a complete structured sampling approach that allows accurate and efficient representation of illumination using interpolating polynomials for scenes with occlusion. Images with accurate shadows can be produced from the structured representation using either ray-casting or polygon rendering hardware. Finally, it is shown that our methodology generalises easily to the global illumination problem. An iterative solution to a Galerkin finite element approach is proposed, and it is shown how the structured algorithms provide a good initial approximation for the iteration, enhance efficiency for numerical integration and allow adaptive mesh modification. The structure driven global illumination algorithm thus promises significant improvement over previous higher-order finite element solutions.

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