Information - Theoretic Refinement Criteria for Image Synthesis

This work is framed within the context of computer graphics starting out from the intersection of three fields: rendering , information theory , and complexity . Initially, the concept of scene complexity is analysed considering three perspectives from a geometric visibility point of view: complexity at an interior point , complexity of an animation, and complexity of a region. The main focus of this dissertation is the exploration and development of new refinement criteria for the global illumination problem. Information-theoretic measures based on Shannon entropy and HarvdaCharvát-Tsallis generalised entropy, together with f-divergences, are analysed as kernels of refinement. We show how they give us a rich variety of efficient and highly discriminative measures which are applicable to rendering in its pixel-driven (ray-tracing) and object-space (hierarchical radiosity) approaches. Firstly, based on Shannon entropy, a set of pixel quality and pixel contrast measures are defined. They are applied to supersampling in ray-tracing as refinement criteria, obtaining a new entropy-based adaptive sampling algorithm with a high rate quality versus cost. Secondly, based on Harvda-CharvátTsallis generalised entropy, and generalised mutual information, three new refinement criteria are defined for hierarchical radiosity. In correspondence with three classic approaches, oracles based on transported information, information smoothness, and mutual information are presented, with very significant results for the latter. And finally, three members of the family of Csiszár’s f-divergences (Kullback-Leibler , chisquare, and Hellinger divergences) are analysed as refinement criteria showing good results for both ray-tracing and hierarchical radiosity.