Information theory (IT) tools, widely used in scientific fields such as engineering, physics, genetics, neuroscience, and many others, are also emerging as useful transversal tools in computer graphics. In this book, we present the basic concepts of IT and how they have been applied to the graphics areas of radiosity, adaptive ray-tracing, shape descriptors, viewpoint selection and saliency, scientific visualization, and geometry simplification. Some of the approaches presented, such as the viewpoint techniques, are now the state of the art in visualization. Almost all of the techniques presented in this book have been previously published in peer-reviewed conference proceedings or international journals. Here, we have stressed their common aspects and presented them in an unified way, so the reader can clearly see which problems IT tools can help solve, which specific tools to use, and how to apply them. A basic level of knowledge in computer graphics is required but basic concepts in IT are presented. The intended audiences are both students and practitioners of the fields above and related areas in computer graphics. In addition, IT practitioners will learn about these applications. Table of Contents: Information Theory Basics / Scene Complexity and Refinement Criteria for Radiosity / Shape Descriptors / Refinement Criteria for Ray-Tracing / Viewpoint Selection and Mesh Saliency / View Selection in Scientific Visualization / Viewpoint-based Geometry Simplification

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 from a geometric visibility point of view. Then, the main focus of this dissertation, the development of new refinement criteria for the global illumination problem is presented. Firstly, based on Shannon entropy, a set of pixel 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-Charvt-Tsallis generalised entropy, new refinement criteria are defined for hierarchical radiosity. Oracles based on transported information, information smoothness, and mutual information are presented, with very significant results for the latter. And finally, three f-divergences are analysed as refinement criteria. These measures 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.