Information Theory Tools for Computer Graphics Mateu Sbert (University of Girona, Spain), Miquel Feixas (University of Girona, Spain), Jaume Rigau (University of Girona, Spain), Miguel Chover (Jaime I University, Spain), Ivan Viola (University of Bergen,

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 Preface......Page 12 Entropy......Page 14 Relative Entropy and Mutual Information......Page 19 Jensen's Inequality......Page 21 Jensen-Shannon Inequality......Page 22 Entropy Rate......Page 23 Entropy and Coding......Page 25 Continuous Channel......Page 26 Information Bottleneck Method......Page 28 f-Divergences......Page 29 Generalized Entropies......Page 30 Radiosity Method......Page 32 Form Factor Computation......Page 35 Scene Information Channel......Page 37 Basic Definitions......Page 38 From Visibility to Radiosity......Page 41 Scene Complexity......Page 43 Continuous Scene Visibility Mutual Information......Page 44 Computation of Scene Visibility Complexity......Page 45 Complexity and Discretisation......Page 46 Loss of Information Transfer due to Discretisation......Page 51 Mutual-Information-Based Oracle for Hierarchical Radiosity......Page 52 Refinement Criteria Based on f-Divergences......Page 54 Background......Page 60 Complexity Measure......Page 61 Inner 3D-shape Complexity Results......Page 63 Inner 2D-shape Complexity Results......Page 65 Outer Shape Complexity......Page 66 Background......Page 70 Pixel Color Entropy......Page 72 Pixel Geometry Entropy......Page 74 Pixel Color Contrast......Page 75 Pixel Geometry Contrast......Page 77 Pixel Color-Geometry Contrast......Page 78 Algorithm......Page 79 Adaptive Sampling......Page 80 Algorithm......Page 83 Implementation......Page 85 Results......Page 86 Algorithm......Page 89 Results......Page 91 Background......Page 96 Viewpoint Entropy and Mutual Information......Page 97 Results......Page 101 Viewpoint Similarity and Stability......Page 102 Selection of N Best Views......Page 106 Object Exploration......Page 107 View-based Polygonal Information and Saliency......Page 108 View-based Polygonal Information......Page 110 View-based Mesh Saliency......Page 111 Importance-driven Viewpoint Selection......Page 113 View Selection in Scientific Visualization......Page 118 Isosurfaces......Page 119 Volumetric Data......Page 120 Visualization of Molecular Structures......Page 122 Guided Navigation in Data Semantics......Page 124 Background......Page 130 Viewpoint-Based Error Metric......Page 131 Analysis......Page 132 Simplification Algorithm......Page 134 Experiments......Page 136 Viewpoint Mutual Information......Page 137 Viewpoint Kullback-Leibler Distance......Page 140 Summary......Page 146 Bibliography......Page 148 Author Biographies......Page 160 Index......Page 162 1. Information theory basics Entropy Relative entropy and mutual information Inequalities Jensen's inequality Log-sum inequality Jensen-Shannon inequality Data processing inequality Entropy rate Entropy and coding Continuous channel Information bottleneck method F-divergences Generalized entropies 2. Scene complexity and refinement criteria for radiosity Background Radiosity method Form factor computation Scene random walk Scene information channel Basic definitions From visibility to radiosity Scene complexity Continuous scene visibility mutual information Computation of scene visibility complexity Complexity and discretisation Refinement criterion based on mutual information Loss of information transfer due to discretisation Mutual-information-based oracle for hierarchical radiosity Refinement criteria based on f-divergences 3. Shape descriptors Background Inner shape complexity Complexity measure Inner 3D-shape complexity results Inner 2D-shape complexity results Outer shape complexity. 4. Refinement criteria for ray-tracing Background Pixel quality Pixel color entropy Pixel geometry entropy Pixel contrast Pixel color contrast Pixel geometry contrast Pixel color-geometry contrast Entropy-based supersampling Algorithm Results Entropy-based adaptive sampling Adaptive sampling Algorithm Implementation Results F-divergences in adaptive sampling for ray-tracing Algorithm Results 5. Viewpoint selection and mesh saliency Background Viewpoint channel Viewpoint entropy and mutual information Results Viewpoint similarity and stability Best view selection and object exploration Selection of N best views Object exploration View-based polygonal information and saliency View-based polygonal information View-based mesh saliency Importance-driven viewpoint selection 6. View selection in scientific visualization Adaptation from polygons to volumes Isosurfaces Volumetric data Integration of domain semantics Visualization of molecular structures Guided navigation in data semantics 7. Viewpoint-based geometry simplification Background Viewpoint-based error metric Analysis Simplification algorithm Experiments Viewpoint entropy Viewpoint mutual information Viewpoint Kullback-Leibler distance Summary Bibliography Author biographies Index.