Information Theory Tools for Computer Graphics

✍ Scribed by Mateu Sbert, Miquel Feixas, Jaume Rigau, Miguel Chover, Ivan Viola

• Publisher: Morgan & Claypool Publishers
• Year: 2009
• Tongue: English
• Leaves: 166
• Series: Synthesis Lectures on Computer Graphics and Animation
• Category: Library

✦ Synopsis

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

✦ Table of Contents

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