Information theory tools for visualization

209 Pages·2017·165.827 MB·English

by  Chen, Min

Information
Theory Tools
for Visualization
A K PETERS VISUALIZATION SERIES
Series Editor: Tamara Munzner
Information Theory Tools for Visualization
Min Chen, Miquel Feixas, Ivan Viola, Anton Bardera, Han-Wei Shen,
and Mateu Sbert
Visualization Analysis and Design
Tamara Munzner
Information
Theory Tools
for Visualization
Min Chen
University of Oxford
United Kingdom
Miquel Feixas
University of Girona
Spain
Ivan Viola
TU Wien
Austria
Anton Bardera
University of Girona
Spain
Han-Wei Shen
The Ohio State University
Columbus, USA
Mateu Sbert
University of Girona
Spain
Tianjin University
China
Boca Raton London New York
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Library of Congress Cataloging‑in‑Publication Data
Names: Chen, Min, 1960 May 25- author.
Title: Information theory tools for visualization / authors, Min Chen, Miquel
Feixas, Ivan Viola, Anton Bardera, Han-Wei Shen, and Mateu Sbert.
Description: Boca Raton : Taylor & Francis, CRC Press, 2017. | Series: A K
Peters visualization series | Includes bibliographical references and
index.
Identifiers: LCCN 2016018492 | ISBN 9781498740937 (alk. paper)
Subjects: LCSH: Information visualization. | Information theory.
Classification: LCC QA76.9.I52 C45 2017 | DDC 001.4/226--dc23
LC record available at https://lccn.loc.gov/2016018492
Visit the Taylor & Francis Web site at
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Contents
Foreword ix
Preface xi
hapter
C 1(cid:4) Basic Concepts of Information Theory 1
1.1 ENTROPY 2
1.2 RELATIVEENTROPYANDMUTUALINFORMATION 4
1.3 INFORMATIONSPECIFICTOAPARTICULARSYMBOL 6
1.4 ENTROPYRATE 8
1.5 JENSEN–SHANNONDIVERGENCE 10
1.6 INFORMATIONBOTTLENECKMETHOD 11
1.7 SUMMARY 12
hapter
C 2(cid:4) Visualization and Information Theory 15
2.1 INFORMATION-THEORETICMEASURESIN
VISUALIZATION 17
2.1.1 Alphabets and Letters 17
2.1.2 Quantifying Visual Information 18
2.1.3 Information Sources and Communication
Channels 22
2.1.3.1 Information Sources 22
2.1.3.2 Channels 24
2.1.4 Visual Coding in Noiseless Channels 26
2.1.5 Visual Coding in Noisy Channels 27
2.2 INFORMATION-THEORETICLAWSFORVISUALIZATION 29
2.3 INFORMATION-THEORETICPROCESSOPTIMIZATION 32
2.3.1 Data Processing Inequality 34
v
vi (cid:4) Contents
2.3.2 Transformation of Alphabets in a Visualization
Process 34
2.3.3 Cost–Benefit Measures for Visualization Processes 36
2.3.4 Examples of Cost–Benefit Analysis 41
2.3.4.1 Interaction in Visualization 42
2.3.4.2 Disseminative Visualization 45
2.3.4.3 Observational Visualization 46
2.3.4.4 Analytical Visualization 47
2.3.4.5 Model-Developmental Visualization 48
2.4 INFORMATION-THEORETICLINKS:VISUALIZATIONAND
PERCEPTION 49
2.4.1 Visual Multiplexing 49
2.4.1.1 Multiplexing in Communication 49
2.4.1.2 Multiplexing in Visualization 49
2.4.1.3 Multiplexing and Information-
Theoretic Measures 55
2.4.2 Information-Theoretic Quality Metrics 57
2.4.2.1 Differentiability of Glyphs 58
2.4.2.2 Hamming Distance 58
2.4.2.3 Quasi-Hamming Distance for Glyph
Design 60
2.4.3 User Studies in the Information-Theoretic
Framework 63
2.5 SUMMARY 64
hapter
C 3(cid:4) Viewpoint Metrics and Applications 65
3.1 VIEWPOINTMETRICSANDBASICAPPLICATIONS 65
3.2 FROMPOLYGONSTOVOLUMES 66
3.2.1 Isosurfaces 66
3.2.2 Volumetric Data 67
3.3 VISIBILITYCHANNELINVOLUMEVISUALIZATION 71
3.3.1 Visibility Channel 71
3.3.2 Voxel Information 74
3.4 IMPORTANCE-DRIVENFOCUSOFATTENTION 75
3.5 VIEWPOINTSELECTIONUSINGVOXELINFORMATION 79
3.6 APPLICATIONTOILLUSTRATIVERENDERING 80
Contents (cid:4) vii
3.6.1 Ambient Occlusion 80
3.6.2 Color Ambient Occlusion 86
3.7 SUMMARY 86
hapter
C 4(cid:4) Volume Visualization 89
4.1 TIME-VARYINGDATA 90
4.2 LEVEL-OF-DETAILCHARACTERIZATION 95
4.3 ISOSURFACES 97
4.4 SPLITTING 104
4.5 TRANSFERFUNCTIONDESIGN 106
4.6 MULTIMODALVOLUMEVISUALIZATION 114
4.7 SUMMARY 123
hapter
C 5(cid:4) Flow Visualization 125
5.1 COMPLEXITYMEASUREOFVECTORFIELDS 126
5.1.1 Entropy Field 127
5.2 COMPLEXITYMEASURESOFSTREAMLINES 129
5.2.1 Information Complexity of Streamlines 129
5.2.2 Geometric Complexity of Streamlines 131
5.2.2.1 Construction of Histograms 131
5.2.3 Streamline Segmentation 133
5.3 INFORMATION-AWARESTREAMLINESEEDING 134
5.3.1 View-Independent Method 134
5.3.1.1 Initial Seeding 134
5.3.1.2 Importance-Based Seed Insertion 134
5.3.1.3 Redundant Streamline Pruning 136
5.3.1.4 Reconstructing a Vector Field from
Streamlines 136
5.3.1.5 Seed Selection Result 137
5.3.2 View-Dependent Method 138
5.3.2.1 Maximal Entropy Projection (MEP) 138
5.3.2.2 Seed Placement 139
5.3.2.3 Entropy-Based Streamline Selection 141
5.3.2.4 Finding Optimal Views 142
5.4 INFORMATIONCHANNELSFORFLOWVISUALIZATION 143
viii (cid:4) Contents
5.5 SUMMARY 146
hapter
C 6(cid:4) Information Visualization 149
6.1 THEORETICALFOUNDATIONSOFINFORMATION
VISUALIZATION 151
6.2 QUALITYMETRICSFORDATAVISUALIZATION 152
6.3 ITMETRICSFORPARALLELCOORDINATES 153
6.4 MAXIMUMENTROPYSUMMARYTREES 156
6.4.1 How to Construct a Maximum Entropy
Summary Tree 159
6.5 MULTIVARIATEDATAEXPLORATION 159
6.5.1 Variable Entropy 160
6.5.2 Mutual Information between Variables 161
6.5.3 Specific Information 163
6.6 TIME-VARYINGMULTIVARIATEDATA 164
6.6.1 Transfer Entropy 165
6.6.2 Visualization of Information Transfer 167
6.7 PRIVACYANDUNCERTAINTY 167
6.7.1 Metrics for Uncertainty 168
6.8 MUTUALINFORMATIONDIAGRAM 170
6.8.1 The Taylor Diagram 171
6.8.2 Mutual Information Diagram 172
6.8.3 Properties of the MI Diagram 175
6.9 SUMMARY 175
Bibliography 177
Index 191
Foreword
Onthisdate100yearsago1,ClaudeShannonwasborninPetoskey,Michigan,
USA. After graduating from MIT in 1940, Shannon joined Bell Labs, where
in 1948 he would produce a two-part memorandum called “A Mathematical
Theory of Communication,” which focused on the problem of how best to
encode the information a sender wants to transmit. In this memorandum,
Shannon developed information entropy as a measure for uncertainty in a
message, which helped to define the new field of information theory.
Fast-forward a century, and we have an exciting new book, Information
Theory Tools for Visualization, which applies information theory to the field
of visual analysis, Each of its six authors, Min Chen, Miquel Feixas, Ivan
Viola, Anton Bardera, Han-Wei Shen, and Mateu Sbert, has made significant
contributions to the nascent field of information theory in visualization. In
fact, the authors represent the avant-garde in the new field of visualization
theory, having produced among them over 30 papers and referenced articles
on the topic before and after the turn of the millennium. One will notice that
the vast number of papers published by the authors and referenced articles
on the topic of information theory in visualization have been published after
the year 2000 (most even more recently). In this book, then, a reader will be
guided into an exciting new field by the very people who are creating it and
generating its new research results.
Information Theory Tools for Visualization begins by introducing basic
concepts in information theory. The book then moves to create a foundation
and metrics for applying information theory in visualization, using analogies
with other fields to make links between information theory and visualization.
In Chapters 3, 4, and 5, the authors apply information theory to different
aspectsofscientificvisualization,specificallyinvestigatinginformationtheory
applications in volume visualization and flow visualization, as well as using
informationtheorytodefineoptimalviewpointmetricsforsurfaceandvolume
visualization applications. The book concludes with a chapter on applying
information theory to information visualization, exploring topics on parallel
coordinates, trees, graphs, and multivariate data.
I hope you will enjoy following the authors as they lead you into the new
field of information theory in visualization.
1During this centennial year of Shannon’s birth, there are a number of wonderful ar-
ticles about Shannon and his work in information theory, including these from the IEEE
InformationTheorySociety:http://www.itsoc.org/resources/Shannon-Centenary
ix