# Information Theory in Scientific Visualization

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## Abstract

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## 1. Introduction

## 2. Visualization and Information Channel

**Figure 1.**The analogy between message transmission and data visualization. Here we only sketch a simple model in one stage transmission. In reality, either message transmission or data visualization consists of multiple stages. Refer to the work by Chen and Jänicke [3] for more detailed illustration.

## 3. Concepts of Information Theory

#### 3.1. Entropy

**Figure 2.**(a) a 2D hurricane field of velocity magnitude. (b) the entropy field derived from velocity magnitude. (c) the entropy field derived from velocity direction. (d) uniformly placed streamlines with color coded entropy derived from velocity direction and magnitude. The entropy value increases from blue to green to red in (b), (c), and (d).

#### 3.2. Joint Entropy and Relative Entropy

#### 3.3. Mutual Information and Conditional Entropy

#### 3.4. Relationships among Information Theory Concepts

**Figure 3.**Left: Relationships among different entropy measures between two random variables X and Y. Right: The goal of data visualization is to maximize the mutual information $I(X;Y)$ between the input data X and the output visualization Y.

## 4. Applications of Information Theory in Scientific Visualization

#### 4.1. View Selection for Volumetric Data

**Figure 4.**Three representative views of a cube showing the increasing amount of information revealed about the object.

#### 4.2. Streamline Seeding and Selection

#### 4.3. Transfer Function for Multimodal Data

#### 4.4. Selection of Representative Isosurfaces

#### 4.5. LOD Selection for Multiresolution Volume Visualization

#### 4.6. Time-varying and Multivariate Data Analysis

#### 4.7. Information Channel between Objects and Viewpoints

**Figure 5.**Illustration of the viewpoint mutual information. Left: a low quality viewpoint indicating a highly dependent view between the viewpoint ${v}_{1}$ and the set of objects $O=\{{o}_{1},{o}_{2}\}$. Right: a high quality viewpoint indicating a more independent view between the viewpoint ${v}_{2}$ and the set of objects O.

## 5. Information Theory in Imaging and Graphics

## 6. Outlook for Future Research

## Acknowledgements

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Wang, C.; Shen, H.-W. Information Theory in Scientific Visualization. *Entropy* **2011**, *13*, 254-273.
https://doi.org/10.3390/e13010254

**AMA Style**

Wang C, Shen H-W. Information Theory in Scientific Visualization. *Entropy*. 2011; 13(1):254-273.
https://doi.org/10.3390/e13010254

**Chicago/Turabian Style**

Wang, Chaoli, and Han-Wei Shen. 2011. "Information Theory in Scientific Visualization" *Entropy* 13, no. 1: 254-273.
https://doi.org/10.3390/e13010254