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To achieve the complex task of interpreting what we see, our brains rely on statistical regularities and patterns in visual data. Knowledge of these regularities can also be considerably useful in visual computing disciplines, such as computer vision, computer graphics, and image processing. The field of natural image statistics studies the regularities to exploit their potential and better understand human vision. With numerous color figures throughout, Image Statistics in Visual Computing covers all aspects of natural image statistics, from data collection to analysis to applications in computer graphics, computational photography, image processing, and art.

The authors keep the material accessible, providing mathematical definitions where appropriate to help readers understand the transforms that highlight statistical regularities present in images. The book also describes patterns that arise once the images are transformed and gives examples of applications that have successfully used statistical regularities. Numerous references enable readers to easily look up more information about a specific concept or application. A supporting website also offers additional information, including descriptions of various image databases suitable for statistics.

Collecting state-of-the-art, interdisciplinary knowledge in one source, this book explores the relation of natural image statistics to human vision and shows how natural image statistics can be applied to visual computing. It encourages readers in both academic and industrial settings to develop novel insights and applications in all disciplines that relate to visual computing.

With numerous color figures throughout, this work covers all aspects of natural image statistics, from data collection to analysis to applications in computer graphics, computational photography, image processing, and art. Collecting state-of-the-art, interdisciplinary knowledge in one source, the book explores the relation of natural image statistics to human vision and shows how natural image statistics can be applied to visual computing. A supporting website offers additional information, including descriptions of various image databases suitable for statistics.

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BACKGROUND
Introduction 
Statistics as Priors 
Statistics as Image Descriptors 
Statistical Pipeline 
Natural Images
Discussion 

The Human Visual System
Radiometric and Photometric Terms 
Human Vision 
The Eyes
The Lateral Geniculate Nucleus and Cortical Processing 
Implications of Human Visual Processing

Image Collection and Calibration 
Image Capture 
Post-Processing and Calibration 
Image Databases

IMAGE STATISTICS
First Order Statistics
Histograms and Moments 
Moment Statistics and Average Distributions 
Material Properties 
Nonlinear Compression in Art 
Dark-Is-Deep Paradigm 
Summary 

Gradients, Edges, and Contrast 
Real-World Considerations
Gradients
Edges 
Linear Scale Space 
Contrast in Images 
Image Deblurring 
Super Resolution 
Inpainting

Fourier Analysis 
Auto-Correlation 
The Fourier Transform 
The Wiener-Khintchine Theorem
Power Spectra 
Phase Spectra 
Human Perception 
Fractal Forgeries 
Image Processing and Categorization 
Texture Descriptors 
Terrain Synthesis 
Art Statistics

Dimensionality Reduction 
Principal Component Analysis 
Independent Components Analysis 
ICA on Natural Images 
Gaussian Mixture Models 

Wavelet Analysis 
Wavelet Transform 
Multiresolution Analysis 
Signal Processing 
Other Bases 
2D Wavelets 
Contourlets, Curvelets, and Ridgelets 
Coefficient Histograms 
Scale Invariance 
Correlations between Coefficients 
Complex Wavelets 
Correlations between Scales 
Application: Image Denoising
Application: Progressive Reconstruction 
Application: Texture Synthesis 

Markov Random Fields
Image Interpretation 
Graphs
Probabilities and Markov Random Fields
MAP-MRF 
Applications 
Complex Models and Patch-Based Regularities 
Statistical Analysis of MRFs

BEYOND TWO DIMENSIONS
Color
Trichromacy and Metamerism 
Color as a 3D Space 
Opponent Processing 
Color Transfer
Color Space Statistics 
Color Constancy and White Balancing 
Summary 

Depth Statistics 
The "Dead Leaves" Model 
Perception of Scene Geometry
Correlations between 2D and Range Statistics 
Depth Reconstruction 

Time and Motion 
The Statistics of Time 
Motion 
Applications That Use Statistical Motion Regularities
Optical Flow

Appendix: Basic Definitions
Bibliography

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