Image Statistics in Visual Computing

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

Biography

Tania Pouli, Erik Reinhard, Douglas W. Cunningham

"This book is a survey of natural image statistics used in these days. It is presented in an accessible fashion full of color images. It contains more than 800 reference entries. So, it is a good starting point for all those who want to easily familiarize with the theory of the presented field. This book is good for computer scientists who want to start their research in digital imaging and for engineers who want to apply the described methods in practice."
—Agnieszka Lisowska (Sosnowiec), in Zentralblatt MATH 1295