Image Statistics in Visual Computing

By Tania Pouli, Erik Reinhard, Douglas W. Cunningham

© 2013 – A K Peters/CRC Press

372 pages | 166 Color Illus.

Purchasing Options:
Hardback: 9781568817255
pub: 2013-12-13
US Dollars$71.95

e–Inspection Copy

About the Book

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.


"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

Table of Contents



Statistics as Priors

Statistics as Image Descriptors

Statistical Pipeline

Natural Images


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


First Order Statistics

Histograms and Moments

Moment Statistics and Average Distributions

Material Properties

Nonlinear Compression in Art

Dark-Is-Deep Paradigm


Gradients, Edges, and Contrast

Real-World Considerations



Linear Scale Space

Contrast in Images

Image Deblurring

Super Resolution


Fourier Analysis


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


Probabilities and Markov Random Fields



Complex Models and Patch-Based Regularities

Statistical Analysis of MRFs



Trichromacy and Metamerism

Color as a 3D Space

Opponent Processing

Color Transfer

Color Space Statistics

Color Constancy and White Balancing


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


Applications That Use Statistical Motion Regularities

Optical Flow

Appendix: Basic Definitions


Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Computer Graphics
MATHEMATICS / Probability & Statistics / General