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Image Statistics in Visual Computing

By Tania Pouli, Erik Reinhard, Douglas W. Cunningham

A K Peters/CRC Press – 2013 – 372 pages

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    978-1-56881-725-5
    December 13th 2013

Description

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.

Contents

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

Name: Image Statistics in Visual Computing (Hardback)A K Peters/CRC Press 
Description: By Tania Pouli, Erik Reinhard, Douglas W. Cunningham. 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,...
Categories: Computer Graphics & Visualization, Regression Analysis and Multivariate Statistics