Table of Contents

• About the Author
• Foreword
• Preface
• Acknowledgements
• Notation
  • Alphabetical
  • Greek
  • Operators
• Glossary
  • Mathematical and Statistical
  • Computer Science
  • Organizational and Standards
• Introduction
  • Imaging Science
  • Signals and Images
  • Image Formation
  • Image Information
  • Image Analysis
  • Digital Image Processing
  • Fundamental Problems
  • About this Book
  • Summary of Important Results
• Part I: Mathematical and Computational Background
  • Chapter 1: Vector Fields
    • 1.1 Scalar Fields
    • 1.2 Vector Fields
    • 1.3 The Divergence Theorem
    • 1.4 Summary of Important Results
  • Chapter 2: 2D Fourier Theory
    • 2.1 The 2D Complex Fourier Series
    • 2.2 The 2D Delta Function
    • 2.3 The 2D Fourier Transform
    • 2.4 Physical Representation
    • 2.5 The Spectrum
    • 2.6 Definitions and Notation
    • 2.7 Some Important Results
    • 2.8 Some Important Theorems
    • 2.9 Convolution and Correlation
    • 2.10 Convolution and Correlation Theorems
    • 2.11 Other Integral Transforms
    • 2.12 Discussion
    • 2.13 Summary of Important Results
  • Chapter 3: The 2D DFT, FFT and FIR Filter
    • 3.1 The Discrete Fourier Transform
    • 3.2 The Sampling Theorem
    • 3.3 The Discrete Spectrum of a Digital Image
    • 3.4 The Fast Fourier Transform
    • 3.5 The Imaging Equation and Convolution in 2D
    • 3.6 The Finite Impulse Response Filter
    • 3.7 Origin of the Imaging Equation
    • 3.8 Summary of Important Results
  • Chapter 4: Field and Wave Equations
    • 4.1 The Langevin Equation
    • 4.2 Maxwell’s Equations
    • 4.3 General Solution to Maxwell’s (Microscopic) Equations
    • 4.4 The Macroscopic Maxwell’s Equations
    • 4.5 EM Waves in a Homogeneous Medium
    • 4.6 EM Waves in an Inhomogeneous Medium
    • 4.7 Elastic Field Equations
    • 4.8 Inhomogeneous Elastic Wave Equation
    • 4.9 Acoustic Field Equations
    • 4.10 Discussion
    • 4.11 Summary of Important Results
  • Chapter 5: Green Functions
    • 5.1 Overview
    • 5.2 Introduction to the Green Function
    • 5.3 The Time Independent Wave Operator
    • 5.4 Wavefields Generated by Sources
    • 5.5 Time Dependent Green Function
    • 5.6 Time Dependent Sources
    • 5.7 Green Function Solution to Maxwell’s Equation
    • 5.8 The Diffusion Equation
    • 5.9 Green Function Solution to the Diffusion Equation
    • 5.10 The Laplace and Poisson Equations
    • 5.11 Discussion
    • 5.12 Summary of Important Results
  • Problems: Part I
• Part II: Imaging Systems Modelling
  • Chapter 6: Scattering Theory
    • 6.1 The Schrödinger and Helmholtz Equations
    • 6.2 Solution to the Helmholtz Equation
    • 6.3 Examples of Born Scattering
    • 6.4 Other Approximation Methods
    • 6.5 The Born Series
    • 6.6 Inverse Scattering
    • 6.7 Surface Scattering Theory
    • 6.8 Summary of Important Results
  • Chapter 7: Imaging of Layered Media
    • 7.1 Pulse-Echo Imaging
    • 7.2 EM Imaging of a Layered Dielectric
    • 7.3 Acoustic Imaging of a Layered Material
    • 7.4 Side-band Systems and Demodulation
    • 7.5 Some Applications
    • 7.6 Case Study: Imaging the Ionosphere
    • 7.7 Case Study: Radar Plasma Screening
    • 7.8 Summary of Important Results
  • Chapter 8: Projection Tomography
    • 8.1 Basic Principles
    • 8.2 Projection Tomography and Scattering Theory
    • 8.3 The Radon Transform
    • 8.4 Back-Projection PSF
    • 8.5 The Central Slice Theorem
    • 8.6 Numerical Methods
    • 8.7 The Hough Transform
    • 8.8 Non-separable Image Processing
    • 8.9 Summary of Important Results
  • Chapter 9: Diffraction Tomography
    • 9.1 Diffraction Tomography using CW Fields
    • 9.2 Pulse Mode Diffraction Tomography
    • 9.3 The Diffraction Slice Theorem
    • 9.4 Quantitative Diffraction Tomography
    • 9.5 EM Diffraction Tomography
    • 9.6 Case Study: Simulation of an Ultrasonic B-Scan
    • 9.7 Summary of Important Results
  • Chapter 10: Synthetic Aperture Imaging
    • 10.1 Synthetic Aperture Radar
    • 10.2 Principles of SAR
    • 10.3 Electromagnetic Scattering Model for SAR
    • 10.4 Case Study: The ‘Sea Spikes’ Problem
    • 10.5 Quantitative Imaging with SAR
    • 10.6 Synthetic Aperture Sonar
    • 10.7 Summary of Important Results
  • Chapter 11: Optical Image Formation
    • 11.1 Optical Diffraction
    • 11.2 The Fourier Transforming Properties of a Lens
    • 11.3 Linear Systems
    • 11.4 Images of Lines and Edges
    • 11.5 Linearity of Optical Imaging Systems
    • 11.6 Coherent Image Formation
    • 11.7 Phase Contrast Imaging
    • 11.8 Incoherent Image Formation
    • 11.9 Coherent and Incoherent Optical Imaging
    • 11.10 Optical Beams
    • 11.11 The Paraxial Wave Equation
    • 11.12 Holographic Imaging
    • 11.13 Case Study: Digital Watermarking
    • 11.14 Summary of Important Results
  • Problems: Part II
• Part III: Digital Image Processing Methods
  • Chapter 12: Image Restoration and Reconstruction
    • 12.1 Introduction
    • 12.2 Image Restoration
    • 12.3 The Inverse Filter
    • 12.4 The Wiener Filter
    • 12.5 The Power Spectrum Equalization Filter
    • 12.6 The Matched Filter
    • 12.7 Maximum Entropy Deconvolution
    • 12.8 Constrained Deconvolution
    • 12.9 Phase Reconstruction and Phase Imaging
    • 12.10 Non-stationary Deconvolution
    • 12.11 Discussion
    • 12.12 Summary of Important Results
  • Chapter 13: Reconstruction of Band-limited Images
    • 13.1 The Gerchberg-Papoulis Method
    • 13.2 Incorporation of a Priori Information
    • 13.3 Example Demonstration and Applications
    • 13.4 Error Reduction Algorithm
    • 13.5 Discussion
    • 13.6 Summary of Important Results
  • Chapter 14: Bayesian Estimation Methods
    • 14.1 Introduction to Probability and Bayes Rule
    • 14.2 The Maximum Likelihood Filter
    • 14.3 The Maximum a Posteriori Filter
    • 14.4 Super Resolution using Bayesian Methods
    • 14.5 Summary of Important Results
  • Chapter 15: Image Enhancement
    • 15.1 Basic Transforms
    • 15.2 Histogram Equalization
    • 15.3 Homomorphic Filtering
    • 15.4 Light Diffusion and the High Emphasis Filter
    • 15.5 Noise Reduction
    • 15.6 The Median Filter
    • 15.7 Summary of Important Results
  • Problems: Part III
• Part IV: Pattern Recognition and Computer Vision
  • Chapter 16: Segmentation and Edge Detection
    • 16.1 Correlation and the Auto-covariance Function
    • 16.2 Thresholding
    • 16.3 Edge Detection
    • 16.4 Second Order Edge Detection
    • 16.5 The Marr-Hildreth Method
    • 16.6 Pixel Clustering
    • 16.7 Clustering Tools
    • 16.8 Hierarchical Data Structures
    • 16.9 Summary of Important Results
  • Chapter 17: Statistical Modelling and Analysis
    • 17.1 Random Scattering Theory
    • 17.2 Statistical Modelling Methods
    • 17.3 Phase Distribution Analysis
    • 17.4 Fully Coherent Scattering Processes
    • 17.5 Statistical Moments
    • 17.6 Noise and Statistical Tests
    • 17.7 Texture Segmentation
    • 17.8 Summary of Important Results
  • Chapter 18: Fractal Images and Image Processing
    • 18.1 Introduction
    • 18.2 Geometry and Dimension
    • 18.3 Fractal Curves and Fractal Signals
    • 18.4 Random Scaling Fractals and Texture
    • 18.5 Methods of Computing the Fractal Dimension
    • 18.6 The Fourier and Fractal Dimensions
    • 18.7 Other Dimensions and Higher Order Fractals
    • 18.8 The Information Dimension
    • 18.9 The Lyapunov Dimension
    • 18.10 Fractal Images and Mandelbrot Surfaces
    • 18.11 Generalized Random Scaling Fractal (RSF) Models
    • 18.12 Multi-Fractal Analysis
    • 18.13 Case Study: Fractional Light Diffusion
    • 18.14 Summary of Important Results
  • Chapter 19: Coding and Compression
    • 19.1 The Reasons for Compression
    • 19.2 Lossless Coding Methods
    • 19.3 Lossy Coding Methods
    • 19.4 Fractal Image Compression
    • 19.5 Properties and Features
    • 19.6 Improved Fractal Compression
    • 19.7 Compression Conscious Operations
    • 19.8 Fractal Texture Maps
    • 19.9 Summary of Important Results
  • Problems: Part IV
• Summary
• Appendix A: Solutions to Problems
  • Solutions to Problems: Part I
  • Solutions to Part II
  • Solutions to Problems: Part III
  • Solutions to Problems: Part IV
• Appendix B: Supplementary Problems
• Appendix C: Fourier Transform of a Fractal
• Appendix D: I/O and Graphics Utilities
  • Reading and Writing Images to and From a Named Data File
  • Displaying a Digital Image
• Index