Digital Image Processing

Mathematical and Computational Methods

1st Edition - November 30, 2005
Author: J M Blackledge
Language: English
Paperback ISBN:
9 7 8 - 1 - 8 9 8 5 6 3 - 4 9 - 5
eBook ISBN:
9 7 8 - 0 - 8 5 7 0 9 - 9 4 6 - 4

This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled… Read more

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This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the ‘physics’ of imaging systems. Case studies reinforce the methods discussed, with examples of current research themes.

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

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Physical Sciences & Engineering

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Health

Digital Image Processing

Mathematical and Computational Methods

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J M Blackledge