Digital Image Processing: Mathematical and Computational Methods

by J M Blackledge

Overview

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. - Provides mathematical methods required to describe images, image formation and different imaging systems - Outlines the principle techniques used for processing digital images - Relates the methods of processing and interpreting digital images to the 'physics' of imaging systems

Product Details

ISBN-13:	9780857099464
Publisher:	Woodhead Publishing, Limited
Publication date:	11/30/2005
Series:	Woodhead Publishing Series in Electronic and Optical Materials
Sold by:	Barnes & Noble
Format:	eBook
Pages:	832
File size:	16 MB
Note:	This product may take a few minutes to download.

About the Author

Jonathan M. Blackledge, Loughborough University, UK

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.