One- and Multidimensional Signal Processing Algorithms and Applications in Image Processing

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ISBN: 9780471805410 | 0471805416
Cover: Hardcover
Copyright: 12/19/2000

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With the constant increase in applications involving image processing and multimedia procedures digital signal processing (DSP) is important for modern information engineering. One- and Multidimensional Signal Processing provides an introduction to the algorithmic basics of image and TV communication systems as well as for systems in automation and robotic applications using sensor based imaging techniques. This novel combination of both one- and multidimensional signal processing discusses the similarities between the two and aids the understanding of one theory over the other. * Presents an applications-oriented approach to image processing including TV signal processing and discusses image scanning and the use of DSP procedures or digital filters * Provides clear and comprehensive coverage of basic concepts such as spatial frequency, spatio-temporal signal processing and the spectral representation of motion and tracking of moving objects * Features examples of applications including image pick-up and display as well as still image filtering and image sequence interpolation * Introduces new design strategies for finite-impulse response (FIR) filters for image processing applciations using spatial and frequency design constraints * Includes an introduction to nonlinear image processing techniques applying edge detection operators, morphological operators and rank order filters Such a practical book will have wide-ranging appeal as a valuable resource for researchers and developers and as an ideal introductory text for senior undergraduate and postgraduate students.

Contents

Preface

Introduction

(6)

Objectives of this book

(2)

Structure of the book

(4)

Multidimensional Signals and Systems

(44)

One-Dimensional Signals and Systems

(6)

Signals and linear systems

(2)

δ-Distribution as a fundamental of signal sampling

(4)

Continuous signal sampling for the formation of discrete signals

(1)

Properties and Representation of Multidimensional Signals and Systems

(26)

2D (MD) distributions

(2)

2D (MD) impulse response, 2D (MD) convolution

(2)

2D (MD) Fourier transform

(4)

2D (MD) transfer function

(2)

Separable signals and their Fourier transform

(1)

2D point singularity (distribution)

(1)

2D line singularities (distribution)

(10)

Spatio-Temporal Signals and Systems

(12)

Separated and nonseparated 3D spatio-temporal systems

(4)

Motion and its spatio-temporal representation

(5)

Tracking and its spatio-temporal representation

(3)

Spatio-Temporal Scanning of Multidimensional Signals

(26)

Spatial Scanning of Two-Dimensional Signals

(5)

2D delta line distribution comb

(1)

Line-by-line (1D) scanning of spatial signals

(1)

2D delta point grid

(1)

2D scanning of 2D (spatial) signals

(2)

Spatio-Temporal Scanning

(6)

3D delta point grid

(1)

Spatio-temporal scanning of 3D image signals

(1)

Temporal scanning of spatial discrete images

(1)

Motion representation with temporal scanning

(3)

Spatial Image Representation with CCD Sensors and LC Displays

(6)

Spatio-Temporal Image Representation with CCD Sensors and LC Displays

(3)

Spatio-Temporal Image Scanning with Line Interlace

(6)

Discrete Signals and Linear Systems

(40)

Definition of Discrete Signals, Sequences

(8)

1D and 2D sequences

(2)

Elementary 1D sequences: unit impulse, unit step and exponential sequences

(1)

Representation of sequences with the 1D unit impulse

(1)

Elementary 2D sequences: unit impulse, unit step and exponential sequences

(1)

2D line impulse sequence

(2)

Separable 2D sequences

(1)

Finite 2D sequences

(1)

Representation of 2D sequences with the 2D unit impulse

(1)

Elementary operations

(1)

Linear Shift Invariant 1D Systems (LSI Systems)

(7)

Properties

(1)

Unit impulse response, discrete convolution

(1)

Cascade LSI systems

(1)

Graphical representation of discrete convolution

(1)

BIBO stability of a system

(1)

Nonrecursive filters (FIR filters)

(3)

Linear Shift Invarient 2D Systems

(6)

General properties

(1)

2D convolution law for discrete 2D systems

(1)

Separable impulse response

(2)

Two-dimensional FIR filter

(2)

1D Transfer Function and 1D Fourier Transform

(8)

Definition of transfer function for discrete 1D systems

(1)

Response to time-dependent excitation

(2)

Fourier transform of discrete original signals

101

(1)

Fourier transform of a product of two sequences, windowing a sequence

102

(2)

Example: cosine equalization

104

(2)

2D Transfer Function and 2D Fourier Transform

106

(11)

Definition of the transfer function

106

(1)

2D Fourier transform of discrete original signals

107

(1)

2D Fourier transform of separable sequences

108

(2)

Example: Frequency response correction of and image sensor (CCD sensor)

110

(2)

Example: Frequency response correction of a tube camera with asymmetrical aperture

112

(5)

Elementary Filter Structures and the z-Transform

117

(46)

Difference Equations to Describe Discrete 1D Systems

117

(7)

Example for a first-order system

118

(1)

General solution for difference equations

119

(1)

Example for the solution of the SDE (first-order system)

120

(2)

Impulse response and difference equation

122

(1)

Transfer function and standard difference equation

122

(2)

Definition of the z-Transform

124

(5)

Transfer function H(z) for 1D Systems

125

(4)

Region of Convergence of the z-Transform

129

(5)

Region of convergence (ROC) of the unilateral z-transform

129

(2)

Region of convergence of the bilateral z-transform

131

(3)

Rules and Properties of the z-Transform

134

(5)

Inverse z-Transform

139

(5)

Basic ID Filter Structures

144

(7)

Basics and Elementary Structures of 2D Filters

151

(12)

2D difference equation

151

(2)

z-Transform for 2D signals and systems

153

(3)

Elementary 2D recursive structures

156

(7)

Discrete Fourier Transform

163

(38)

One-Dimensional Discrete Fourier Transform

163

(13)

Discretization of the time function

164

(1)

Windowing of the sequence

164

(2)

Discretization of the spectrum

166

(2)

Transform equations

168

(3)

Matrix vector product of the DFT

171

(2)

DFT for finite sequences, interpolation theorem

173

(1)

Convolution theorem of the DFT, periodic convolution

174

(2)

Fast Fourier Transform

176

(7)

FFT algorithm with powers to base 2

177

(5)

FFT algorithms for convolution of finite sequences

182

(1)

Two-Dimensional Discrete Fourier Transformation

183

(14)

Orthogonal 2D scanning

185

(1)

2D windowing

185

(2)

2D Discrete Fourier Transform (2D DFT)

187

(2)

Harmonic analysis using DFT

189

(1)

Linearity of the DFT

190

(2)

Image examples for the DFT

192

(1)

Shift theorem of the DFT

192

(2)

DFT for separable 2D periodic sequnces

194

(1)

Product theorem, duality, reflection during DFT

194

(1)

Realization of the 2D DFT by separation

195

(1)

Example: 2D interpolation

195

(2)

The 2D DFT and the Discrete Cosine Transform

197

(4)

Design of IIR Filters

201

(26)

Direct IIR Filter Design in the z-Domain

202

(5)

Design techniques

202

(3)

Discrete frequency transformations

205

(2)

Selected Analog Filters with Tolerance Schemes in the Frequency Domain

207

(7)

Butterworth filter

208

(2)

Filters with Chebyshev behaviour in the passband

210

(2)

Chebyshev approximation in the stopband

212

(1)

Elliptic filters

213

(1)

Filter Design by Impulse Invariant Transfomation

214

(4)

Example for an impulse invariant filter design

216

(2)

Filter Design using the Bilinear Transformation

218

(9)

Example for a filter design with the bilinear transformation

222

(2)

Example for a filter design using the impulse invariant transformation

224

(3)

Characteristics and Design of FIR Filters

227

(26)

Characteristics of Nonrecursive Filters

227

(3)

FIR Filter Design by Minimization of the Mean Square Error

230

(9)

Example: Approximation of an ideal lowpass filter

231

(2)

MSE criterion and windowing sequences

233

(3)

Example: Approximation of a differentiator

236

(3)

FIR Filter Design using Windowing

239

(9)

Kaiser window

242

(2)

Cosine roll-off

244

(4)

Chebyshev FIR Filters

248

(5)

Characteristics and Design of 2D FIR Filters for Video Signal Processing

253

(28)

Design of 2D FIR Filters using Window Design Methods

253

(8)

Design of 2D FIR Filters using the McClellan Transfomation

261

(3)

FIR Filters for Video Signal Processing

264

(6)

Optimization of Video Signal Filters by Evolution Strategies

270

(11)

Frequency response deviation

271

(1)

Transition width between passband and stopband

272

(1)

DC component amplification

273

(1)

Cut-off frequency amplitude

273

(1)

Amplitude of the step response's first overshoot

273

(1)

Position of the step response's first overshoot

273

(1)

Deviation of the step response's higher-order overshoots

274

(1)

Relative step gradient

274

(1)

Evolution strategy for the minimization of the cost function

275

(1)

Mutation

275

(1)

Recombination

276

(1)

Selection

276

(5)

Operators for Image Processing

281

(32)

General Concepts for Image Processing

281

(2)

Grey Level Transformations

283

(2)

Local Operators

285

(3)

Local linear operators

286

(1)

Local nonlinear operators

287

(1)

Edge Detection and Edge Localization

288

(10)

Gradient operators

289

(2)

Laplacian operators

291

(2)

Sobel operators

293

(2)

Edge localization procedures

295

(3)

Morphological Operators for Image Processing

298

(15)

Structuring element

298

(1)

Translation

299

(1)

Dilation

300

(1)

Erosion

301

(2)

Properties of dilation and erosion

303

(1)

Duality of erosion and dilation

303

(1)

Decomposition of structuring elements

304

(1)

Opening and closing, higher-order operators

305

(2)

Example application: Morphological edge detection

307

(6)

Rank Order Filters

313

(36)

Median Filters

314

(3)

History of median filters

314

(1)

Definition of median filters

315

(2)

Edge Preservation Properties of Median Filters

317

(1)

Deterministic Properties of the Median Filter

318

(7)

Shape of root signals

320

(1)

Two-dimensional root signals

321

(1)

Construction of root signals

322

(2)

Convergence behaviour of median filters

324

(1)

Statistical Description of Rank Order and Median Filters

325

(5)

Noise Reduction by Median Filters

330

(4)

Median filtering of white Gaussian noise

330

(2)

Filtering of impulsive noise with median filters

332

(2)

Threshold Decomposition of Median Filters

334

(3)

Weighted Median Filters

337

(8)

Example application for weighted median filters: Fault tolerant interpolation of intermediate images

342

(3)

Further Types of Rank Order Filters

345

(4)

Separable median filters

345

(1)

Recursive median filters

345

(1)

Multistage and hybrid median filters

346

(3)

Bibliography

349

(6)

Index

355

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One- and Multidimensional Signal Processing Algorithms and Applications in Image Processing

Summary

Author Biography

Table of Contents

Supplemental Materials