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Digital Image Processing[3rd][Rafael C. Gonzalez][Richard E. Woods].pdf
Cover
Copyright Page
Contents
Preface
Acknowledgments
The Book Web Site
About the Authors
1 Introduction
1.1 What Is Digital Image Processing?
1.2 The Origins of Digital Image Processing
1.3 Examples of Fields that Use Digital Image Processing
1.3.1 Gamma-Ray Imaging
1.3.2 X-Ray Imaging
1.3.3 Imaging in the Ultraviolet Band
1.3.4 Imaging in the Visible and Infrared Bands
1.3.5 Imaging in the Microwave Band
1.3.6 Imaging in the Radio Band
1.3.7 Examples in which Other Imaging Modalities Are Used
1.4 Fundamental Steps in Digital Image Processing
1.5 Components of an Image Processing System
Summary
References and Further Reading
2 Digital Image Fundamentals
2.1 Elements of Visual Perception
2.1.1 Structure of the Human Eye
2.1.2 Image Formation in the Eye
2.1.3 Brightness Adaptation and Discrimination
2.2 Light and the Electromagnetic Spectrum
2.3 Image Sensing and Acquisition
2.3.1 Image Acquisition Using a Single Sensor
2.3.2 Image Acquisition Using Sensor Strips
2.3.3 Image Acquisition Using Sensor Arrays
2.3.4 A Simple Image Formation Model
2.4 Image Sampling and Quantization
2.4.1 Basic Concepts in Sampling and Quantization
2.4.2 Representing Digital Images
2.4.3 Spatial and Intensity Resolution
2.4.4 Image Interpolation
2.5 Some Basic Relationships between Pixels
2.5.1 Neighbors of a Pixel
2.5.2 Adjacency, Connectivity, Regions, and Boundaries
2.5.3 Distance Measures
2.6 An Introduction to the Mathematical Tools Used in Digital Image Processing
2.6.1 Array versus Matrix Operations
2.6.2 Linear versus Nonlinear Operations
2.6.3 Arithmetic Operations
2.6.4 Set and Logical Operations
2.6.5 Spatial Operations
2.6.6 Vector and Matrix Operations
2.6.7 Image Transforms
2.6.8 Probabilistic Methods
Summary
References and Further Reading
Problems
3 Intensity Transformations and Spatial Filtering
3.1 Background
3.1.1 The Basics of Intensity Transformations and Spatial Filtering
3.1.2 About the Examples in This Chapter
3.2 Some Basic Intensity Transformation Functions
3.2.1 Image Negatives
3.2.2 Log Transformations
3.2.3 Power-Law (Gamma) Transformations
3.2.4 Piecewise-Linear Transformation Functions
3.3 Histogram Processing
3.3.1 Histogram Equalization
3.3.2 Histogram Matching (Specification)
3.3.3 Local Histogram Processing
3.3.4 Using Histogram Statistics for Image Enhancement
3.4 Fundamentals of Spatial Filtering
3.4.1 The Mechanics of Spatial Filtering
3.4.2 Spatial Correlation and Convolution
3.4.3 Vector Representation of Linear Filtering
3.4.4 Generating Spatial Filter Masks
3.5 Smoothing Spatial Filters
3.5.1 Smoothing Linear Filters
3.5.2 Order-Statistic (Nonlinear) Filters
3.6 Sharpening Spatial Filters
3.6.1 Foundation
3.6.2 Using the Second Derivative for Image Sharpening—The Laplacian
3.6.3 Unsharp Masking and Highboost Filtering
3.6.4 Using First-Order Derivatives for (Nonlinear) Image Sharpening—The Gradient
3.7 Combining Spatial Enhancement Methods
3.8 Using Fuzzy Techniques for Intensity Transformations and Spatial Filtering
3.8.1 Introduction
3.8.2 Principles of Fuzzy Set Theory
3.8.3 Using Fuzzy Sets
3.8.4 Using Fuzzy Sets for Intensity Transformations
3.8.5 Using Fuzzy Sets for Spatial Filtering
Summary
References and Further Reading
Problems
4 Filtering in the Frequency Domain
4.1 Background
4.1.1 A Brief History of the Fourier Series and Transform
4.1.2 About the Examples in this Chapter
4.2 Preliminary Concepts
4.2.1 Complex Numbers
4.2.2 Fourier Series
4.2.3 Impulses and Their Sifting Property
4.2.4 The Fourier Transform of Functions of One Continuous Variable
4.2.5 Convolution
4.3 Sampling and the Fourier Transform of Sampled Functions
4.3.1 Sampling
4.3.2 The Fourier Transform of Sampled Functions
4.3.3 The Sampling Theorem
4.3.4 Aliasing
4.3.5 Function Reconstruction (Recovery) from Sampled Data
4.4 The Discrete Fourier Transform (DFT) of One Variable
4.4.1 Obtaining the DFT from the Continuous Transform of a Sampled Function
4.4.2 Relationship Between the Sampling and Frequency Intervals
4.5 Extension to Functions of Two Variables
4.5.1 The 2-D Impulse and Its Sifting Property
4.5.2 The 2-D Continuous Fourier Transform Pair
4.5.3 Two-Dimensional Sampling and the 2-D Sampling Theorem
4.5.4 Aliasing in Images
4.5.5 The 2-D Discrete Fourier Transform and Its Inverse
4.6 Some Properties of the 2-D Discrete Fourier Transform
4.6.1 Relationships Between Spatial and Frequency Intervals
4.6.2 Translation and Rotation
4.6.3 Periodicity
4.6.4 Symmetry Properties
4.6.5 Fourier Spectrum and Phase Angle
4.6.6 The 2-D Convolution Theorem
4.6.7 Summary of 2-D Discrete Fourier Transform Properties
4.7 The Basics of Filtering in the Frequency Domain
4.7.1 Additional Characteristics of the Frequency Domain
4.7.2 Frequency Domain Filtering Fundamentals
4.7.3 Summary of Steps for Filtering in the Frequency Domain
4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
4.8 Image Smoothing Using Frequency Domain Filters
4.8.1 Ideal Lowpass Filters
4.8.2 Butterworth Lowpass Filters
4.8.3 Gaussian Lowpass Filters
4.8.4 Additional Examples of Lowpass Filtering
4.9 Image Sharpening Using Frequency Domain Filters
4.9.1 Ideal Highpass Filters
4.9.2 Butterworth Highpass Filters
4.9.3 Gaussian Highpass Filters
4.9.4 The Laplacian in the Frequency Domain
4.9.5 Unsharp Masking, Highboost Filtering, and High-Frequency- Emphasis Filtering
4.9.6 Homomorphic Filtering
4.10 Selective Filtering
4.10.1 Bandreject and Bandpass Filters
4.10.2 Notch Filters
4.11 Implementation
4.11.1 Separability of the 2-D DFT
4.11.2 Computing the IDFT Using a DFT Algorithm
4.11.3 The Fast Fourier Transform (FFT)
4.11.4 Some Comments on Filter Design
Summary
References and Further Reading
Problems
5 Image Restoration and Reconstruction
5.1 A Model of the Image Degradation/Restoration Process
5.2 Noise Models
5.2.1 Spatial and Frequency Properties of Noise
5.2.2 Some Important Noise Probability Density Functions
5.2.3 Periodic Noise
5.2.4 Estimation of Noise Parameters
5.3 Restoration in the Presence of Noise Only—Spatial Filtering
5.3.1 Mean Filters
5.3.2 Order-Statistic Filters
5.3.3 Adaptive Filters
5.4 Periodic Noise Reduction by Frequency Domain Filtering
5.4.1 Bandreject Filters
5.4.2 Bandpass Filters
5.4.3 Notch Filters
5.4.4 Optimum Notch Filtering
5.5 Linear, Position-Invariant Degradations
5.6 Estimating the Degradation Function
5.6.1 Estimation by Image Observation
5.6.2 Estimation by Experimentation
5.6.3 Estimation by Modeling
5.7 Inverse Filtering
5.8 Minimum Mean Square Error (Wiener) Filtering
5.9 Constrained Least Squares Filtering
5.10 Geometric Mean Filter
5.11 Image Reconstruction from Projections
5.11.1 Introduction
5.11.2 Principles of Computed Tomography (CT)
5.11.3 Projections and the Radon Transform
5.11.4 The Fourier-Slice Theorem
5.11.5 Reconstruction Using Parallel-Beam Filtered Backprojections
5.11.6 Reconstruction Using Fan-Beam Filtered Backprojections
Summary
References and Further Reading
Problems
6 Color Image Processing
6.1 Color Fundamentals
6.2 Color Models
6.2.1 The RGB Color Model
6.2.2 The CMY and CMYK Color Models
6.2.3 The HSI Color Model
6.3 Pseudocolor Image Processing
6.3.1 Intensity Slicing
6.3.2 Intensity to Color Transformations
6.4 Basics of Full-Color Image Processing
6.5 Color Transformations
6.5.1 Formulation
6.5.2 Color Complements
6.5.3 Color Slicing
6.5.4 Tone and Color Corrections
6.5.5 Histogram Processing
6.6 Smoothing and Sharpening
6.6.1 Color Image Smoothing
6.6.2 Color Image Sharpening
6.7 Image Segmentation Based on Color
6.7.1 Segmentation in HSI Color Space
6.7.2 Segmentation in RGB Vector Space
6.7.3 Color Edge Detection
6.8 Noise in Color Images
6.9 Color Image Compression
Summary
References and Further Reading
Problems
7 Wavelets and Multiresolution Processing
7.1 Background
7.1.1 Image Pyramids
7.1.2 Subband Coding
7.1.3 The Haar Transform
7.2 Multiresolution Expansions
7.2.1 Series Expansions
7.2.2 Scaling Functions
7.2.3 Wavelet Functions
7.3 Wavelet Transforms in One Dimension
7.3.1 The Wavelet Series Expansions
7.3.2 The Discrete Wavelet Transform
7.3.3 The Continuous Wavelet Transform
7.4 The Fast Wavelet Transform
7.5 Wavelet Transforms in Two Dimensions
7.6 Wavelet Packets
Summary
References and Further Reading
Problems
8 Image Compression
8.1 Fundamentals
8.1.1 Coding Redundancy
8.1.2 Spatial and Temporal Redundancy
8.1.3 Irrelevant Information
8.1.4 Measuring Image Information
8.1.5 Fidelity Criteria
8.1.6 Image Compression Models
8.1.7 Image Formats, Containers, and Compression Standards
8.2 Some Basic Compression Methods
8.2.1 Huffman Coding
8.2.2 Golomb Coding
8.2.3 Arithmetic Coding
8.2.4 LZW Coding
8.2.5 Run-Length Coding
8.2.6 Symbol-Based Coding
8.2.7 Bit-Plane Coding
8.2.8 Block Transform Coding
8.2.9 Predictive Coding
8.2.10 Wavelet Coding
8.3 Digital Image Watermarking
Summary
References and Further Reading
Problems
9 Morphological Image Processing
9.1 Preliminaries
9.2 Erosion and Dilation
9.2.1 Erosion
9.2.2 Dilation
9.2.3 Duality
9.3 Opening and Closing
9.4 The Hit-or-Miss Transformation
9.5 Some Basic Morphological Algorithms
9.5.1 Boundary Extraction
9.5.2 Hole Filling
9.5.3 Extraction of Connected Components
9.5.4 Convex Hull
9.5.5 Thinning
9.5.6 Thickening
9.5.7 Skeletons
9.5.8 Pruning
9.5.9 Morphological Reconstruction
9.5.10 Summary of Morphological Operations on Binary Images
9.6 Gray-Scale Morphology
9.6.1 Erosion and Dilation
9.6.2 Opening and Closing
9.6.3 Some Basic Gray-Scale Morphological Algorithms
9.6.4 Gray-Scale Morphological Reconstruction
Summary
References and Further Reading
Problems
10 Image Segmentation
10.1 Fundamentals
10.2 Point, Line, and Edge Detection
10.2.1 Background
10.2.2 Detection of Isolated Points
10.2.3 Line Detection
10.2.4 Edge Models
10.2.5 Basic Edge Detection
10.2.6 More Advanced Techniques for Edge Detection
10.2.7 Edge Linking and Boundary Detection
10.3 Thresholding
10.3.1 Foundation
10.3.2 Basic Global Thresholding
10.3.3 Optimum Global Thresholding Using Otsu’s Method
10.3.4 Using Image Smoothing to Improve Global Thresholding
10.3.5 Using Edges to Improve Global Thresholding
10.3.6 Multiple Thresholds
10.3.7 Variable Thresholding
10.3.8 Multivariable Thresholding
10.4 Region-Based Segmentation
10.4.1 Region Growing
10.4.2 Region Splitting and Merging
10.5 Segmentation Using Morphological Watersheds
10.5.1 Background
10.5.2 Dam Construction
10.5.3 Watershed Segmentation Algorithm
10.5.4 The Use of Markers
10.6 The Use of Motion in Segmentation
10.6.1 Spatial Techniques
10.6.2 Frequency Domain Techniques
Summary
References and Further Reading
Problems
11 Representation and Description
11.1 Representation
11.1.1 Boundary (Border) Following
11.1.2 Chain Codes
11.1.3 Polygonal Approximations Using Minimum-Perimeter Polygons
11.1.4 Other Polygonal Approximation Approaches
11.1.5 Signatures
11.1.6 Boundary Segments
11.1.7 Skeletons
11.2 Boundary Descriptors
11.2.1 Some Simple Descriptors
11.2.2 Shape Numbers
11.2.3 Fourier Descriptors
11.2.4 Statistical Moments
11.3 Regional Descriptors
11.3.1 Some Simple Descriptors
11.3.2 Topological Descriptors
11.3.3 Texture
11.3.4 Moment Invariants
11.4 Use of Principal Components for Description
11.5 Relational Descriptors
Summary
References and Further Reading
Problems
12 Object Recognition
12.1 Patterns and Pattern Classes
12.2 Recognition Based on Decision-Theoretic Methods
12.2.1 Matching
12.2.2 Optimum Statistical Classifiers
12.2.3 Neural Networks
12.3 Structural Methods
12.3.1 Matching Shape Numbers
12.3.2 String Matching
Summary
References and Further Reading
Problems
Appendix A
Bibliography
Index
A
B
C
D
E
F
G
H
I
J
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z
Digital Image
Processing
Third Edition
Rafael C. Gonzalez
University of Tennessee
Richard E. Woods
MedData Interactive
Upper Saddle River, NJ 07458
Library of Congress Cataloging-in-Publication Data on File
Vice President and Editorial Director, ECS: Marcia J. Horton
Executive Editor: Michael McDonald
Associate Editor: Alice Dworkin
Editorial Assistant: William Opaluch
Managing Editor: Scott Disanno
Production Editor: Rose Kernan
Director of Creative Services: Paul Belfanti
Creative Director: Juan Lopez
Art Director: Heather Scott
Art Editors: Gregory Dulles and Thomas Benfatti
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Manufacturing Buyer: Lisa McDowell
Senior Marketing Manager: Tim Galligan
© 2008 by Pearson Education, Inc.
Pearson Prentice Hall
Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved. No part of this book may be reproduced, in any form, or by any means, without
permission in writing from the publisher.
Pearson Prentice Hall® is a trademark of Pearson Education, Inc.
The authors and publisher of this book have used their best efforts in preparing this book.These efforts include
the development, research, and testing of the theories and programs to determine their effectiveness.The authors
and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the
documentation contained in this book.The authors and publisher shall not be liable in any event for incidental or
consequential damages with, or arising out of, the furnishing, performance, or use of these programs.
Printed in the United States of America.
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1
ISBN 0-13-168728-x
978-0-13-168728-8
Pearson Education Ltd., London
Pearson Education Australia Pty. Ltd., Sydney
Pearson Education Singapore, Pte., Ltd.
Pearson Education North Asia Ltd., Hong Kong
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To Samantha
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To Janice, David, and Jonathan
This page intentionally left blank
Contents
Preface xv
Acknowledgments
The Book Web Site
About the Authors
xix
xx
xxi
1 Introduction 1
1.1 What Is Digital Image Processing?
1.2 The Origins of Digital Image Processing 3
1.3 Examples of Fields that Use Digital Image Processing 7
1
1.3.1 Gamma-Ray Imaging 8
1.3.2 X-Ray Imaging 9
1.3.3
1.3.4
1.3.5
1.3.6
1.3.7 Examples in which Other Imaging Modalities Are Used 20
Imaging in the Ultraviolet Band 11
Imaging in the Visible and Infrared Bands 12
Imaging in the Microwave Band 18
Imaging in the Radio Band 20
1.4 Fundamental Steps in Digital Image Processing 25
1.5 Components of an Image Processing System 28
Summary 31
References and Further Reading 31
2 Digital Image Fundamentals
35
2.1 Elements of Visual Perception 36
2.1.1 Structure of the Human Eye
2.1.2
Image Formation in the Eye
2.1.3 Brightness Adaptation and Discrimination 39
36
38
2.2 Light and the Electromagnetic Spectrum 43
2.3
48
Image Acquisition Using a Single Sensor
Image Acquisition Using Sensor Strips
Image Acquisition Using Sensor Arrays
50
Image Sensing and Acquisition 46
2.3.1
2.3.2
2.3.3
2.3.4 A Simple Image Formation Model
Image Sampling and Quantization 52
2.4.1 Basic Concepts in Sampling and Quantization 52
2.4.2 Representing Digital Images 55
2.4.3 Spatial and Intensity Resolution 59
2.4.4
Image Interpolation 65
48
50
2.4
v
vi
■ Contents
2.5 Some Basic Relationships between Pixels
68
2.5.1 Neighbors of a Pixel
2.5.2 Adjacency, Connectivity, Regions, and Boundaries
2.5.3 Distance Measures
68
71
68
2.6 An Introduction to the Mathematical Tools Used in Digital Image
72
Processing 72
2.6.1 Array versus Matrix Operations
2.6.2 Linear versus Nonlinear Operations 73
2.6.3 Arithmetic Operations 74
2.6.4 Set and Logical Operations
2.6.5 Spatial Operations 85
2.6.6 Vector and Matrix Operations
Image Transforms 93
2.6.7
2.6.8 Probabilistic Methods
Summary 98
References and Further Reading 98
Problems
80
92
96
99
3 Intensity Transformations and
Spatial Filtering
104
3.1 Background 105
3.1.1 The Basics of Intensity Transformations and Spatial Filtering 105
3.1.2 About the Examples in This Chapter
107
3.2 Some Basic Intensity Transformation Functions 107
Image Negatives 108
3.2.1
3.2.2 Log Transformations
3.2.3 Power-Law (Gamma) Transformations
110
3.2.4 Piecewise-Linear Transformation Functions
109
3.3 Histogram Processing 120
115
3.3.1 Histogram Equalization 122
3.3.2 Histogram Matching (Specification)
3.3.3 Local Histogram Processing 139
3.3.4 Using Histogram Statistics for Image Enhancement
128
139
3.4 Fundamentals of Spatial Filtering 144
3.4.1 The Mechanics of Spatial Filtering 145
3.4.2 Spatial Correlation and Convolution 146
3.4.3 Vector Representation of Linear Filtering 150
3.4.4 Generating Spatial Filter Masks 151
3.5 Smoothing Spatial Filters
152
3.5.1 Smoothing Linear Filters
3.5.2 Order-Statistic (Nonlinear) Filters 156
152
3.6 Sharpening Spatial Filters
157
3.6.1 Foundation 158
3.6.2 Using the Second Derivative for Image Sharpening—The
Laplacian 160
■ Contents
vii
3.6.3 Unsharp Masking and Highboost Filtering 162
3.6.4 Using First-Order Derivatives for (Nonlinear) Image
Sharpening—The Gradient
165
3.7 Combining Spatial Enhancement Methods
3.8 Using Fuzzy Techniques for Intensity Transformations and Spatial
169
Introduction 173
Filtering 173
3.8.1
3.8.2 Principles of Fuzzy Set Theory 174
3.8.3 Using Fuzzy Sets 178
3.8.4 Using Fuzzy Sets for Intensity Transformations
3.8.5 Using Fuzzy Sets for Spatial Filtering 189
Summary 192
References and Further Reading 192
Problems
193
186
4 Filtering in the Frequency Domain 199
4.1 Background 200
4.1.1 A Brief History of the Fourier Series and Transform 200
4.1.2 About the Examples in this Chapter
201
4.2 Preliminary Concepts
202
4.2.1 Complex Numbers 202
4.2.2 Fourier Series
4.2.3
4.2.4 The Fourier Transform of Functions of One Continuous
Impulses and Their Sifting Property 203
203
Variable
205
4.2.5 Convolution 209
4.3 Sampling and the Fourier Transform of Sampled Functions 211
4.3.1 Sampling 211
4.3.2 The Fourier Transform of Sampled Functions
4.3.3 The Sampling Theorem 213
4.3.4 Aliasing 217
4.3.5 Function Reconstruction (Recovery) from Sampled Data
220
4.4.1 Obtaining the DFT from the Continuous Transform of a
4.4 The Discrete Fourier Transform (DFT) of One Variable
212
219
4.4.2 Relationship Between the Sampling and Frequency
Sampled Function 221
Intervals
223
4.5 Extension to Functions of Two Variables 225
4.5.1 The 2-D Impulse and Its Sifting Property 225
4.5.2 The 2-D Continuous Fourier Transform Pair
4.5.3 Two-Dimensional Sampling and the 2-D Sampling
226
Theorem 227
4.5.4 Aliasing in Images
4.5.5 The 2-D Discrete Fourier Transform and Its Inverse
228
235
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