《Digital Image Processing》Second Edition，Rafael C. Gonzalez Richard E. Woods

Digital image Processing Second edition Rafael C. gonzalez University of Tennessee Richard e woods MedData interactive Prentice Hall Prentice hall Upper Saddle River, New jersey 07458

Digital Image Processing Second Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive Prentice Hall Upper Saddle River, New Jersey 07458 GONZFM-i-xxii. 5-10-2001 14:22 Page iii

Library of Congress Cataloging-in-Pubblication Data Gonzalez. Rafael C. Digital Image Processing Richard E Woods N0-201 1. Digital Imaging. 2. Digital Techniques. I. Title. TA1632G662001 2001035846 Vice-President and Editorial Director. ECS: Marcia. Horton Publisher: tom robbins Associate Editor: Alice Dworkin Editorial Assistant: Jody McDonnell Vice President and director of production and manufacturing ESM: David w riccardi Executive Managing Editor: Vince O Brien Managing Editor: David A. George Production editor: rose kernan Composition: Prepare, Inc. Director of Creative Services: Paul Belfanti Creative Director: Carole anson Art Director and cover designer: heather scott Art Editor: Greg Dulles Manufacturing Manager: Trudy Pisciotta Manufacturing Buyer: Lisa McDowell Senior Marketing Manager: Jennie Burger Prentis o 2002 by Prentice-Hall Inc. Upper Saddle River, New Jersey 07458 All rights reserved. No part of this book may be produced, in any form or by any means, without permission in writing from the publisher include the development, research, and testing of the theories and programs to determine thel o The author and publisher of this book have used their best efforts in preparing this book. These efforts effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Printed in the united States of america 10987654321 IsBN:口-己01-1吕075-吕 Pearson Education ltd. London Pearson Education Australia Ptv, Limited, Sydney Pearson Education Singapore, Pte. Ltd Pearson Education North Asia Ltd, Hong Kong Pearson Education Canada Ltd, Toronto Pearson Education de mexico. s.A. de C.v. Pearson Education--Japan, Toky Pearson Education Malaysia, Pte Ltd Education, Upper Saddle River, New Jersey

Library of Congress Cataloging-in-Pubblication Data Gonzalez, Rafael C. Digital Image Processing / Richard E. Woods p. cm. Includes bibliographical references ISBN 0-201-18075-8 1. Digital Imaging. 2. Digital Techniques. I. Title. TA1632.G66 2001 621.3—dc21 2001035846 CIP Vice-President and Editorial Director, ECS: Marcia J. Horton Publisher: Tom Robbins Associate Editor: Alice Dworkin Editorial Assistant: Jody McDonnell Vice President and Director of Production and Manufacturing, ESM: David W. Riccardi Executive Managing Editor: Vince O’Brien Managing Editor: David A. George Production Editor: Rose Kernan Composition: Prepare, Inc. Director of Creative Services: Paul Belfanti Creative Director: Carole Anson Art Director and Cover Designer: Heather Scott Art Editor: Greg Dulles Manufacturing Manager: Trudy Pisciotti Manufacturing Buyer: Lisa McDowell Senior Marketing Manager: Jennie Burger © 2002 by Prentice-Hall, 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. The author 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 author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 0-201-18075-8 Pearson Education Ltd., London Pearson Education Australia Pty., Limited, Sydney Pearson Education Singapore, Pte. Ltd. Pearson Education North Asia Ltd., Hong Kong Pearson Education Canada, Ltd., Toronto Pearson Education de Mexico, S.A. de C.V. Pearson Education—Japan, Tokyo Pearson Education Malaysia, Pte. Ltd. Pearson Education, Upper Saddle River, New Jersey GONZFM-i-xxii. 5-10-2001 14:22 Page iv

Contents Preface xu Acknowledgements xviii About the authors xix Introduction 15 1.1 What Is Digital Image Processing? 1.2 The Origins of Digital Image Processing 17 1.3 Examples of Fields that Use Digital Image Processing 21 1.3.1 Gamma-Ray Imaging 22 1.3.2 X-ray Imaging 23 1.3.3 Imaging in the Ultraviolet Band 2 1.3.4 Imaging in the Visible and Infrared Bands 26 1.3.5 Imaging in the Microwave Band 32 1.3.6 Imaging in the Radio Band 34 1.3.7 Examples in which Other Imaging Modalities Are Used 34 1.4 Fundamental Steps in Digital Image Processing 39 1.5 Components of an Image Processing System 42 References and Further Reading 45 Digital Image Fundamentals 34 2.1 Elements of Visual Perception 34 2.1.1 Structure of the Human Eye 35 2.1.2 Image Formation in the Eye 37 2.1.3 Brightness Adaptation and Discrimination 38 2.2 Light and the Electromagnetic Spectrum 42 2.3 Image Sensing and Acquisition 45 2.3.1 Image Acquisition Using a Single Sensor 47 2.3.2 Image Acquisition Using Sensor Strips 48 2.3.3 Image Acquisition Using Sensor Arrays 49 2.3.4 A Simple Image Formation Model 50 2.4 Image Sampling and Quantization 52 2.4.1 Basic Concepts in Sampling and Quantization 52 2.4.2 Representing Digital Images 54 2.4.3 Spatial and Gray-Level Resolution 57 2.4.4 Aliasing and Moire Patterns 62 2.4.5 Zooming and Shrinking Digital Images 64 vI

Contents Preface xv Acknowledgements xviii About the Authors xix 1 Introduction 15 1.1 What Is Digital Image Processing? 15 1.2 The Origins of Digital Image Processing 17 1.3 Examples of Fields that Use Digital Image Processing 21 1.3.1 Gamma-Ray Imaging 22 1.3.2 X-ray Imaging 23 1.3.3 Imaging in the Ultraviolet Band 25 1.3.4 Imaging in the Visible and Infrared Bands 26 1.3.5 Imaging in the Microwave Band 32 1.3.6 Imaging in the Radio Band 34 1.3.7 Examples in which Other Imaging Modalities Are Used 34 1.4 Fundamental Steps in Digital Image Processing 39 1.5 Components of an Image Processing System 42 Summary 44 References and Further Reading 45 2 Digital Image Fundamentals 34 2.1 Elements of Visual Perception 34 2.1.1 Structure of the Human Eye 35 2.1.2 Image Formation in the Eye 37 2.1.3 Brightness Adaptation and Discrimination 38 2.2 Light and the Electromagnetic Spectrum 42 2.3 Image Sensing and Acquisition 45 2.3.1 Image Acquisition Using a Single Sensor 47 2.3.2 Image Acquisition Using Sensor Strips 48 2.3.3 Image Acquisition Using Sensor Arrays 49 2.3.4 A Simple Image Formation Model 50 2.4 Image Sampling and Quantization 52 2.4.1 Basic Concepts in Sampling and Quantization 52 2.4.2 Representing Digital Images 54 2.4.3 Spatial and Gray-Level Resolution 57 2.4.4 Aliasing and Moiré Patterns 62 2.4.5 Zooming and Shrinking Digital Images 64 vii GONZFM-i-xxii. 5-10-2001 14:22 Page vii

vil■ Contents 2.5 Some Basic Relationships Between Pixels 66 5.1 Neighbors of a Pixel 5.2 Adjacency, Connectivity, Regions, and Boundaries 66 2.5.3 Distance Measures 68 2.5.4 Image Operations on a Pixel Basis 69 2.6 Linear and Nonlinear Operations 70 eferences and Further Reading 70 Problems 71 Image enhancement in the spatial domain 75 3.1 Background 76 3.2 Some Basic Gray Level Transformations 78 3.2.1 Image Negatives 78 3.2.2 Log Transformations 79 3.2.3 Power-Law Transformations 80 3.2.4 Piecewise-Linear Transformation Functions 85 3.3 Histogram Processing 88 3.3.1 Histogram Equalization 91 3. 2 Histogram Matching(Specification) 94 3.3.3 Local Enhancement 103 3.3.4 Use of Histogram Statistics for Image Enhancement 103 3.4 Enhancement Using Arithmetic/Logic Operations 108 3.4.1 Image Subtraction 110 3.4.2 Image Averaging 112 3.5 Basics of Spatial Filtering 116 3.6 Smoothing Spatial Filters 119 3.6.1 Smoothing Linear Filters 119 3.6.2 Order-Statistics Filters 12 3.7 Sharpening Spatial Filters 125 3.7.1 Foundation 125 3.7.2 Use of Second Derivatives for Enhancement- The Laplacian 128 3.7.3 Use of first Derivatives for enhancement--The gradient 1 Combining Spatial Enhancement Methods 137 41 References and Further reading 142 Problems 142 Image enhancement in the Frequency Domain 147 4.1 Background 148

2.5 Some Basic Relationships Between Pixels 66 2.5.1 Neighbors of a Pixel 66 2.5.2 Adjacency, Connectivity, Regions, and Boundaries 66 2.5.3 Distance Measures 68 2.5.4 Image Operations on a Pixel Basis 69 2.6 Linear and Nonlinear Operations 70 Summary 70 References and Further Reading 70 Problems 71 3 Image Enhancement in the Spatial Domain 75 3.1 Background 76 3.2 Some Basic Gray Level Transformations 78 3.2.1 Image Negatives 78 3.2.2 Log Transformations 79 3.2.3 Power-Law Transformations 80 3.2.4 Piecewise-Linear Transformation Functions 85 3.3 Histogram Processing 88 3.3.1 Histogram Equalization 91 3.3.2 Histogram Matching (Specification) 94 3.3.3 Local Enhancement 103 3.3.4 Use of Histogram Statistics for Image Enhancement 103 3.4 Enhancement Using Arithmetic/Logic Operations 108 3.4.1 Image Subtraction 110 3.4.2 Image Averaging 112 3.5 Basics of Spatial Filtering 116 3.6 Smoothing Spatial Filters 119 3.6.1 Smoothing Linear Filters 119 3.6.2 Order-Statistics Filters 123 3.7 Sharpening Spatial Filters 125 3.7.1 Foundation 125 3.7.2 Use of Second Derivatives for Enhancement– The Laplacian 128 3.7.3 Use of First Derivatives for Enhancement—The Gradient 134 3.8 Combining Spatial Enhancement Methods 137 Summary 141 References and Further Reading 142 Problems 142 4 Image Enhancement in the Frequency Domain 147 4.1 Background 148 viii ■ Contents GONZFM-i-xxii. 5-10-2001 14:22 Page viii

4.2 Introduction to the Fourier Transform and the Frequency Domain 149 4.2.1 The One-Dimensional Fourier Transform and its Inverse 150 4.2.2 The Two-Dimensional DFT and Its Inverse 154 4.2.3 Filtering in the Frequency Domain 15 4.2.4 Correspondence between Filtering in the Spatial and Frequency domains 161 4.3 Smoothing Frequency-Domain Filters 167 4.3.1 Ideal Lowpass Filters 167 4.3.2 Butterworth Lowpass Filters 173 4.3.3 Gaussian Lowpass Filters 175 4.3.4 Additional Examples of Lowpass Filtering 4.4 Sharpening Frequency Domain Filters 180 4.4.1 Ideal Highpass Filters 182 4.4.2 Butterworth Highpass Filters 183 4.4.3 Gaussian Highpass Filters 184 4.4.4 The Laplacian in the Frequency Domain 185 4.4.5 Unsharp Masking, High-Boost Filtering and High-Frequency Emphasis Filtering 18 4.5 Homomorphic Filtering 191 4.6 Implementation 194 4.6.1 Some Additional Properties of the 2-D Fourier Transform 194 4.6.2 Computing the Inverse Fourier Transform Using a Forward Transform Algorithm 198 4.6.3 More on Periodicity: the Need for Padding 199 4.6.4 The Convolution and Correlation Theorems 205 4.6.5 Summary of Properties of the 2-D Fourier Transform 208 4.6.6 The Fast Fourier Transform 208 4.6.7 Some Comments on Filter Design 213 Summary 214 References 214 Problems 215 Image Restoration 220 5.1 A Model of the Image Degradation/Restoration Process 221 5.2 Noise models 222 5.2.1 Spatial and Frequency Properties of Noise 222 5.2.2 Some Important Noise Probability Density Functions 222 5.2.3 Periodic Noise 227 5.2.4 Estimation of Noise Parameters 227 5.3 Restoration in the Presence of Noise Only-Spatial Filtering 230 5.3.1 Mean Filters 231 5.3.2 Order-Statistics Filters 233 5.3.3 Adaptive Filters 237

4.2 Introduction to the Fourier Transform and the Frequency Domain 149 4.2.1 The One-Dimensional Fourier Transform and its Inverse 150 4.2.2 The Two-Dimensional DFT and Its Inverse 154 4.2.3 Filtering in the Frequency Domain 156 4.2.4 Correspondence between Filtering in the Spatial and Frequency Domains 161 4.3 Smoothing Frequency-Domain Filters 167 4.3.1 Ideal Lowpass Filters 167 4.3.2 Butterworth Lowpass Filters 173 4.3.3 Gaussian Lowpass Filters 175 4.3.4 Additional Examples of Lowpass Filtering 178 4.4 Sharpening Frequency Domain Filters 180 4.4.1 Ideal Highpass Filters 182 4.4.2 Butterworth Highpass Filters 183 4.4.3 Gaussian Highpass Filters 184 4.4.4 The Laplacian in the Frequency Domain 185 4.4.5 Unsharp Masking, High-Boost Filtering, and High-Frequency Emphasis Filtering 187 4.5 Homomorphic Filtering 191 4.6 Implementation 194 4.6.1 Some Additional Properties of the 2-D Fourier Transform 194 4.6.2 Computing the Inverse Fourier Transform Using a Forward Transform Algorithm 198 4.6.3 More on Periodicity: the Need for Padding 199 4.6.4 The Convolution and Correlation Theorems 205 4.6.5 Summary of Properties of the 2-D Fourier Transform 208 4.6.6 The Fast Fourier Transform 208 4.6.7 Some Comments on Filter Design 213 Summary 214 References 214 Problems 215 5 Image Restoration 220 5.1 A Model of the Image Degradation/Restoration Process 221 5.2 Noise Models 222 5.2.1 Spatial and Frequency Properties of Noise 222 5.2.2 Some Important Noise Probability Density Functions 222 5.2.3 Periodic Noise 227 5.2.4 Estimation of Noise Parameters 227 5.3 Restoration in the Presence of Noise Only–Spatial Filtering 230 5.3.1 Mean Filters 231 5.3.2 Order-Statistics Filters 233 5.3.3 Adaptive Filters 237 ■ Contents ix GONZFM-i-xxii. 5-10-2001 14:22 Page ix