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Companion Website: Digital Image Processing, 2/E www.prenhall.com/gonzalezwoods Digital Image Processing, 2/E is a completely self-contained book. The companion web site offers useful support in a number of important areas. For the Student or Independent Reader the site contains: Brief tutorials on probability, statistics, vectors, and matrices. Complete solutions to selected problems. A database containing images from the book and other educational sources. For the Instructor the site contains: Suggested curricula and sample laboratory projects. Material removed from the previous edition, downloadable in convenient PDF format. Presentation materials for the classtoom. Instructor's Manual containing complete-solutions to all the problems in the book and solutions to sample laboratory projects. (Available only to instructors who have adopted the book for classroom use.) For the Practitioner the book web site contains: Links to sites that deal with various complementary aspects of image processing. Listing of selected recent publications. Bulletin board with announcements of conferences and other professional events in the field of image processing. Listing of public domain and commercial image databases. The web site provides the means to refresh material between editions by including new topics, digital images, recent developments, and information on emerging technology. Reference to the book's web site is designated in the margins of the book by use of the icon that appears below. sm k, Digital Image Processing To Connie, Ralph, and Robert and To Janice, David, and Jonathan Contents Preface xy Acknowledgements xviii About the Authors xix ] Introduction 1 1.1 What Is Digital Image Processing? 1 1.2 The Origins of Digital Image Processing 3 13 Examples of Fields that Use Digital Image Processing 7 13.1 Gamma-Ray Imaging 8 13.2 X-raylmaging 9 1.3.3 Imaging in the Ultraviolet Band 11 1.34 Imaging in the Visible and Infrared Bands 12 1.3.5 Imaging in the Microwave Band 18 1.3.6 Imaging in the Radio Band 20 1.3.7 Examples in which Other Imaging Modalities Are Used 20 14 Fundamental Steps in Digital Image Processing 25 15 Components of an Image Processing System 28 Summary 30 References and Further Reading 31 Digital Image Fundamentals 34 21 Elements of Visual Perception 34 2.1.1. Structure of the Human Eye 35 2.1.2 Image Formation in the Eye 37 21.3 Brighiness Adaptation and Discrimination 38 22 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 24 Image Sampling and Quantization 52 241 Basic Concepts in Sampling and Quantization 52 24,2 Representing Digital Images 54 24.3 Spatial and Gray-Level Resolution 57 2.4.4 Aliasing and Moiré Patterns 62 24.5 Zooming and Shrinking Digital Images 64 vii A.2 4.3 44 45 4.6 Contents Introduction to the Fourier Transform and the Frequency Domain 149 4.2.1 The One-Dimensional Fourier Transform and its Inverse 150 42.2 The Two-Dimensional DFT and Its Inverse 154 4.23 Filtering in the Frequency Domain 156 42.4 Correspondence between Tiltering in the Spatial and Frequency Domains 161 Smocthing Frequency-Domain Filters 167 4.3,] Ideal Lowpass Filters 167 43.2 Butterworth Lowpass Filters 173 4.33 Gaussian Lowpass Filters 175 43.4 Additional Examples of Lowpass Filtering 178 Sharpening Frequency Domain Filters 180 4.41 Ideal Highpass Filters 182 4.4.2 Butterworth Highpass Filters 183 44,3 Gaussian Highpass Filters 184 +44 The Laplacian in the Frequency Domain 185 44.5 Unsharp Masking, High-Boost Filtering, and High-Frequency Emphasis Filtering 187 Homomorphkic Filtering 191 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 198 463 More on Periodicity: the Need for Padding 199 4.64 The Convolution and Correlation Theorems 205 4.6.5 Summary of Properties of the 2-1 Fourier Transform 208 4.66 The Fast Fourier Transform 208 4.6.7 Some Comments on Filter Design 213 Summary 214 References 214 Problems 215 Image Restoration 220 A Model of the Image Degradation/Restoration Process 221 Noise Models 222 5.2.1 Spatial and Frequency Properties of Noise 222 5.2.2 Some Important Nojse Probability Density Functions 222 5.2.3 Periodic Noise 227 5.24 Estimation of Noise Parameters 227 Restoration in the Presence of Noise Oniy-Spatial Filtering 230 5.3.1 Mean Filters 231 5.3.2 Order-Statistics Filters 233 5.3.3 Adaptive Filters 237 3x Contents 54 Periodic Noise Reduction by Frequency Domain Filtering 243 5.4.1 Bandreject Filters 244 5.4.2 Bandpass Filters 245 5.43 Notch Filters 246 5.44 Optimum Notch Filtering 248 5.5 Linear, Position-Invariant Degradations 254 5.6 Estimating the Degradation Function 256 3.6.1 Estimation by Image Observation 256 5.6.2 Estimation by Experimentation 257 5.6.3 Estimation by Modeling 258 5.7 Inverse Filtering 261 5.8 Minimum Mean Square Error (Wiener) Filtering 262 5.9 Constrained Least Squares Filtering 266 5.10 Geometric Mean Filter 270 5.11 Geometric Transformations 270 5.11.1 Spatial Transformations 271 5.11.2 Gray-Level Interpolation 272 Summary 276 References and Further Reading 277 Problems 278 6 Color Image Processing 282 6.1 Color Fundamentals 283 6.2 Color Models 289 6.2.1 The RGB Color Model 290 6.2.2 The CMY and CMYK Color Models 294 6.2.3 The HSI Color Model 295 6.3 Pseudocolor Image Processing 302 6.3.1 Intensity Shcing 303 6.3.2 Gray Level to Color Transformations 308 6.4 Basics of Full-Color Image Processing 313 6.5 Color Transformations 315 6.5.1 Formulation 315 6.5.2 Color Complements 318 6.53 Color Slicing 320 Tone and Color Corrections 322 6.5.5 Histogram Processing 326 6.6 Smoothing and Sharpening 327 6.6.1 Color Image Smoothing 328 6.6.2 Color Image Sharpening 330 6.7 ColorSegmentation 331 6.7.1 Segmentation in HS] Color Space 331 -7.2. Segmentation in RGB Vector Space 333 .7.3 Color Edge Detection 335 xil Contents 8.6 9.2 9.3 9.4 3.5 9.6 84.2 ZW Coding 446 843 Bit-Plane Coding 448 8.44 Lossless Predictive Coding 456 Lossy Compression 459 85.1 Lossy Predictive Coding 459 8.5.2 Transform Coding 467 8.53 WaveletCoding 486 Image Compression Standards 492 8.6.1 Binary Image Compression Standards 493 8.6.2 Continuous Tone Still Image Compression Standards 498 8.6.3 Video Compression Standards 510 Summary 513 References and Further Reading 513 Problems 514 Morphological Image Processing 519 Pretiminaries 520 9.1.1 Some Basic Concepts from Set Theory 520 9.1.2 Logic Operations Involving Binary Images 522 Dilation and Erosion 523 9.21 Dilation 523 9.22 Erosion 525 Opening and Closing 528 The Hit-or-Miss Transformation 532 Some Basic Morphological Algorithms 534 9.5.1 Boundary Extraction 534 2.5.2 Region Filling 535 9.5.3 Extraction of Connected Components 536 9.54 Convex Hull 539 9.5.5 Thinning 541 9.96 Thickening 541 9.5.7 Skeletons 543 9.58 Pruning 545 9.59. Summary of Morphological Operations on Binary Images 547 Extensions to Gray-Scale Images 550 9.6.1 Dilation 550 9.6.2 Erosion 552 9.63 Opening and Closing 554 9.6.4 Some Applications of Gray-Scale Morphology 556 Summary 560 References and Further Reading 560 Problems 560 Contents | | Image Segmentation 567 10.1 Detection of Discontinuities 568 1011 Point Detection 569 10.1,2 Line Detection 570 10.13 Edge Detection 572 10.2 Edge Linking and Boundary Detection 585 10,21 Local Processing 585 10.2.2 Global Processing via the Hough Transform 587 10.2.3 Global Processing via Graph-Theorelic Techniques 591 10.3 Thresholding 595 10.31 Foundation 595 10.3.2 The Role of Illumination 596 10.3.3 Basic Global Thresholding 598 10.34 Basic Adaptive Thresholding 600 10.3.5 Optimal Global and Adaptive Thresholding 602 10.36 Usc of Boundary Characteristics for Histogram Improvement and Local Thresholding 608 10.3.7 Thresholds Based on Several Variables 611 10.4 Region-Based Segmentation 612 10.41 Basic Formulation 612 104.2 Region Growing 613 10.4.3 Region Splitting and Merging 615 10.5 Segmentation by Morphological Watersheds 617 10.5.1 Basic Concepts 617 10.5.2 Dam Construction 620 10.5.3 Watershed Segmentation Algorithm 622 10.5.4 The Use of Markers 624 10,6 The Use of Motion in Segmentation 626 10.6.1 Spatial Techniques 626 10.6.2 Prequency Domain Techniques 630 Summary 634 References and Further Reading 634 Problems 636 | ] Representation and Description 643 11.1 Representation 644 11.1.1 Chain Codes 644 111.2 Polygonal Approximations 646 1.3 Signatures 648 11.14 Boundary Segments 649 11.1.5 Skeletons 650 xlif Preface When something can be read without effor, great effort has gone into its writing. Enrique Jardiel Poncela This edition is the most comprehensive revision of Digital image Processing since the book first appcared in 1977. As the 1977 and 1987 editions by Gonzalez and Wintz, and the 1992 edition by Gonzalez and Woods, the present edition was prepared with students and instructors in mind. Thus. the principal objectives of the book continue to be to provide an introduction to basic concepts and methodologies for digital image processing, and to develop a foundation that can be used as the basis for further study and research in this ficld. To achieve these objectives, wc again focused on material that wc believe is fundamental and has a scope of application that is not limited to the solution of specialized prob- lems, The mathematical complexity of the book remains at a level well within the grasp of collcge seniors and first-year graduate students who have intro- ductory preparation in mathematical analysis, vectors, matrices. probability, sta- tistics, and rudimentary computer programming. The present edition was influenced significantly by a recent market survey conducied by Prentice Hall. The major findings of this survey were: 1. A need for more motivation in the introductory chapter regarding the spec- trum of applications of digital image processing. 2. À simplification and shortening of material in the carly chapters in order to*pet to Lhe subject matter” as quickly as possible. + À more intuitivo presentation in some areas. such as image transforms and image restoration. . Individual chapter coverage of color image processing, wavelets, and image morphology. + An increase in the breadth of problems at the end of each chapter. ta da m The reorganization that resulted in this edition is our attempt at providing a reasonable degree of balance between rigor in the presentation, the findings of the market survey. and suggestions made by students, readers. and colteagues since the last edition of the book. The major changes made in the bovk are as follows. Chapter | was rewritten completely. The main focus of the current treatment is on examples ot areas that usc digilal image processing. While far from ex- haustive, the examples shown will leave little doubt in the reader's mind re- garding the breadth of application of digital image processing methodologies. Chapter 2 is totally new also. The focus of the presentation in lhis chapter is on how digital images are generated, and en the closely related concepts of Xv xvi Preface sampling, aliasing. Moiré patterns, and image zooming and sbrinking. The new material and the manner in which these two chapters were rcorganized address directly the first two findings in the market survey mentioncd above. Chapters 3 though 6 in the current edition cover the same concepts as Chap- ters 3 through 5 in the previous edition, but the scope is expanded and the pre- sentation is totally different. In the previous edition. Chapter 3 was devoted exclusively to image transforms. One of the major changes in the book is that image transforms are now introduced when they are needed. This allowed us to begin discussion of image processing techniques much earlier than before, fur- ther addressing the second finding of the market survey. Chapters 3 and 4in the current edition deal with image enhancement, as opposed to a single chapter (Chapter 4) in the previous edition. The new organization of this material does not imply that image enhancement is more important than other areas. Rather, we used it as an avenue to introduce spatial methods for image processing (Chapter 3), as well as the Fourter transform, the frequenty domain, and image filtering (Chapter 4). Our purpose for introducing these concepls in the context of image enhancement (a subject particularly appealing to beginners) was to in- crease the level of intuitiveness in the presentation, thus addressing partially the third major finding in the marketing survey. This organization also gives in- structors flexibility in the amount of frequency-domain material lhey wish to cover. Chapter 5 also was rewritten completely in a mure intuitive manner. The coverage of this topic in earlier editions of the book wás based on matrix theory. Although unified and elegant, this type of presentation is difficult to follow. particularly by undergraduates. The new presentation covers cssentially the same ground, but the discussion does not rely on matrix thcory and is much easier to understand, due in part to numerous new examples. The price paid for this newly gained simplicity is the loss of a unified approach, in the sense that in the earlier treatment a number of restoration results could bc derived from one basic formulation. On balance, however, we believe that readers (cspecial- ty beginners) will find the new treatment much more appcaling and casicr to fol- low. Also, as indicated below, the old material is stored in the book Web site for easy access by individuals preferring to follow a matrix-theory formutation. Chapter 6 dealing with color image processing is new. Interest in this area has increased significantly in the past [ew years as a result of growth in the use of digital images for Internet applications. Our treatment of this topic represents a significant expansion of Lhe material from previous editions. Similarly Chap- ter 7, dealing with wavelets, is new. In addition to a number of signal process- ing applications, interest in this area is motivated by the need for more sophisticated methods for image compression. a topic that in turn is motivated by a increase in the number of images transmitted over the Internet or stored in web servers. Chapter 8 dealing with image compression was updated to in- clude new compression methods and standards, but its fundamental structure remains Lhe same as in the previous edition. Several image transforms, previously covered in Chapter 3 and whose principal use is compression, were moved to this chapter. xvitii Acknowledgments We are indebted to a number of individuals in academic circles as well as in in- dustry and government who have contributed to this edition of the book. Their contributions have been important in so many different ways that we find it difficult to acknowledge them in any other manner but alphabetically. In par- ticular, we wish to extend our appreciation to our colleagues Mongi A. Abidi, William E. Blass, Ramiro Jordan, Yongmin Kim, Bryan Morse, Andrew Oldroyd, AM. Reza, Edgardo Felipe Riveron, and Jose Ruiz Shulcloper, for their many suggestions on how to improve the presentation and/or the scope of coverage in the book, Numerous individuals and organizations provided us with valuable assis- tance during the writing of this edition. Again, we list them alphabetically. We are particularly indebted to Steve Eddins and Naomi Fernandes at The Math- Works for providing us with MATLAB software and support that were important in our ability to create or clarify many of the examples and experimental results included in this edition of the book, À significant percentage of the new images Used in this edition (and in some cases their history and interpretation) were ob- tained through lhe efforts of individuals whose contributions are sincerely ap- preciated, In particular. we wish to acknowledge the eftorts of Serge Beucher, Melissa D. Binde, James Blankenship, Uwe Boos, Ernesto Bribiesca, Dragana Brzakovic, Michael E. Cascy. D. R. Cate, Michael W. Davidson, Thomas R. Gest, Lalit Gupta, Zhong He, Roger Heady, Juan Herrera, John M. Hudak, Michael Hurwitz, Chris J. Johannscn, Rhonda Knighton, Ashley Mohamed. A. Morris, Curtis C. Ober, Joseph E. Pascente, David R. Pickens. Michael Robinson, Bar- rett À, Schaefer, Michacl Shaffer, Petc Sites. Sally Stowe, Craig Watson, and David K. Wehe. We also wish to acknowledge other individuals and organiza- tions cited in the captions of numerous figures throughout Lhe book for their per- mission to usc that matcrial. Special thanks go to Tom Robbins, Rose Kernan. Alice Dworkin, Vince O'Brien, Jody McDonnell, and Heather Scott at Prentice Hall for their com- mitment to excellence in all aspects of the production of this edition of the book. Their crcativity. assistance, and patience are truly appreciated. RCG REW About the Authors Rafael C. Gonzalez R.C. Gonzalez received the B.S.E.E, degree from the University of Miami in 1965 and the M.E. and Ph.D. degrees in electrical engineering trom the Uni- versity of Florida, Guinesville. in 1967 and 1970, respectively. Ie joined the Electrical and Computer Engineering Department at University of Tennessee, Knoxville (UTK) in 1970. where he became Associate Professor in 1973. Pro- fessor in 1978, and Distinguished Service Professor in 1984, He served as Chair- man of the deparment from 1994 through 1997. He is currently a Professor Emeritus at UTK. Gonzalez is the founder of the Image & Pattern Analysis Laboratory and the Robotics & Computer Vision Laboratory at the University of Tennessee. Hc also faunded Perceptics Corporation in 1982 and was its president until 1992. The last threc years of this period were spent under a full-time employment contract with Westinghouse Corporation, who acquired the company in 1989. Under his direction. Perceptics became highly successful in image process- ing, computer vision, and laser disk storage technology. In its initial ten vears, Perceptics introduced a series of innovative products, including: The world's first commercially-available computer vision system for automatically reading the license plate on moving vehicles; a series of large-scale image processing and archiving systems used by the U.S. Navy at six different manufacturing sites throughout the country to inspect the rocket motors of missiles in the Trident N Submarine Program: the market teading family of imaging boards tor ad- vanced Macintosh computers: and a line of trillion-bytc Jaser disk products. He is a frequent consuitant to industry and government in the areas of pat- ler recognition, image processing, and machine learning. His academic honors for work in these fields include the 1977 UTK College of Engineering Faculty Achievement Award: the 1978 UTK Chancellor's Research Scholar Award: the 1980 Magnavox Engincering Professor Award; and the 1980 ME. Brooks Dis- tinguished Professor Award, In 198] he became an IBM Professor at the Uni- versily of Tennessee and in 1984 he was named à Distinguished Service Professor there. He was awarded a Distinguished Alumnus Award by the University of Miami in 1985, the Phi Kappa Phi Scholar Award in 1986. and the University of Tennessee's Nathan W Dougherty Award for Excellence in Enginccring in 1992. Honors for industrial accomplishment include the 1987 ICEE Outstanding Engineer Award far Commercial Development in Tennessee: the 1988 Albert Rose Nat Award for Excellence in Commercial Image Processing; thc 1989 B. Otto Wheeley Award for Excellence in Technology Transfer: lhe 1989 Coopers and Lybrand Entreprencur of the Year Award: the 1992 IEEE Region 3 Out- standing Engineer Award: and the 1993 Automated Imaging Association Na- tional Award for Technology Development. xix Digital Image Processing Introduction One picture is worth more then ten thousand words. Anonymous Preview Interest in digital image processing methods stems from two principal applica- tion areas: improvement of pictorial information [or human interpretation; and processing of image dala for storage. transmission, and representation for au- tonomous machine perception. This chapter has several objectives: (1) to define the scope of the ficid that we call image processing: (2) to give a historical per- spective of Lhe origins of this field; (3) ta give an idea of the state of the artin image processing by examining some of the principal areas in which it is ap- plied; (4) to discuss bricfly the principal approaches uscd in digital image pro- cessing: (5) to give an overview of the components containcd in a typical, general-purpose image processing system; and (6) to provide direction to the books and other literature where image processing work normally is reported. What Is Digital Image Processing? An image may be defined as a two-dimensional function. f(x, y), where x and vare spatial (plane) coordinates, and thc amplitude of f at any pair of coordi- nates (x, v) is called (he intensity or gray level of the image at that point. When *. y, and the amplitude values of f arc all inite, discrete quantities, we call the image a dígita! image. The field of digital inage processing refers Lo processing digital images by means of a digital computer. Note that a digital image is com- posed of a finite number of elements, each ot which has à particular location and 
