Digital Image Processing

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1 Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International

2 Contents Preface xv Acknowledgments The Book Web Site xx About the Authors xxi I Introduction What Is Digital Image Processing? The Origins of Digital Image Processing Examples of Fields that Use Digital Image Processing Gamma-Ray Imaging X-Ray Imaging Imaging in the Ultraviolet Band Imaging in the Visible and Infrared Bands Imaging in the Microwave Band Imaging in the Radio Band Examples in which Other Imaging Modalities Are Used 1.4 Fundamental Steps in Digital Image Processing Components of an Image Processing System 28 Summary 31 References and Further Reading 31 L Digital Image Fundamentals Elements of Visual Perception Structure of the Human Eye Image Formation in the Eye Brightness Adaptation and Discrimination Light and the Electromagnetic Spectrum Image Sensing and Acquisition Image Acquisition Using a Single Sensor Image Acquisition Using Sensor Strips Image Acquisition Using Sensor Arrays A Simple Image Formation Model Image Sampling and Quantization Basic Concepts in Sampling and Quantization Representing Digital Images Spatial and Intensity Resolution Image Interpolation 65

3 vi Contents 2.5 Some Basic Relationships between Pixels Neighbors of a Pixel Adjacency, Connectivity, Regions, and Boundaries Distance Measures An Introduction to the Mathematical Tools Used in Digital Image Processing Array versus Matrix Operations Linear versus Nonlinear Operations Arithmetic Operations Set and Logical Operations Spatial Operations Vector and Matrix Operations Image Transforms Probabilistic Methods 96 Summary 98 References and Further Reading 98 Problems 99 J Intensity Transformations and Spatial Filtering Background The Basics of Intensity Transformations and Spatial Filtering About the Examples in This Chapter Some Basic Intensity Transformation Functions Image Negatives Log Transformations Power-Law (Gamma) Transformations Piecewise-Linear Transformation Functions Histogram Processing Histogram Equalization Histogram Matching (Specification) Local Histogram Processing Using Histogram Statistics for Image Enhancement Fundamentals of Spatial Filtering The Mechanics of Spatial Filtering Spatial Correlation and Convolution Vector Representation of Linear Filtering Generating Spatial Filter Masks Smoothing Spatial Filters Smoothing Linear Filters Order-Statistic (Nonlinear) Filters Sharpening Spatial Filters Foundation Using the Second Derivative for Image Sharpening The Laplacian 160

4 Contents vii Unsharp Masking and Highboost Filtering Using First-Order Derivatives for (Nonlinear) Image Sharpening The Gradient Combining Spatial Enhancement Methods Using Fuzzy Techniques for Intensity Transformations and Spatial Filtering Introduction Principles of Fuzzy Set Theory Using Fuzzy Sets Using Fuzzy Sets for Intensity Transformations Using Fuzzy Sets for Spatial Filtering 189 Summary 192 References and Further Reading 192 Problems Filtering in the Frequency Domain Background A Brief History of the Fourier Series and Transform About the Examples in this Chapter Preliminary Concepts Complex Numbers Fourier Series Impulses and Their Sifting Property The Fourier Transform of Functions of One Continuous Variable Convolution Sampling and the Fourier Transform of Sampled Functions Sampling The Fourier Transform of Sampled Functions The Sampling Theorem Aliasing Function Reconstruction (Recovery) from Sampled Data The Discrete Fourier Transform (DFT) of One Variable Obtaining the DFT from the Continuous Transform of a Sampled Function Relationship Between the Sampling and Frequency Intervals Extension to Functions of Two Variables The 2-D Impulse and Its Sifting Property The 2-D Continuous Fourier Transform Pair Two-Dimensional Sampling and the 2-D Sampling Theorem Aliasing in Images The 2-D Discrete Fourier Transform and Its Inverse 235

5 viii Contents 4.6 Some Properties of the 2-D Discrete Fourier Transform Relationships Between Spatial and Frequency Intervals Translation and Rotation Periodicity Symmetry Properties Fourier Spectrum and Phase Angle The 2-D Convolution Theorem Summary of 2-D Discrete Fourier Transform Properties The Basics of Filtering in the Frequency Domain Additional Characteristics of the Frequency Domain Frequency Domain Filtering Fundamentals Summary of Steps for Filtering in the Frequency Domain Correspondence Between Filtering in the Spatial and Frequency Domains Image Smoothing Using Frequency Domain Filters Ideal Lowpass Filters Butterworth Lowpass Filters Gaussian Lowpass Filters Additional Examples of Lowpass Filtering Image Sharpening Using Frequency Domain Filters Ideal Highpass Filters Butterworth Highpass Filters Gaussian Highpass Filters The Laplacian in the Frequency Domain Unsharp Masking, Highboost Filtering, and High-Frequency- Emphasis Filtering Homomorphic Filtering Selective Filtering Bandreject and Bandpass Filters Notch Filters Implementation Separability of the 2-D DFT Computing the IDFT Using a DFT Algorithm The Fast Fourier Transform (FFT) Some Comments on Filter Design 303 Summary 303 References and Further Reading 304 Problems 304 J Image Restoration and Reconstruction A Model of the Image Degradation/Restoration Process Noise Models Spatial and Frequency Properties of Noise Some Important Noise Probability Density Functions 314

6 5.2.3 Periodic Noise Estimation of Noise Parameters Restoration in the Presence of Noise Only Spatial Filtering Mean Filters Order-Statistic Filters Adaptive Filters Periodic Noise Reduction by Frequency Domain Filtering Bandreject Filters Bandpass Filters Notch Filters Optimum Notch Filtering Linear, Position-Invariant Degradations Estimating the Degradation Function Estimation by Image Observation Estimation by Experimentation Estimation by Modeling Inverse Filtering Minimum Mean Square Error (Wiener) Filtering Constrained Least Squares Filtering Geometric Mean Filter Image Reconstruction from Projections Introduction Principles of Computed Tomography (CT) Projections and the Radon Transform The Fourier-Slice Theorem Reconstruction Using Parallel-Beam Filtered Backprojections Reconstruction Using Fan-Beam Filtered Backprojections 381 Summary 387 References and Further Reading 388 Problems Color Image Processing Color Fundamentals Color Models The RGB Color Model The CMY and CMYK Color Models The HSI Color Model Pseudocolor Image Processing Intensity Slicing Intensity to Color Transformations Basics of Full-Color Image Processing Color Transformations Formulation Color Complements 430

7 X Contents Color Slicing Tone and Color Corrections Histogram Processing Smoothing and Sharpening Color Image Smoothing Color Image Sharpening Image Segmentation Based on Color Segmentation in HSI Color Space Segmentation in RGB Vector Space Color Edge Detection Noise in Color Images Color Image Compression 454 Summary 455 References and Further Reading 456 Problems 456 / Wavelets and Multiresolution Processing Background Image Pyramids Subband Coding The Haar Transform Multiresolution Expansions Series Expansions Scaling Functions Wavelet Functions Wavelet Transforms in One Dimension The Wavelet Series Expansions The Discrete Wavelet Transform The Continuous Wavelet Transform The Fast Wavelet Transform Wavelet Transforms in Two Dimensions Wavelet Packets 510 Summary 520 References and Further Reading 520 Problems 521 Image Compression Fundamentals Coding Redundancy Spatial and Temporal Redundancy Irrelevant Information Measuring Image Information Fidelity Criteria 534

8 Contents xi Image Compression Models Image Formats, Containers, and Compression Standards Some Basic Compression Methods Huffman Coding Golomb Coding Arithmetic Coding LZW Coding Run-Length Coding Symbol-Based Coding Bit-Plane Coding Block Transform Coding Predictive Coding Wavelet Coding Digital Image Watermarking 614 Summary 621 References and Further Reading 622 Problems Morphological Image Processing Preliminaries Erosion and Dilation Erosion Dilation Duality Opening and Closing The Hit-or-Miss Transformation Some Basic Morphological Algorithms Boundary Extraction Hole Filling Extraction of Connected Components Convex Hull Thinning Thickening Skeletons Pruning Morphological Reconstruction Summary of Morphological Operations on Binary Images Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 676 Summary 679 References and Further Reading 679 Problems 680

9 xii Contents 1 Image Segmentation Fundamentals Point, Line, and Edge Detection Background Detection of Isolated Points Line Detection Edge Models Basic Edge Detection More Advanced Techniques for Edge Detection Edge Linking and Boundary Detection Thresholding Foundation Basic Global Thresholding Optimum Global Thresholding Using Otsu's Method Using Image Smoothing to Improve Global Thresholding Using Edges to Improve Global Thresholding Multiple Thresholds Variable Thresholding Multivariable Thresholding Region-Based Segmentation Region Growing Region Splitting and Merging Segmentation Using Morphological Watersheds Background Dam Construction Watershed Segmentation Algorithm The Use of Markers The Use of Motion in Segmentation Spatial Techniques Frequency Domain Techniques 782 Summary 785 References and Further Reading 785 Problems 787 I Representation and Description Representation Boundary (Border) Following Chain Codes Polygonal Approximations Using Minimum-Perimeter Polygons Other Polygonal Approximation Approaches Signatures 808

10 Contents xiii Boundary Segments Skeletons Boundary Descriptors Some Simple Descriptors Shape Numbers Fourier Descriptors Statistical Moments Regional Descriptors Some Simple Descriptors Topological Descriptors Texture Moment Invariants Use of Principal Components for Description Relational Descriptors 852 Summary 856 References and Further Reading 856 Problems 857 Object Recognition Patterns and Pattern Classes Recognition Based on Decision-Theoretic Methods Matching Optimum Statistical Classifiers Neural Networks Structural Methods Matching Shape Numbers String Matching 904 Summary 906 References and Further Reading 906 Problems 907 Appendix A 910 Bibliography 915 Index 943

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