Digital Image Processing : A Signal Processing and Algorithmic Approach

This book offers readers an essential introduction to the fundamentals of digital image processing. Pursuing a signal processing and algorithmic approach, it makes the fundamentals of digital image processing accessible and easy to learn. It is written in a clear and concise manner with a large number of 4 x 4 and 8 x 8 examples, figures and detailed explanations. Each concept is developed from the basic principles and described in detail with equal emphasis on theory and practice. The book is accompanied by a companion website that provides several MATLAB programs for the implementation of image processing algorithms. The book also offers comprehensive coverage of the following topics: Enhancement, Transform processing, Restoration, Registration, Reconstruction from projections, Morphological image processing, Edge detection, Object representation and classification, Compression, and Color processing. Preface 5 About the Book 7 Contents 8 About the Author 14 Abbreviations 15 1 Introduction 16 1.1 Image Acquisition 17 1.2 Digital Image 18 1.2.1 Representation in the Spatial Domain 18 1.2.2 Representation in the Frequency Domain 21 1.3 Quantization and Sampling 22 1.3.1 Quantization 23 1.3.2 Spatial Resolution 26 1.3.3 Sampling and Aliasing 27 1.3.4 Image Reconstruction and the Moiré Effect 30 1.4 Applications of Digital Image Processing 31 1.5 The Organization of This Book 31 1.6 Summary 33 2 Image Enhancement in the Spatial Domain 37 2.1 Point Operations 37 2.1.1 Image Complement 38 2.1.2 Gamma Correction 38 2.2 Histogram Processing 40 2.2.1 Contrast Stretching 41 2.2.2 Histogram Equalization 43 2.2.3 Histogram Specification 46 2.3 Thresholding 51 2.4 Neighborhood Operations 54 2.4.1 Linear Filtering 56 2.4.2 Median Filtering 69 2.5 Summary 72 3 Fourier Analysis 79 3.1 The 1-D Discrete Fourier Transform 80 3.2 The 2-D Discrete Fourier Transform 89 3.3 DFT Representation of Images 90 3.4 Computation of the 2-D DFT 96 3.5 Properties of the 2-D DFT 101 3.6 The 1-D Fourier Transform 115 3.7 The 2-D Fourier Transform 116 3.8 Summary 117 4 Image Enhancement in the Frequency Domain 122 4.1 1-D Linear Convolution Using the DFT 123 4.2 2-D Linear Convolution Using the DFT 124 4.3 Lowpass Filtering 125 4.3.1 The Averaging Lowpass Filter 125 4.3.2 The Gaussian Lowpass Filter 130 4.4 The Laplacian Filter 136 4.4.1 Amplitude and Phase Distortions 137 4.5 Frequency-Domain Filters 139 4.5.1 Ideal Filters 139 4.5.2 The Butterworth Lowpass Filter 142 4.5.3 The Butterworth Highpass Filter 145 4.5.4 The Gaussian Lowpass Filter 147 4.5.5 The Gaussian Highpass Filter 147 4.5.6 Bandpass and Bandreject Filtering 147 4.6 Homomorphic Filtering 149 4.7 Summary 151 5 Image Restoration 155 5.1 The Image Restoration Process 155 5.2 Inverse Filtering 156 5.3 Wiener Filter 157 5.3.1 The 2-D Wiener Filter 162 5.4 Image Degradation Model 163 5.5 Characterization of the Noise and Its Reduction 166 5.5.1 Uniform Noise 166 5.5.2 Gaussian Noise 166 5.5.3 Periodic Noise 167 5.5.4 Noise Reduction 167 5.6 Summary 170 6 Geometric Transformations and Image Registration 174 6.1 Interpolation 174 6.1.1 Nearest-Neighbor Interpolation 175 6.1.2 Bilinear Interpolation 175 6.2 Affine Transform 178 6.2.1 Scaling 178 6.2.2 Shear 180 6.2.3 Translation 183 6.2.4 Rotation 184 6.3 Correlation 190 6.3.1 1-D Correlation 190 6.3.2 2-D Correlation 191 6.4 Image Registration 193 6.5 Summary 195 7 Image Reconstruction from Projections 200 7.1 The Normal Form of a Line 201 7.2 The Radon Transform 204 7.2.1 Properties of the Radon Transform 207 7.2.2 The Discrete Approximation of the Radon Transform 209 7.2.3 The Fourier-Slice Theorem 213 7.2.4 Reconstruction with Filtered Back-projections 217 7.3 Hough Transform 220 7.4 Summary 224 8 Morphological Image Processing 228 8.1 Binary Morphological Operations 229 8.1.1 Dilation 229 8.1.2 Erosion 231 8.1.3 Opening and Closing 234 8.1.4 Hit-and-Miss Transformation 240 8.1.5 Morphological Filtering 242 8.2 Binary Morphological Algorithms 244 8.2.1 Thinning 244 8.2.2 Thickening 247 8.2.3 Noise Removal 248 8.2.4 Skeletons 250 8.2.5 Fill 251 8.2.6 Boundary Extraction 252 8.2.7 Region Filling 254 8.2.8 Extraction of Connected Components 255 8.2.9 Convex Hull 255 8.2.10 Pruning 256 8.3 Grayscale Morphology 257 8.3.1 Dilation 258 8.3.2 Erosion 259 8.3.3 Opening and Closing 259 8.3.4 Top-Hat and Bottom-Hat Transformations 260 8.3.5 Morphological Gradient 261 8.4 Summary 261 9 Edge Detection 268 9.1 Edge Detection 268 9.1.1 Edge Detection by Compass Gradient Operators 275 9.2 Canny Edge Detection Algorithm 277 9.3 Laplacian of Gaussian 284 9.4 Summary 289 10 Segmentation 292 10.1 Edge-Based Segmentation 293 10.1.1 Point Detection 293 10.1.2 Line Detection 293 10.2 Threshold-Based Segmentation 295 10.2.1 Thresholding by Otsu's Method 297 10.3 Region-Based Segmentation 301 10.3.1 Region Growing 301 10.3.2 Region Splitting and Merging 304 10.4 Watershed Algorithm 306 10.4.1 The Distance Transform 306 10.4.2 The Watershed Algorithm 311 10.5 Summary 314 11 Object Description 320 11.1 Boundary Descriptors 321 11.1.1 Chain Codes 321 11.1.2 Signatures 322 11.1.3 Fourier Descriptors 323 11.2 Regional Descriptors 328 11.2.1 Geometrical Features 328 11.2.2 Moments 330 11.2.3 Textural Features 332 11.3 Principal Component Analysis 345 11.4 Summary 350 12 Object Classification 356 12.1 The k-Nearest Neighbors Classifier 356 12.2 The Minimum-Distance-to-Mean Classifier 358 12.2.1 Decision-Theoretic Methods 360 12.3 Decision Tree Classification 361 12.4 Bayesian Classification 363 12.5 k-Means Clustering 367 12.6 Summary 369 13 Image Compression 374 13.1 Lossless Compression 376 13.1.1 Huffman Coding 376 13.1.2 Run-Length Encoding 379 13.1.3 Lossless Predictive Coding 380 13.1.4 Arithmetic Coding 382 13.2 Transform-Domain Compression 393 13.2.1 The Discrete Wavelet Transform 394 13.2.2 Haar 2-D DWT 398 13.2.3 Image Compression with Haar Filters 400 13.3 Image Compression with Biorthogonal Filters 402 13.3.1 CDF 9/7 Filter 402 13.4 Summary 412 14 Color Image Processing 417 14.1 Color Models 418 14.1.1 The RGB Model 418 14.1.2 The XYZ Color Model 422 14.1.3 The CMY and CMYK Color Models 422 14.1.4 The HSI Color Model 424 14.1.5 The NTSC Color Model 429 14.1.6 The YCbCr Color Model 430 14.2 Pseudocoloring 432 14.2.1 Intensity Slicing 432 14.3 Color Image Processing 434 14.3.1 Image Complement 434 14.3.2 Contrast Enhancement 436 14.3.3 Lowpass Filtering 437 14.3.4 Highpass Filtering 438 14.3.5 Median Filtering 439 14.3.6 Edge Detection 439 14.3.7 Segmentation 442 14.4 Summary 444 Appendix A Computation of the DFT 449 A.1 The DFT Problem Formulation 449 A.2 Half-Wave Symmetry of Periodic Waveforms 450 A.3 The DFT and the Half-Wave Symmetry 450 A.4 The PM DIF DFT Algorithm 451 A.5 The PM DIT DFT Algorithm 457 Bibliography 458 Answers to Selected Exercises 459 Index 472 Front Matter ....Pages i-xvii Introduction (D. Sundararajan)....Pages 1-21 Image Enhancement in the Spatial Domain (D. Sundararajan)....Pages 23-64 Fourier Analysis (D. Sundararajan)....Pages 65-107 Image Enhancement in the Frequency Domain (D. Sundararajan)....Pages 109-141 Image Restoration (D. Sundararajan)....Pages 143-161 Geometric Transformations and Image Registration (D. Sundararajan)....Pages 163-188 Image Reconstruction from Projections (D. Sundararajan)....Pages 189-216 Morphological Image Processing (D. Sundararajan)....Pages 217-256 Edge Detection (D. Sundararajan)....Pages 257-280 Segmentation (D. Sundararajan)....Pages 281-308 Object Description (D. Sundararajan)....Pages 309-344 Object Classification (D. Sundararajan)....Pages 345-362 Image Compression (D. Sundararajan)....Pages 363-405 Color Image Processing (D. Sundararajan)....Pages 407-438 Back Matter ....Pages 439-468