Nonlinear Image Processing (eBook)

Cover 1
Contents 6
Preface 10
Chapter 1. Analysis and Optimization of Weighted Order Statistic and Stack Filters 18
1.1 Introduction 18
1.2 Median and Order Statistic Filters 18
1.3 Stack Filters 19
1.4 Image Processing Applications 38
1.5 Summary 39
Chapter 2. Image Enhancement and Analysis with Weighted Medians 44
2.1 Introduction 44
2.2 Weighted Median Smoothers and Filters 45
2.3 Image Denoising 62
2.4 Image Zooming 66
2.5 Image Sharpening 69
2.6 Optimal Frequency Selection WM Filtering 75
2.7 Edge Detection 79
2.8 Conclusion 82
Chapter 3. Spatial–Rank Order Selection Filters 86
3.1 Introduction 86
3.2 Selection Filters and Spatial–Rank Ordering 89
3.3 Spatial-Rank Order Selection Filters 98
3.4 Optimization 111
3.5 Applications 113
3.6 Future Directions 122
Chapter 4. Signal-Dependent Rank-Ordered-Mean (SD-ROM) Filter 128
4.1 Introduction 128
4.2 Impulse Noise Model 129
4.3 Definitions 130
4.4 The SD-ROM Filter 131
4.5 Generalized SD-ROM Method 133
4.6 Experimental Results 138
4.7 Restoration of Images Corrupted by Streaks 143
4.8 Concluding Remarks 148
Chapter 5. Nonlinear Mean Filters and Their Applications in Image Filtering and Edge Detection 152
5.1 Introduction 152
5.2 Nonlinear Mean Filters 153
5.3 Signal-Dependent Noise Filtering by Nonlinear Means 157
5.4 Edge Detectors Based on Nonlinear Means 158
5.5 Grayscale Morphology Using £p Mean Filters 159
5.6 Ultrasonic Image Processing Using £2 Mean Filters 164
5.7 Sorting Networks Using £p Mean Comparators 174
5.8 Edge Preserving Filtering by Combining Nonlinear Means and Order Statistics 177
5.9 Summary 180
Chapter 6. Two-Dimensional Teager Filters 184
6.1 Introduction 184
6.2 Discrete Volterra Series and Properties 184
6.3 Interpretation of Frequency Responses 188
6.4 The Teager Algorithm and One-Dimensional Extensions 189
6.5 Spectrum of the Output Signal 194
6.6 Mean-Weighted Highpass Filters 196
6.7 Least-Squares Design of Edge Extracting Filters 202
6.8 Summary 211
6.9 Appendix 212
Chapter 7. Polynomial and Rational Operators for Image Processing and Analysis 220
7.1 Introduction 220
7.2 Theoretical Survey of Polynomial and Rational Filters 221
7.3 Applications of Polynomial Filters 225
7.4 Applications of Rational Filters 231
7.5 Conclusions and Remaining Issues 238
Chapter 8. Nonlinear Partial Differential Equations in Image Processing 242
8.1 Introduction 242
8.2 Segmentation of Scalar and Multivalued Images 245
8.3 Nonlinear PDEs in General Manifolds: Harmonic Maps and Direction Diffusion 252
Chapter 9. Region-Based Filtering of Images and Video Sequences: A Morphological Viewpoint 266
9.1 Introduction 266
9.2 Classical Filtering Approaches 268
9.3 Connected Operators 271
9.4 Connected Operators Based on Reconstruction Processes 273
9.5 Connected Operators Based on Region-Tree Pruning 281
9.6 Conclusions 300
Chapter 10. Differential Morphology 306
10.1 Introduction 306
10.2 2D Morphological Systems and Slope Transforms 311
10.3 PDEs for Morphological Image Analysis 317
10.4 Curve Evolution 325
10.5 Distance Transforms 327
10.6 Eikonal PDE and Distance Propagation 335
10.7 Conclusions 340
Chapter 11. Coordinate Logic Filters: Theory and Applications in Image Analysis 348
11.1 Introduction 348
11.2 Coordinate Logic Operations on Digital Signals 350
11.3 Derivation of the Coordinate Logic Filters 354
11.4 Properties of Coordinate Logic Filters 356
11.5 Morphological Filtering Using Coordinate Logic Operations on Quantized Images 357
11.6 Image Analysis and Pattern Recognition Applications 359
11.7 Concluding Remarks 369
Chapter 12. Nonlinear Filters Based on Fuzzy Models 372
12.1 Introduction 372
12.2 Fuzzy Models 373
12.3 Fuzzy Weighted Mean (FWM) Filters 376
12.4 FIRE Filters 380
12.5 Evolutionary Neural Fuzzy Filters: A Case Study 383
12.6 Concluding Remarks and Future Trends 389
Chapter 13. Digital Halftoning 392
13.1 Introduction 392
13.2 Halftone Statistics 398
13.3 Blue-Noise Dithering 402
13.4 Green-Noise Dithering 407
13.5 Conclusions 415
Chapter 14. Intrinsic Dimensionality: Nonlinear Image Operators and Higher-Order Statistics 420
14.1 Introduction 420
14.2 Transdisciplinary Relevance of Intrinsic Dimensionality 423
14.3 i2D-Selective Nonlinear Operators 430
14.4 Frequency Design Methods for i2D Operators 438
14.5 i2D Operators and Higher-Order Statistics 449
14.6 Discussion 454
Index 466
Color Plate Section 474