Nonlinear image processing

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