Nonlinear Image Processing

Preface1. "Analysis and Optimization of Weighted Order Statistics and Stack Filters" S. Siren, P. Kuosmainen, K. Egiazarian, M. Gabbouj and J. Astola1.1 Introduction1.2 Median and Order Statistic Filters1.3 Stack Filters1.4 Image Processing Applications1.5 Summary2. "Image Enhancement and Analysis with Weighted Medians" G. Arce and J. L. Paredes2.1 Introduction 2.2 Weighted Median Smoothers and Filters2.3 Image Denoising 2.4 Image Zooming2.5 Image Sharpening2.6 Optimal Frequency Selection WM Filtering2.7 Edge Detection2.8 Conclusion3. "Spatial-Rank Order Selection Filters" R. Hardie and K. Barner3.1 Introduction3.2 Selection Filters and Spatial-Rank Ordering3.3 Spatial-Rank Order Selection Filters3.4 Optimization3.5 Applications3.6 Future Directions4. "Signal-Dependent Rank-Ordered Mean (SD-ROM) Filter" E. Abreu4.1 Introduction4.2 Impulse Noise Model4.3 Definitions4.4 The SD-ROM Filter4.5 Generalized SD-ROM Method4.6 Experimental Results4.7 Restoration of Images Corrupted by Streaks4.8 Conclusing Remarks5. "Nonlinear Mean Filters and Their Applications in Image Filtering and Edge Detection" M. Pappas and I. Pitas5.1 Introduction5.2 Nonlinear Mean Filters5.3 Signal-Dependent Filtering by Nonlinear Means5.4 Edge Detectors Based on Nonlinear Means5.5 Grayscale Morphology Using Lp Mean Filters5.6 Ultrasonic Umage Processing Using L2 Men Filters5.7 Sorting Networks Using Lp Mean Comparators5.8 Edge Preserving Filtering by Combining Nonlinear Means and Order Statistics 6. "Two-Dimensional Teager Filters" S. Thurnhofer6.1 Introduction6.2 Discrete Volterra Series and Properties6.3 Interpretation of Frequency Responses6.4 The Teager Algorithm and One-Dimensional Extensions6.5 Spectrum of the Output Signal6.6 Mean-Weighted Highpass Filters6.7 Least-Squares Design of Edge Extracting Filters6.8 Summary6.9 Appendix7. "Polynomial and Rational Operators for Image Processing and Analysis" G. Ramponi7.1 Introduction7.2 Theoretical Survey of Polynomial and Rational Filters7.3 Applications of Polynomial Filters7.4 Applications of Rational Filters7.5 Conclusions and Remaining Issues8. "Nonlinear Partial Differential Equations in Image Processing" G. Sapiro8.1 Introduction8.2 Segmentation of Scalar and Multivalued Images8.3 Nonlinear PDEs in General Manifolds: Harmonic Maps and Direction Diffusion9. "Region-Based Filtering of Images and Video Sequences: a Morphological Viewpoint" P. Salembier9.1 Introduction9.2 Classical Filtering Approaches9.3 Connected Operators9.4 Connected Operators Based on Reconstruction Processes9.5 Connected Operators Based on Region-Tree Pruning9.6 Conclusions10. "Differential Morphology" P. Maragos10.1 Introduction10.2 2D Morphological Systems and Slope Transforms10.3 PDEs for Morphological Image Analysis10.4 Curve Evolution10.5 Distance Tranforms10.6 Eikonal PDE and Distance Propagation11. "Coordinate Logic Filters" B.G. Mertzios and K. Tsirikolias11.1 Introduction11.2 Coordinate Logic Operations on Digital Signals11.3 Derivation of the Coordinate Logic Filters11.4 Properties of Coordinate Logic Filters11.5 Morphological Filtering Using Coordinate Logic Operations on Quantized Images11.6 Image Analysis and Pattern Recognition Applications11.7 Concluding Remarks12. "Nonlinear Filters Based on Fuzzy Models" F. Russo12.1 Introduction12.2 Fuzzy Models 12.3 Fuzzy Weighted Mean (FWM) Filters12.4 FIRE Filters12.5 Evolutionary Neural Fuzzy Filters: A Case Study12.6 Concluding Remarks Future Trends13. "Digital Halftoning" G. Arce and D. Lau13.1 Introduction13.2 Halftone Statistics13.3 Blue-Noise Dithering13.4 Green-Noise Dithering13.5 Conclusions14. "Intrinsic Dimensionality: Nonlinear Image Operators and Higher Order Statistics" C. Zetzsche and G. Krieg14.1 Introduction14.2 Transdisciplinary Relevance of Intrinsic Dimensionality14.3 i2D-Selective Nonlinear Operators14.4 Frequence Design Methods for i2D Operators14.5 i2D Operators and Higher-Order Statistics14.6 DiscussionsINDEX