Nonlinear Image Processing


  • Giovanni Sicuranza, University of Trieste, Italy

Edited By

  • Sanjit Mitra, University of California, Santa Barbara, U.S.A.


Electrical and computer engineers.


Book information

  • Published: September 2000
  • ISBN: 978-0-12-500451-0


"The book considers the following filter families, with varying emphasis, according to popularity and impact in image processing tasks:

  • honomorphic filters, relying on a generalized superposition principle
  • nonlinear mean filters, using nonlinear definitions of means
  • morphological filters, based on geometrical rather than analytical properties
  • order statistics filters, based on ordering properties of the input samples
  • polynomial filters, using polynomial expressions in the input and output samples
  • fuzzy filters, applying fuzzy reasoning to model the uncertainty typical of some image processing issues
  • nonlinear operations modeled in terms of nonlinear partial differential equations."


Table of Contents

1. Analysis and Optimization of Weighted Order Statistics and Stack Filters
S. Siren, P. Kuosmainen, K. Egiazarian, M. Gabbouj and J. Astola
1.1 Introduction
1.2 Median and Order Statistic Filters
1.3 Stack Filters
1.4 Image Processing Applications
1.5 Summary
2. Image Enhancement and Analysis with Weighted Medians
G. Arce and J. L. Paredes
2.1 Introduction
2.2 Weighted Median Smoothers and Filters
2.3 Image Denoising
2.4 Image Zooming
2.5 Image Sharpening
2.6 Optimal Frequency Selection WM Filtering
2.7 Edge Detection
2.8 Conclusion
3. Spatial-Rank Order Selection Filters
R. Hardie and K. Barner
3.1 Introduction
3.2 Selection Filters and Spatial-Rank Ordering
3.3 Spatial-Rank Order Selection Filters
3.4 Optimization
3.5 Applications
3.6 Future Directions
4. Signal-Dependent Rank-Ordered Mean (SD-ROM) Filter
E. Abreu
4.1 Introduction
4.2 Impulse Noise Model
4.3 Definitions
4.4 The SD-ROM Filter
4.5 Generalized SD-ROM Method
4.6 Experimental Results
4.7 Restoration of Images Corrupted by Streaks
4.8 Conclusing Remarks
5. Nonlinear Mean Filters and Their Applications in Image Filtering and Edge Detection
M. Pappas and I. Pitas
5.1 Introduction
5.2 Nonlinear Mean Filters
5.3 Signal-Dependent Filtering by Nonlinear Means
5.4 Edge Detectors Based on Nonlinear Means
5.5 Grayscale Morphology Using Lp Mean Filters
5.6 Ultrasonic Umage Processing Using L2 Men Filters
5.7 Sorting Networks Using Lp Mean Comparators
5.8 Edge Preserving Filtering by Combining Nonlinear Means and Order Statistics
6. Two-Dimensional Teager Filters
S. Thurnhofer
6.1 Introduction
6.2 Discrete Volterra Series and Properties
6.3 Interpretation of Frequency Responses
6.4 The Teager Algorithm and One-Dimensional Extensions
6.5 Spectrum of the Output Signal
6.6 Mean-Weighted Highpass Filters
6.7 Least-Squares Design of Edge Extracting Filters
6.8 Summary
6.9 Appendix
7. Polynomial and Rational Operators for Image Processing and Analysis
G. Ramponi
7.1 Introduction
7.2 Theoretical Survey of Polynomial and Rational Filters
7.3 Applications of Polynomial Filters
7.4 Applications of Rational Filters
7.5 Conclusions and Remaining Issues
8. Nonlinear Partial Differential Equations in Image Processing
G. Sapiro
8.1 Introduction
8.2 Segmentation of Scalar and Multivalued Images
8.3 Nonlinear PDEs in General Manifolds: Harmonic Maps and Direction Diffusion
9. Region-Based Filtering of Images and Video Sequences: a Morphological Viewpoint
P. Salembier
9.1 Introduction
9.2 Classical Filtering Approaches
9.3 Connected Operators
9.4 Connected Operators Based on Reconstruction Processes
9.5 Connected Operators Based on Region-Tree Pruning
9.6 Conclusions
10. Differential Morphology
P. Maragos
10.1 Introduction
10.2 2D Morphological Systems and Slope Transforms
10.3 PDEs for Morphological Image Analysis
10.4 Curve Evolution
10.5 Distance Tranforms
10.6 Eikonal PDE and Distance Propagation
11. Coordinate Logic Filters
B.G. Mertzios and K. Tsirikolias
11.1 Introduction
11.2 Coordinate Logic Operations on Digital Signals
11.3 Derivation of the Coordinate Logic Filters
11.4 Properties of Coordinate Logic Filters
11.5 Morphological Filtering Using Coordinate Logic Operations on Quantized Images
11.6 Image Analysis and Pattern Recognition Applications
11.7 Concluding Remarks
12. Nonlinear Filters Based on Fuzzy Models
F. Russo
12.1 Introduction
12.2 Fuzzy Models
12.3 Fuzzy Weighted Mean (FWM) Filters
12.4 FIRE Filters
12.5 Evolutionary Neural Fuzzy Filters: A Case Study
12.6 Concluding Remarks Future Trends
13. Digital Halftoning
G. Arce and D. Lau
13.1 Introduction
13.2 Halftone Statistics
13.3 Blue-Noise Dithering
13.4 Green-Noise Dithering
13.5 Conclusions
14. Intrinsic Dimensionality: Nonlinear Image Operators and Higher Order Statistics
C. Zetzsche and G. Krieg
14.1 Introduction
14.2 Transdisciplinary Relevance of Intrinsic Dimensionality
14.3 i2D-Selective Nonlinear Operators
14.4 Frequence Design Methods for i2D Operators
14.5 i2D Operators and Higher-Order Statistics
14.6 Discussions