Nonlinear Image Processing book cover

Nonlinear Image Processing

Electrical and computer engineers.

Hardbound, 455 pages

Published: September 2000

Imprint: Academic Press

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."



  • Preface
    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


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