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Spie Press Book

An Introduction to Nonlinear Image Processing
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Book Description

From a strict semantic point of view, nonlinear image processing encompasses all image processing that is not based on linear operators; however, from a practical, evolutionary point of view, the name itself is usually associated with the study of nonlinear filters, mainly the deterministic and nondeterministic analysis and design of logic-based operators. This Tutorial Text volume explores logic-based operators with emphasis on representation, design, and statistical optimization of nonlinear filters.

Book Details

Date Published: 1 February 1994
Pages: 192
ISBN: 9780819415608
Volume: TT16

Table of Contents
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Preface xi
Chapter 1. Introduction
Chapter 2. Basic Binary Operations
2.1 Introduction
2.2 Erosion
2.3 Dilation
2.4 Opening and Closing
Chapter 3. Binary Filtering with Opening and Closing
3.1 Filter Properties
3.2 Application of Opening and Closing Filters
3.3 Alternating Sequential Filters
3.4 Invariance
3.5 Opening by Reconstruction
3.6 T-Openings
3.7 Granulometries
Chapter 4. Representation of Binary Operators
4.1 Window Logic and Increasing Operators
4.2 Representation of Increasing Operators
4.3 Hit-or-Miss Transform
4.4 Hit-or-Miss Filtering
Chapter 5. Gray-Scale Morphological Operators
5.1 Mathematical Preliminaries
5.2 Gray-Scale Erosion
5.3 Gray-Scale Dilation
5.4 Gray-Scale Opening and Closing
5.5 Filter Properties
5.6 Umbra Transform
5.7 Flat Structuring Elements
5.8 Erosion Representation for Increasing Nonlinear Filters
Chapter 6. Median and Order Statistics
6.1 Two-Dimensional Median
6.2 Algorithms
Chapter 7. Stack Filters
Chapter 8. Statistical Properties of Median-type and Stack Filters
8.1 Noise Attenuation
8.2 Median as Maximum Likelihood Estimator
Chapter 9. Optimization of Weighted Median Filters
Chapter 10. Optimal Binary Filters
10.1 Optimal Mean-Absolute-Error Filtering
10.2 Optimal Erosions
10.3 Optimal Increasing Filters via the Matheron Representation
10.4 Implementation: Design Constraints and Error Representation
10.5 Optimal Nonincreasing Filters
Chapter 11. Some Particular Nonlinear Filters
11.1 Introduction
11.2 Morphological Pseudoconvolutions
11.3 Soft Morphological Filters
11.4 Weighted Majority with Minimum Range Filters
11.5 L-Filters
11.6 Linear-Median Hybrid Filters
11.7 Homomorphic Filters
11.8 Polynomial Filters Bibliography Index |

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