Biomedical Image Processing with Morphology-Based Nonlinear Filters

Mark A. Schulze

Ph.D. Dissertation

The University of Texas at Austin, 1994

Table of Contents

Abstract

1. Introduction
1.1. Overview
1.2. Organization

2. Mathematical Morphology
2.1. Definitions
2.1.1. Basic Morphological Operators
2.1.2. Compound Morphological Operators
2.1.3. Examples
2.2. Deterministic Properties
2.2.1. Median Filter Root Signals
2.2.2. Relationship of Morphological and Median Filtered Signals
2.3. Statistical Properties
2.3.1. One-Dimensional Properties
2.3.2. Two-Dimensional Properties
2.4. Summary

3. New Filter Structures
3.1. Introduction
3.2. Linear Combinations of Morphological Operators
3.2.1. Definitions
3.2.2. Deterministic Properties
3.2.3. Statistical Properties
3.3. Value-and-Criterion Filter Structure
3.3.1. Introduction
3.3.2. Definition
3.3.3. The Mean of Least Variance (MLV) Filter
3.3.4. Deterministic Properties
3.3.5. Statistical Properties

4. New Analysis Techniques
4.1. Introduction
4.2. Continuous Time Analysis
4.2.1. Introduction and Definitions
4.2.2. Results
4.3. Breakdown Point
4.3.1. Definition and Analysis
4.3.2. Order Statistic Limited (a-Limited) Filters
4.3.3. Conclusions
4.4. Corner Response Analysis
4.4.1. Definitions
4.4.2. Results
4.5. Conclusions

5. Applications
5.1. Introduction
5.2. Thermography
5.2.1. Thermal Image Noise Processes
5.2.2. Filter Selection
5.2.3. Examples
5.3. Magnetic Resonance Imaging (MRI)
5.3.1. Introduction
5.3.2. Anisotropic Diffusion
5.3.3. Noise Estimation
5.3.4. Results
5.3.5. Evaluating Filter Performance Using a Phantom Image
5.3.6. Conclusions
5.4. Ultrasound
5.5. Conclusions

6. Conclusions

Appendix: Geometric Derivations of Corner Responses
A.1. Total Area of Corner
A.2. Corner Response of Morphological Opening
A.3. Corner Response of Erosion and the Midrange Filter
A.4. Corner Response of the Square Median Filter
A.5. Corner Response of the Averaging Filter
A.6. Corner Response of the Plus-Shaped Median Filter

Bibliography

© Copyright by Mark A. Schulze, 1994.

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Mark A. Schulze
http://www.markschulze.net/
mark@markschulze.net

Last Updated: 17 July 2003