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.
Complete text in PDF (Acrobat) format (1.2 MB)
Mark A. Schulze
http://www.markschulze.net/
mark@markschulze.net
Last Updated: 17 July 2003