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Mathematics
Morphology
1. Introduction to Mathematical Morphology
2. Foundational Mathematical Concepts
3. Structuring Elements
4. Primary Morphological Operations
5. Compound Morphological Operations
6. Morphological Filtering and Enhancement
7. Pattern Detection and Shape Analysis
8. Grayscale Morphology
9. Advanced Morphological Concepts
10. Theoretical Frameworks and Extensions
11. Implementation and Computational Aspects
12. Practical Applications
8.
Grayscale Morphology
8.1.
Theoretical Foundation
8.1.1.
Extension from Set Theory to Functions
8.1.2.
Umbra Representation
8.1.3.
Top Surface Concept
8.2.
Grayscale Dilation
8.2.1.
Mathematical Definition
8.2.2.
Implementation Algorithms
8.2.3.
Effects on Bright Regions
8.2.4.
Intensity Value Changes
8.3.
Grayscale Erosion
8.3.1.
Mathematical Definition
8.3.2.
Implementation Algorithms
8.3.3.
Effects on Dark Regions
8.3.4.
Intensity Value Changes
8.4.
Grayscale Opening and Closing
8.4.1.
Definition and Properties
8.4.2.
Smoothing Effects
8.4.3.
Peak and Valley Processing
8.4.4.
Intensity Distribution Changes
8.5.
Grayscale Morphological Gradients
8.5.1.
Edge Detection in Grayscale
8.5.2.
Gradient Magnitude Computation
8.5.3.
Multi-Scale Analysis
8.6.
Grayscale Top-Hat Transforms
8.6.1.
Bright Feature Enhancement
8.6.2.
Dark Feature Enhancement
8.6.3.
Contrast Manipulation
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9. Advanced Morphological Concepts