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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
3.
Structuring Elements
3.1.
Definition and Purpose
3.1.1.
Role in Morphological Operations
3.1.2.
Local Neighborhood Definition
3.1.3.
Geometric Interpretation
3.2.
Common Shapes
3.2.1.
Square Structuring Elements
3.2.2.
Disk Structuring Elements
3.2.3.
Line Structuring Elements
3.2.4.
Diamond Structuring Elements
3.2.5.
Cross Structuring Elements
3.3.
Size Considerations
3.3.1.
Small vs. Large Elements
3.3.2.
Impact on Operation Results
3.4.
Origin Point
3.4.1.
Definition of Origin
3.4.2.
Positioning Effects
3.4.3.
Symmetry Considerations
3.5.
Custom Structuring Elements
3.5.1.
Arbitrary Shapes
3.5.2.
Application-Specific Design
3.6.
Decomposition Techniques
3.6.1.
Separable Structuring Elements
3.6.2.
Computational Efficiency
3.6.3.
Sequential Operations
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4. Primary Morphological Operations