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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
2.
Foundational Mathematical Concepts
2.1.
Set Theory for Image Processing
2.1.1.
Basic Set Definitions
2.1.1.1.
Sets and Elements
2.1.1.2.
Pixels as Set Elements
2.1.2.
Set Relationships
2.1.2.1.
Subsets and Supersets
2.1.2.2.
Inclusion Properties
2.1.3.
Set Operations
2.1.3.1.
Union
2.1.3.2.
Intersection
2.1.3.3.
Complement
2.1.3.4.
Difference
2.2.
Spatial Transformations
2.2.1.
Translation of Sets
2.2.1.1.
Definition and Properties
2.2.1.2.
Geometric Interpretation
2.2.2.
Reflection of Sets
2.2.2.1.
Definition and Properties
2.2.2.2.
Role in Morphological Operations
2.3.
Minkowski Set Operations
2.3.1.
Minkowski Addition
2.3.1.1.
Mathematical Definition
2.3.1.2.
Geometric Interpretation
2.3.2.
Minkowski Subtraction
2.3.2.1.
Mathematical Definition
2.3.2.2.
Geometric Interpretation
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1. Introduction to Mathematical Morphology
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3. Structuring Elements