Morphology

5.

Compound Morphological Operations

5.1.

5.1.1.

5.1.1.1.

Erosion Followed by Dilation

5.1.1.2.

Mathematical Formulation

5.1.2.

Geometric Interpretation

5.1.2.1.

Smoothing Object Boundaries

5.1.2.2.

Removing Small Protrusions

5.1.3.

5.1.3.1.

Anti-Extensivity

5.1.3.2.

5.1.3.3.

5.1.4.

5.1.4.1.

5.1.4.2.

Shape Simplification

5.1.4.3.

Object Separation

5.2.

5.2.1.

5.2.1.1.

Dilation Followed by Erosion

5.2.1.2.

Mathematical Formulation

5.2.2.

Geometric Interpretation

5.2.2.1.

Filling Small Holes

5.2.2.2.

Connecting Nearby Objects

5.2.3.

5.2.3.1.

5.2.3.2.

5.2.3.3.

5.2.4.

5.2.4.1.

5.2.4.2.

Object Connection

5.2.4.3.

Boundary Smoothing

5.3.

Duality of Opening and Closing

5.3.1.

Mathematical Relationship

5.3.2.

Complementary Effects

5.3.3.

Combined Applications

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4. Primary Morphological Operations

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6. Morphological Filtering and Enhancement