Morphology

10.

Theoretical Frameworks and Extensions

10.1.

Complete Lattices

10.1.1.

Lattice Theory in Morphology

10.1.2.

Supremum and Infimum Operations

10.1.3.

Morphological Operators as Lattice Mappings

10.1.4.

Adjunction Properties

10.2.

Algebraic Morphology

10.2.1.

Morphological Operators

10.2.2.

Composition and Decomposition

10.2.3.

Operator Properties

10.2.4.

Morphological Filters

10.3.

Graph-Based Morphology

10.3.1.

Graph Representation of Images

10.3.2.

Morphological Operations on Graphs

10.3.3.

Connectivity Considerations

10.3.4.

Applications to Irregular Structures

10.4.

Fuzzy Mathematical Morphology

10.4.1.

Fuzzy Set Theory Foundation

10.4.2.

Fuzzy Membership Functions

10.4.3.

Fuzzy Dilation and Erosion

10.4.4.

T-Norms and T-Conorms

10.4.5.

Applications in Uncertain Data

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9. Advanced Morphological Concepts

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11. Implementation and Computational Aspects