Morphology

9.

Advanced Morphological Concepts

9.1.

Geodesic Morphology

9.1.1.

Geodesic Distance Concept

9.1.2.

Geodesic Dilation

9.1.2.1.

Definition and Properties

9.1.2.2.

Mask-Constrained Operations

9.1.3.

Geodesic Erosion

9.1.3.1.

Definition and Properties

9.1.3.2.

Constrained Shrinking

9.1.4.

Applications in Constrained Processing

9.2.

Morphological Reconstruction

9.2.1.

Reconstruction by Dilation

9.2.1.1.

Marker and Mask Images

9.2.1.2.

Iterative Process

9.2.1.3.

Convergence Properties

9.2.2.

Reconstruction by Erosion

9.2.2.1.

Dual Reconstruction Process

9.2.3.

Hole Filling Applications

9.2.4.

Peak and Valley Extraction

9.2.5.

Connected Component Processing

9.3.

9.3.1.

Size Distribution Analysis

9.3.2.

Pattern Spectrum Computation

9.3.3.

Particle Size Measurement

9.3.4.

Multi-Scale Characterization

9.3.5.

Statistical Analysis of Results

9.4.

Watershed Transformation

9.4.1.

Catchment Basin Concept

9.4.2.

Watershed Lines

9.4.3.

Classical Watershed Algorithm

9.4.4.

Marker-Based Watershed

9.4.4.1.

Marker Selection Strategies

9.4.4.2.

Over-Segmentation Control

9.4.5.

Applications in Image Segmentation

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8. Grayscale Morphology

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10. Theoretical Frameworks and Extensions