SHAPE ANALYSIS AND CLASSIFICATION: THEORY AND PRACTICE

and Roberto M. Cesar Junior

CRC Press

Chapter 6

Shape Characterization

6.1 STATISTICS FOR SHAPE DESCRIPTORS

6.2 SOME GENERAL DESCRIPTORS

• 6.2.1 Perimeter
• 6.2.2 Area
• 6.2.3 Centroid (center of mass)
• 6.2.4 Maximum and Minimum Distance to Centroid
• 6.2.5 Distance to the Boundary
• 6.2.6 Diameter
• 6.2.7 Maximum Chord
• 6.2.8 Norm Sizes
• 6.2.9 Maximum Arc Length
• 6.2.10 Major and Minor Axis
• 6.2.11 Thickness
• 6.2.12 Holes-based Shape Features
• 6.2.13 Topological Descriptors
• 6.2.14 Polygonal Approximation-Based Shape Descriptors
• 6.2.15 Shape Descriptors based on Regions and on Graphs
• 6.2.16 Complexity Descriptors

6.3 FRACTAL GEOMETRY FOR COMPLEXITY DESCRIPTORS

• 6.3.1 Preliminary Considerations and Definitions
• 6.3.2 The Box-Counting Approach
• 6.3.3 Case Example: The Classical Koch Curve
• 6.3.4 Implementing the Box-Counting Method
• 6.3.5 The Minkowski Sausage or Dilation Method

6.4 CURVATURE

• 6.4.1 Biological Motivation
• 6.4.2 Simple Approaches to Curvature
• 6.4.3 Curvature-Based Shape Descriptors
• 6.4.4 c-Curvature

6.5 SHAPE SIGNATURES

6.6 FOURIER DESCRIPTORS

• 6.6.1 Alternative Fourier Descriptors