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by Azriel Rosenfeld, Reinhard Klette
Digital Geometry
Cover image
Title page
Table of Contents
Copyright
Preface
Dedication
Inside Front Cover
Structure of this Book
Errata
Chapter 1: Introduction
1.1 Pictures
1.2 Digital Geometry and Related Disciplines
1.3 Exercises
1.4 Commented Bibliography
Chapter 2: Grids and Digitization
2.1 The Grid Pointand Grid Cell Modesls
2.2 Connected Components
2.3 Digitization Models
2.4 Property Estimation
2.5 Exercises
2.6 Commented Bibliography
Chapter 3: Metrics
3.1 Basics About Metrics
3.2 Grid Point Metrics
3.3 Grid Cell Metrics
3.4 Metrics on Pictures
3.5 Exercises
3.6 Commented Bibliography
Chapter 4: Adjacency Graphs
4.1 Graphs, Adjacency Structures, and Adjacency Graphs
4.2 Some Basics of Graph Theory
4.3 Oriented Adjacency Graphs
4.4 Combinatorial Maps
4.5 Exercises
4.6 Commented Bibliography
Chapter 5: Incidence Pseudographs
5.1 Incidence Structures
5.2 Boundaries, Frontiers, and the Euler Characteristic
5.3 The Regular Case
5.4 Pictures on Incidence Grids
5.5 Exercises
5.6 Commented Bibliography
Chapter 6: Topology
6.1 Topologic Spaces
6.2 Digital Topologies
6.3 Topologic Concepts
6.4 Combinatorial Topology
6.5 Exercises
6.6 Commented Bibliography
Chapter 7: Curves and Surfaces: Topology
7.1 Curves in the Euclidean Topology
7.2 Curves in Incidence Grids
7.3 Curves in Adjacency Grids
7.4 Surfaces in the Euclidean Topology
7.5 Surfaces and Separations in 3D Grids
7.6 Exercises
7.7 Commented Bibliography
Chapter 8: Curves and Surfaces: Geometry
8.1 Planar Curves and Arcs
8.2 Space Curves and Arcs
8.3 Surfaces and Solids
8.3.3 Example: an ellipsoid
8.3.4 Gauss ’ definition of surface curvature
8.3.5 Principal, Gaussian, and mean surface curvature
8.3.6 Volume
8.3.7 Isothetic polyhedra
8.4 Surface Tracing and Approximation
8.5 Exercises
8.6 Commented Bibliography
Chapter 9: 2D Straightness
9.1 Basics
9.2 Supporting Lines
9.3 Self-Similarity
9.4 Periodicity
9.5 Number-Theoretic Properties
9.6 Algorithms
9.7 Exercises
9.8 Commented Bibliography
Chapter 10: 2D Arc Length; Curvature and Corners
10.1 The Length of a Digital Curve
10.2 Definitions of 2D Arc Length Estimators
10.3 Evaluation of 2D Arc Length Estimators
10.4 The Curvature of a Planar Digital Curve
10.5 Exercises
10.6 Commented Bibliography
Chapter 11: 3D Straightness and Planarity
11.1 3D Straightness
11.2 Digital Planes in 3D Adjacency Grids
11.3 Digital Planes in the 3D Incidence Grid
11.4 DPS Recognition and Generation
11.5 Exercises
11.6 Commented Bibliography
Chapter 12: 3D Arc Length, Surface Area, and Curvature
12.1 3D Arcs
12.2 Surface Area Estimation
12.3 Surface Curvature Estimation
12.4 Exercises
12.5 Commented Bibliography
Chapter 13: Hulls and Diagrams
13.1 Hulls
13.2 2D Digital Convexity
13.3 Diagrams
13.4 Exercises
13.5 Commented Bibliography
Chapter 14: Transformations
14.1 Geometries
14.2 Axiomatic Digital Geometry
14.3 Transformation Groups and Symmetries
14.4 Neighborhood-Preserving Transformations
14.5 Applying Transformations to Pictures
14.6 Magnification and Demagnification
14.7 Digital Tomography
14.8 Exercises
14.9 Commented Bibliography
Chapter 15: Morphologic Operations
15.1 Dilation
15.2 Erosion
15.3 Combining Dilations and Erosions
15.4 Simplification
15.5 Segmentation
15.6 Decomposition
15.7 Exercises
15.8 Commented Bibliography
Chapter 16: Deformations
16.1 Topology-Preserving Deformations and Simple Pixels
16.2 Shrinking
16.3 Thinning
16.4 Deformations of Curves
16.5 Interchangeable Pairs of Pixels
16.6 Deformations of 3D Pictures
16.7 Deformations of Multivalued Pictures
16.8 Exercises
16.9 Commented Bibliography
Chapter 17: Picture Properties and Spatial Relations
17.1 Properties
17.2 Moments
17.3 Experimental Evaluation of Moment Estimates
17.4 Operations on Pictures and Invariant Properties
17.5 Spatial Relations
17.6 Exercises
17.7 Commented Bibliography
List of Algorithms
List of Symbols
List of Axioms and Properties
Bibliography
Index
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