Book description
Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures.*A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data*Includes exercises, examples, and references to related or more advanced work
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Dedication
- Inside Front Cover
- Structure of this Book
- Errata
- Chapter 1: Introduction
- Chapter 2: Grids and Digitization
- Chapter 3: Metrics
- Chapter 4: Adjacency Graphs
- Chapter 5: Incidence Pseudographs
- Chapter 6: Topology
- Chapter 7: Curves and Surfaces: Topology
-
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
- Chapter 10: 2D Arc Length; Curvature and Corners
- Chapter 11: 3D Straightness and Planarity
- Chapter 12: 3D Arc Length, Surface Area, and Curvature
- Chapter 13: Hulls and Diagrams
- Chapter 14: Transformations
- Chapter 15: Morphologic Operations
- Chapter 16: Deformations
- Chapter 17: Picture Properties and Spatial Relations
- List of Algorithms
- List of Symbols
- List of Axioms and Properties
- Bibliography
- Index
Product information
- Title: Digital Geometry
- Author(s):
- Release date: September 2004
- Publisher(s): Morgan Kaufmann
- ISBN: 9780080477268
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