Digital Geometry

Geometric Methods for Digital Picture Analysis

By

  • Reinhard Klette, The University of Auckland, New Zealand
  • Azriel Rosenfeld, University of Maryland, College Park, U.S.A.

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.
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Audience

Those who want to extract information from digital images for work and personal applications, and researchers and students in digital image processing, computer vision, and computer graphics.

 

Book information

  • Published: August 2004
  • Imprint: MORGAN KAUFMANN
  • ISBN: 978-1-55860-861-0

Reviews

"[This is] a serious work. The authors have made a huge effort to present the major problems of digital geometry...It will be a very useful resource for a diversity of readers from engineers to mathematicians and from undergraduate students to scientists at the highest level."—Dr. Jovisa Zunic, Cardiff University "This book would be a great asset for professionals in the field of picture analysis, and would be ideal as a textbook in graduate courses on that subject. One must note that the book uses a standard mathematical/technical language, instead of image processing jargon, and thus is very appropriate for those engineers and scientists in other specialties who need to learn about, and work with, computer pictures." - Computing Reviews



Table of Contents

Introduction. Grids and Digitization. Metrics. Adjacency Graphs. Incidence Pseudographs. Topology: Basics. Curves and Surfaces: Topology. Curves and Surfaces: Geometry. Straightness. Arc Length and Curvature. 3D Straightness and Planarity. Surface and Area Curvature. Hulls and Diagrams. Transformations. Morphological Operations. Deformations. Other Properties and Relations. Bibliography.