Digital Geometry

"[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

Reinhard Klette is Professor of Information Technology in the department of computer science at the University of Auckland, New Zealand, and director of the Center for Image Technology and Robotics (CITR), Tamaki. His research interests are directed toward theoretical and applied subjects in image data computing, robot vision, visualization, pattern recognition, image analysis, and image understanding. He has published more than 200 journal and conference papers on many topics in computer science, as well as books about parallel processing, image processing, and shape recovery based on visual information. He has been a plenary speaker at several major international conferences in Europe, North America, and Australasia. The late Azriel Rosenfeld was a tenured research professor, a distinguished university professor, and the Founding Director of the Center for Automation Research at the University of Maryland in College Park, where he also held affiliate professorships in the departments of computer science, electrical engineering, and psychology. Dr. Rosenfeld was widely regarded as the leading researcher in the world in the field of computer image analysis. Over a period of nearly 40 years, he made fundamental and pioneering contributions to nearly every area of that field. He wrote the first textbook in the field, was founding editor of its first journal, and was co-chairman of its first international conference. He published over 30 books and over 600 book chapters and journal articles, and directed nearly 60 Ph.D. dissertations. Dr. Rosenfeld's research on digital image analysisspecifically on digital geometry and topology and the accurate measurement of statistical features of digital images in the 1960s and 1970sformed the foundation for a generation of industrial vision inspection systems that have found widespread applications from the automotive to the electronics industry. He was a Fellow of the IEEE and the Washington Academy of Sciences; a Founding Fellow of the AAAI, the ACM, and the IAPR. Among his numerous awards and honors are the IEEE's Emanuel Piore Award, its Third Millennium Medal, and its Distinguished Service Award for Lifetime Achievement in Computer Vision and Pattern Recognition.

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.