Digital Geometry GEOMETRIC METHODS FOR DIGITAL PICTURE ANALYSIS

Computer graphics is about taking mathematical representations of objects and transforming them into visual displays. Digital geometry concerns the reverse process; it is about deriving geometric information from digital pictures. There have been over one thousand papers published in the forty-year history of digital geometry, but until now, never a book that defines and covers the field. Digital Geometry: Geometric Methods for Digital Picture Analysis details the concepts, algorithms, and practices of the field. It is a discipline studied by a huge number of researchers in fields such as digital image processing, medical imaging, robotics, and of course computer graphics. However, digital geometry is relatively new and still emerging as a unique field and the lack of books has made it difficult for researchers in many areas (including applied mathematics) to benefit from this work. Digital Geometry charts the rich connections of this subject to these other fields and to present a detailed analysis of results from more than 40 years of research.

Approx. 672 pages

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.

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 analysis specifically on digital geometry and topology and the accurate measurement of statistical features of digital images in the 1960s and 1970s formed 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.