Scope and reports
Discrete geometry plays an essential role in the field of image analysis, computer graphics, pattern recognition, shape modelling, computer vision, and document analysis. The main reason is, of course, that all data in the computer is unavoidably discrete. It has some well known and used concepts, new results regularly appear, and useful theorems and developments have still to be proposed. Discrete geometry provides both a theoretical and a computational framework for digital images.
Discrete geometry is not a new discipline, but has appeared as a main field of computer imagery since more than 40 years. The foundations of discrete geometry are coming from the need of definitions and transformations based on the discrete space, rather than application of continuous and Euclidean notions. Well-known scientistss such as A. Rosenfeld, J-L. Pfaltz, G. Herman, and E. Khalimsky were the precursors of these researches, and many others followed their ideas.
The development of efficient devices for image or video acquisition and processing, the increasing number of applications for both specific domains (medicine and biology, remote sensing, control, design) and common uses (DVD, Internet, HDTV, etc) are also important motivations and reasons to develop new results for the discrete space.
Consequently, dealing with images implies developing discrete models to be used in the above mentioned fields. For this reason, discrete geometry plays an important role. Several more precise topics of research dealing directly with discrete spaces can be given such as topology, digitized objects, shape representation and understanding, geometrical transforms, metrics, coding and compression, curves, surfaces and volumes, shape recovery, image reconstruction, visualisation, and feature extraction.