Digital Geometry

Preface

Digital geometry deals with the geometric properties of subsets of digital pictures and with the approximation of geometric properties of objects by making use of the properties of the digital picture subsets that represent the objects. It emerged in the second half of the 20th century with the initiation of research in the fields of computer graphics and digital image analysis. It has its mathematical roots in graph theory and discrete topology; it deals with sets of grid points which are also studied in number theory (since C.F. Gauss) and the geometry of numbers, or with cell complexes (which have been studied in topology since the middle of the 19th century). Studies of gridding techniques, such as those by Gauss, Dirichlet, or ...