Discrete geometry aims for a characterisation of the geometrical properties of a set of discrete points. Geometrical properties of a set are understood to be global properties. In discrete geometry, points are grouped, thus forming discrete objects, and it is the properties of these discrete objects that are under study. In contrast, digital topology as described in Chapter 1 allows for the study of the local properties between discrete points within such an object. In short, topological properties such as connectivity and neighbourhood are first used to define discrete objects and discrete geometry then characterises the properties of these discrete objects. A possible approach is to consider discrete object as digitisation of continuous objects and to map the properties of the original continuous object in the classic Euclidean geometry onto properties in discrete geometry. In this context, there is first a need for definitions and models of digitisaition schemes. The resulting discrete geometrical properties will clearly be highly dependent on the digitisation scheme. Ideally, one would rather seek discrete geometrical properties that are unrelated to the context in which the discrete object is studied (i.e. independent of the digitisation scheme used). Generally, a combined approach is used. Definitions of concepts in discrete geometry are given via relations to their continuous counterparts (e.g. straightness, convexity). However, characterisations of such properties are derived in a purely discrete approach. The aim of such characterisations is the development of algorithms related to geometric properties. For example, given a set of discrete points, one would be able to test it against a definition of discrete straightness (i.e. the fact that it is a digital straight segment or otherwise) without any reference to a specific continuous segment. . . . . . . . . . ㅅㅂㅂ......................