In this paper we present conditions which guarantee that every digitization process preserves important topological and differential geometric properties. These conditions also allow us to determine the correct digitization resolution for a given class of real objects. Knowing that these properties are invariant under digitization, we can then use them in feature-based recognition. Moreover, these conditions imply that only a few digital patterns can occur as neighborhoods of boundary points in the digitization. This is very useful for noise detection, since if the neighborhood of a boundary point does not match one of these patterns, it must be due to noise. Our definition of a digitization approximates many real digitization processes. The digitization process is modeled as a mapping from continuous sets representing real objects to discrete sets represented as digital images. We show that an object A and the digitization of A are homotopy equivalent. This, for example, implies that the digitization of A preserves connectivity of the object and its complement. Moreover, we show that the digitization of A will not change the qualitative differential geometric properties of the boundary of A, i.e. a boundary point which is locally convex cannot be digitized to a locally concave pixel and a boundary point which is locally concave cannot be digitized to a locally convex pixel.