Digitization Approach

Abstract

In this Chapter we relate topological and geometric properties of digital objects to their continuous originals by digitization and embedding approaches. A digitization is modeled as a mapping from the real plane or space to a discrete graph structure. Based on technical properties of sampling devices which are the main source of spatial information for artificial systems, the graph structure is usually assumed to form a square grid and is modeled as a finite subset of Z ² (or Z ³ for computer tomography scanners) with some adjacency relations. For example, digital images obtained by a CCD camera are represented as finite rectangular subsets of Z ². We characterize a digitization as a function that maps subset of the real plane to discrete objects represented in a graph structure. Our starting point is a digitization and segmentation scheme defined in Pavlidis [120] and in Gross and Latecki [55], in which the sensor value depends on the area of the object in the square at which the sensor is centered.