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.KeywordsAdjacency GraphHomotopy EquivalentOrthographic ProjectionTopology PreservationDigital LineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.