Algebraic Models for Feature Displacement in the Generalization of Digital Map Data Using Morphological Techniques

Abstract

Feature displacement is one of the many operations (or operators) in map-data generalization. It has become a priority item on the research agenda. This paper describes some algebraic models (or mathematical models) for this operation. These models are based on the operators developed in mathematical morphology, which is a science dealing with form, shape, and structure of objects. Feature displacements can be classified into two groups, i.e., feature translation and feature modification. For the first type, a set of structuring elements (key elements in morphological operators) are developed. Using this set of structuring elements, the two basic morphological operators, i.e., dilation and erosion, can be used for translating features in any of the eight directions, freely. Translation of features in other directions can be achieved by a combination of these eight directions. For the second type of feature displacement, a number of models have been developed to suit different cases, i.e., an area feature and a linear feature, two linear features, etc. These models have also been tested using various examples. The results show that these techniques are very promising.