Line Generalization by Waterlining And Medial-Axis Transformation. Successes and Issues in an Implementation of Perkal's Proposal

Abstract

The hydrography of Cat Island, a rather small, albeit interesting feature in the Gulf of Mexico, is the subject of six generalizations executed with a procedure that replicates and extends Julian Perkal's proposal for an objective generalization. The automated procedure, based on the two operations known as waterlining and Medial-Axis Transformation, is shown to lead to results that should be similar to those achieved by a trained cartographer working with the traditional manual method. Three aspects of generalization are covered by the procedure: line simplification in general, and dropping and aggregation of features of simple configurations. As regards Perkal's original objective, this presentation proves that it can be achieved by a combination of waterlining operations. The Medial-Axis Transformation, a concept developed within Pattern Recognition, is proposed as the best choice for spanning Perkal's boundary zones. The six generalizations are offered as evidence that the method preserves the general shape of features for lower scale factors and yields simple and compact shapes for larger factors. However, two problems were encountered that suggest that the method still needs further development in order to maintain its fully automated character, Or, alternatively, the method may need to be interlaced with the occasional use of interactive aids. The first of those two problems is encountered in attempting to bridge boundary zones of complex configurations. The second problem arises from the specifications for an autonomous feature dropping procedure and with the need to invoke it. Both problems are considered in some depth.