Primal/Dual Spatial Relationships and Applications PRIMAL/DUAL SPATIAL RELATIONSHIPS AND APPLICATIONS

It is well known that extraction of the skeleton of a polygon from its outline may aid in the perception or classification of its form. It has also been suggested that the ‘exoskeleton’ may be used to express the relationships between objects in space. A new algorithm has been developed that extracts both the boundary and the skeleton of the spatial representation of an object in one easy step, based on local properties of the Delaunay/Voronoi diagram, without requiring additional information, such as point order or polygon labelling. This displays and preserves the fundamental relationships between the boundary and the skeleton that helps considerably in many cartographic problems. Illustrations include contour map input and terrain visualization; watershed and flow estimation from river network input, and drainage network estimation from basin boundaries; topological reconstruction from scanned map input, and text recognition and placement in cadastral maps. The concept of preservation of the ‘form’ of the skeleton suggests methods for map generalization without significant loss of meaning. Spatial uncertainty may also be addressed in terms of the boundary sampling requirements and permissible locational error without loss of the ability to interpret the basic form, spatial relationships and meaning of the map. Introduction Blum’s Medial Axis Transform In a previous paper (Gold, 1992) we argued that the medial axis transform/skeleton might form part of our perceptual processes. Here we would like to extend that to suggest that given the