A raster-based method for computing Voronoi diagrams of spatial objects using dynamic distance transformation

Abstract

The Voronoi diagram has been suggested as an appropriate model for the description of relations between spatial objects (Gold 1992) and it is the only possible solution (which is currently available) to dynamic (measurement-based) GIS (Wright and Goodchild 1997). A Voronoi diagram can be computed either in vector mode or in raster mode. Most existing methods are vector-based. However, vector-based methods are complex for line sets and area sets. To overcome this serious deficiency, attempts have also been made to use rasterbased methods. This paper describes a raster-based method for computing Voronoi diagrams of spatial objects (including points, line and areas) using dynamic distance transformation achieved by the dilation operator in mathematical morphology. Furthermore, an extension is presented to accommodate complex spatial objects.