Functional Extensions of a Raster Representation for Topological Relations

Abstract

Topological relations are not well defined for raster representations. In particular the widely used classification of topological relations based on the nine-intersection [8,5] cannot be applied to raster representations [9]. But a raster representation can be completed with edges and corners [14] to become a cell complex with the usual topological relations [16]. Although it is fascinating to abolish some conceptual differences between vector and raster, such a model appeared as of theoretical interest only.

In this paper definitions for topological relations on a raster – using the extended model – are given and systematically transformed to functions which can be applied to a regular raster representation. The extended model is used only as a concept; it need not to be stored. It becomes thus possible to determine the topological relation between two regions, given in raster representation, with the same reasoning as in vector representations. This contributes to the merging of raster and vector operations. It demonstrates how the same conceptual operations can be used for both representations, thus hiding in one more instance the difference between them.