A Grammar for Maps

Publisher Summary This chapter describes a grammar for maps. Grammars whose sentences are not strings of symbols, but rather sets of symbols that can be interconnected in more general ways, are of importance in connection with the formal theory of picture processing and description. One of the most general formalisms of this kind deals with sentences, which are labeled directed graphs, that is, webs. Webs arise naturally in connection with descriptions of pictures; a description can present the relations among objects or regions in the given picture, so that it can be represented by a web whose vertices represent regions and whose edges indicate related pairs of regions. As pictures are planar, the webs that arise in this way can mostly be planar. When a graph is used to represent the adjacency relation between regions in the plane, not all of the topological information about the regions is preserved.