Restricting Scalability with Granularity

Granularity as described by Hobbs [5] is a parameter of context that restricts a) the available objects and b) the categories and properties for characterizing objects. Geographic spatial granularity is mainly determined by size, and surfaces in geography as scale-dependency. Goodchild [4] points out that one main specialty of geographic attributes is scale-specificity : A region that is assigned the attribute urban is linked to a specific scale. Zooming in on the region should result in details being displayed; the urban region dissolves into city blocks, parks, streets, etc. Zooming out, the region will disappear and an annotated dot will represent the city visually. Spatial information systems are often ignorant on issues of spatial granularity. Vector graphics are supposed to be arbitrarily scalable, and consequently arbitrarily exact. Geographic entities—as objects determined by approximative measurement—are therefore not accurately represented by data formats like vector graphics, if we cannot restrict scalability. Bennett [2] introduces a concept of forest as dependent on levels of granularity. The forest is a good example for a geographic entity which is not arbitrarily scalable: We may be uncertain about whether a certain given tree at the border of a forest still belongs to the forest, but it seems odd to ask whether a certain leaf on a tree belongs to the forest. An answer of common sense could be: yes, if the tree belongs to the forest; no, if not. The trees constitute the forest, and the region of the forest is derived from the locations of the trees. The common sense concepts of forest and tree depend on human object recognition: We know when we are in a forest. One could conclude that we know where the region of the forest is, because we obviously seem to know whether the region we occupy is inside the region of the forest. But do we then also know whether some arbitrarily small portion of space belongs to this region? Is a breach in the branches of a tree a hole in the forest? The two questions obviously contain an error in granularity which is closely linked to the scale-specificity of geographic information in general. We can decide whether a region of a given minimal grain size is inside the forest, but not whether a smaller region or even a point belongs to the region, because there is a procedure that determines the