Place Names

A central idea behind gazetteers is that they give the user access to informa- tion items based not just on thematic but also on spatial relevance. This raises the computational problem of deciding which geographic footprints are rele- vant in respect to a given footprint. Generally, the problem is solved by defin- ing an appropriate metric on the space of geographic footprints. For points, a chessboard metric is easily obtained by superimposing a grid onto the map space. Points lying in the same grid cell as the given point (distance 0) are considered most relevant; next come points from the four immediately neigh- boring cells (distance 1).

We concentrate on the most important case, homogeneous decomposition by tessellations.

Footprints

Footprints are essential for spatial reasoning capabilities of gazetteers. Most state-of-the-practice gazetteers, however, use simple types of footprints. We distinguish between (a) point, (b) bounding box, and (c) polygons. They are shown in figure 5.4. All footprints use geographic coordinates. They are either complex and require a high data volume with high computational costs or are rather simple with limited spatial reasoning capabilities. Some state-of-the-

Fig. 5.4. Various footprints using geographical coordinates and spatial indices.

art gazetteers (e.g., GEIN7) use other types of footprints using spatial indices based on a uniform reference grid. Figure 5.4d shows an example. A clear advantage of these kinds of footprints is the ability to represent undeterminate boundaries. Also, topological relations as well as distances can be inferred. On the other hand, their fixed grid dimensions are rather counter-intuitive and from the GIS point of view they are no standard.

These shortcomings lead to a new type of footprint based on a pSRT as defined in section 5.2.1. Figure 5.5 gives an example. In the following, this footprint is used. The polygons in the plane will also be referred to as

reference units. Place names are extensionalized in terms of reference units which simply means that there exists a binary relation between a place name and a reference unit.

In a homogeneous decomposition by tessellation two kinds of structure with spatial character interact. Firstly, there is the recursive structure of the decomposition reflected by the decomposition tree. Secondly, there exists a neighborhood structure due to fact that a polygon shares each of its edges or each of its vertices with at most one other polygon.

http://www.gein.de, German Environmental Information Network, verified on June, 1st, 2003.

Fig. 5.5. Reference tessellation footprint.

Neighborhood Graph

We focus on direct neighborhoods, i.e., neighbors defined by shared edges. The following example shows that but not is a neighbor of because these polygons possess a common edge. The neighborhood structure is expressed by a graph (fig. 5.6).

Definition 5.8

The neighborhood graph of a homogeneous decomposition by tessellation is a graph with the set of undecomposed polygons as nodes and all pairs of neighboring polygons as edges

If there is no interesting information items linked to a polygonal footprint, a good place to search for further information are its neighboring polygons. Alternatively, one could search in those polygons that are part of the same de- composition. Obviously, this leads to two different criteria of spatial relevance, which will be discuss later. In other words, a spatial relevance metric can be based on either the decomposition tree or the neighborhood graph (fig. 5.6). [99] discussed the issues about inferring relevance from spatial neighborhood and concluded that known approaches based on neighborhood graphs such as the RCC calculus are not sufficient enough to provide satisfactory results if using planar polygons as a basic model.

A basic problem is linked to multiple neighborhoods. A solution to this problem of finding an adequate abstraction for a decomposition is to represent it by a connection graph.

Connection Graph

Connection graphs are planar graphs which encode topological neighborhood relations between the polygons of a tessellation. Therefore, pSRTs can be reduced to a set of connection graphs (representing neighborhood relations at different levels of granularity), which are interconnected by a decomposition tree (representing the hierarchical partonomy of reference units).

Definition 5.9

The connection graph of a homogeneous decomposition by tessellation with

neighborhood graph is a graph together with

the combinatorial embedding of in the plane. where E is the exterior, unbounded polygonal region. contains an edge for each connected sequence of polygon edges that and share. The combinatorial embedding of consists in the circular ordering of the edges from at each vertex from

Fig. 5.7. Connection graph representation of a decomposition by tessellation.

Figure 5.7 shows the connection graph of a homogeneous decomposition by tessellation D. Each polygon from D is represented by a vertex from In addition, there is the node 1 representing the external polygonal region. The edges from which are incident with a vertex are easily obtained together with their circular ordering by scanning the contour of the corresponding polygon (figure 5.7a. For polygon 5 the following circular sequence of neighbors is obtained (see additional edges in figure 5.7b): 1, 2, 4, 6, 7, 9. Note that polygon 2 which shares three edges with 5 appears only once because the three edges

are connected. The same holds for polygon 4, 6, and 9 with two edges. They have the same representation as polygon 7, which only has one edge connected to 5. As the example shows, the connection graph is a multi-graph in which several edges can join the same pair of vertices.

The connection graph representation supports a number of graph- theoretical operations which can be used to draw inferences about spatial relevance (spatial neighborhood). For example, polygonal footprints spatially relevant to a given footprint can be determined by breadth-first search in the connection graph. Another example is, to determine polygonal footprints spa- tially relevant to a given set of footprints. This can be done by the use of ordinal information given by the combinatorial embedding.

5.2.3 Place Name Structures

To overcome the mentioned limitations in reasoning capabilities we have de- veloped a new representation scheme for place names in the form of place name structures (PNS). Place name structures provide representations of the regional extent of spatial objects in geographic space. They are formalized with the help of both topological and partonomic relations to reference units provided by the pSRT.

The polygonal standard reference tessellations can be seen as an analogon to the common vocabulary described in section 4. This way, we are able to integrate heterogenous place name structures. They provide means to exten- sionally define approximate locations within a reference tessellation.

Fig. 5.8. Place name structure with binary projection on pSRT.

Figure 5.8 shows an example of such an extensional definition. The place names Land of Coburg, Fränkische Alb, and Thüringer forest are extension- alized onto a polygonal standard reference tessellation. Please note that any

place name can be extensionalized. This means that also the South-German stepland can be mapped onto the tessellation. In addition, we can derive in- tensional information out of the PNS using the partonomic structure. This kind of spatial modeling allows us to define two relations: close-to and part-of.

One might think that PNS are some kind of geo-ontology. We can argue that PNS is a specific conceptualization of geographic space, however, these “concepts” are rather instances. Also, PNS should not be confused with “on- tologies and geographic kinds” [104], where the authors argue that geographic objects are not merely located in space but are tied intrinsically to space. Furthermore, they state, that this means their spatial boundaries are in many cases the most salient features for categorization. Our place name structures are, as mentioned earlier, an extension of gazetteers and represent a specific conceptual view.