Conceptual Aspects: How Landmarks Can Be Described in Data Models - Landmarks: GIScience for Intelligent Services - page 124

￿ The Voronoi diagram assumes equally-weighted objects, but according to obser-

vations like the ones by Sadalla et al. distances are perceived asymmetrically.
A better reflection of neighborhoods of weighted objects would be a weighted
Voronoi diagram.

4.2.5.2 Hierarchies by Spatial Granularity

The hierarchy by spatial granularity is typically part of the data structures of a spatial
database. Such hierarchic structures exist for gazetteers, which can link each entity
to the larger object it belongs to [ 26 ] , as well as geometric spatial databases, which
provide the topological structures between layers of object categories in order to rea-
son for containment. Here, we refer to models that actually make use of these hier-
archic structures in either generating or understanding place descriptions [ 57 , 68 ] .

4.2.5.3 Hierarchies by Cognitive Salience

Hierarchy by cognitive salience cannot be derived from database content. It depends
on the partial order that is imposed by cognitive and social properties such as
prominence or uniqueness. Prominence imposes a partial order between objects by
ranking them for being known by a population. A partial order by uniqueness can be
established by the size of the region in which an object is unique. For example, the
Royal Melbourne Hospital is unique in Melbourne, and the corner store opposite of
the hospital is unique within the vista space of the hospital, but not within the city.
Alternatively, a partial order can be produced directly from the cognitive and social
properties of the objects. These properties, we have seen before, may be outstanding
only to some degree, but not be unique. Sorrows and Hirtle [ 53 ] considered visible,
structural and semantic properties of objects as relevant in this context, and others
have developed a measure of salience based on these properties [ 33 , 46 ] .
The partial order is useful to establish a leveled hierarchy. The quantitative
prominence or salience measures can be linked together with the spatial neighbor-
hood structure of the reference regions to define these levels [ 66 ] . The process starts
with the Voronoi diagram of all known landmarks. Each landmark's reference region
is the area where the dominance of this landmark is stronger than the dominance of
any other competing landmark, but with the high density of landmarks these refer-
ence regions will be relatively small even for very prominent landmarks. Thus, in an
recursive procedure the quantity of landmarkness is considered for each cell, such
that the local maxima are lifted to the next level of the hierarchy, and a new Voronoi
diagram is computed. This way the reference regions grow from level to level, as
the seed elements of the Voronoi diagram are focusing on the more salient ones.
For example, Fig. 4.1 shows the Voronoi Diagram of the set of Melbourne's inner
city train stations Melbourne Central , Southern Cross , Flagstaff , Parliament ,and
Flinders Street . Considering that these train stations have largely varying landmark-
ness, proportional to the traffic they attract, a partial order can be established. The