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and many 
of its concepts from both cartography and the object 
oriented approaches of computer science. This mixture 
of the idiom of different disciplines leads often to 
confusion so that the concepts that are covered by the 
terminology become fuzzy. This confusion may send 
researchers in the wrong direction when they want to 
solve multi-scale problems. In this paper a data base 
perspective for multi-scale approaches will be presented, 
emphasising the role of topologic and semantic (hierarchi- 
cal) data models. 
The different concepts that play arole in the generalization 
of spatial data will be discussed in relation to several 
strategies which can be used for solving multi-scale 
problems. 
1.2 Spatial Databases and Multi-Scale Problems 
A spatial database contains data that representin principle 
elementary statements about some spatial situation. These 
elementary statements refer to the relationships between 
objects and geometric data and thematic data etc. Query 
operations are applied to derive other statements that 
contain more relevant information for the user, e.g. about 
the state of the objects and about their mutual relation- 
ships. The semantics of the derived statements is generally 
of a higher level of complexity than the stored data. They 
should help the user to understand the structure of the 
mapped area, therefore they often refer to spatial 
relationships between the mapped objects. If the area 
structure should be understood at a higher abstraction 
level though, these derived statements could also refer 
to relationships among aggregated objects. The under- 
standing of the structure of an area at several abstraction 
levels is strongly related to the problem of spatial 
generalization and multi scale representations. 
Aggregation hierarchies for spatial objects can serve as 
basic tools for multiple representations of geo-data within 
the context of conceptual generalization (information 
abstraction) processes. These aggregation hierarchies can 
be based on the formal data structure (FDS) for single 
valued vector maps (Molenaar 1989), which combines 
aspects of object-oriented and topologic datamodels. 
Point-, line- and area objects are represented with their 
geometric and thematic data. Their geometric represen- 
tation supports the analysis of topologic object relation- 
ships, whereas their thematic description is structured in 
object classes that form generalization hierarchies. These 
class hierarchies together with the topologic object 
relationships support the definition of aggregation 
hierarchies of objects. The classification- and aggregation 
hierarchies play an important role in linking the definition 
of spatial objects at several scale levels. Accordingly, 
these structures are fundamental in the definition of rules 
for modelling generalization of spatial information at 
different resolution levels. The capacity of Geographical 
Information Systems (GIS) to register and handle 
topological information in combination with object 
hierarchies makes them very useful tools for the automa- 
tion of conceptual generalization of spatial data. 
In a cartographic context, generalization can be defined 
as the process of abstracting the representation of 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
geographic information when the scale of a map is changed. 
It is a complex process involving abstraction of thematic 
as well as geometric data of objects. The process usually 
involves two phases: 
a) a conceptual generalization phase, which implies 
the determination of the content of arepresentation 
in the generalized situation (information abstraction), 
and the definition of rules how the generalized 
objects can be derived from the objects at lower 
generalization level 
b) a graphical generalization phase (cartographic 
generalization), which implies the application of 
algorithms for geometric simplification of shapes 
and for symbolization to assure map legibility. 
Information abstraction in these subprocesses is mainly 
determined by expert knowledge and can usually be 
expressed as logical rules. These rules are susceptible to 
be translated as database management procedures in a 
GIS environment (Martinez Casasnovas 1994, Richardson 
1993). Regarding information abstraction, several processes 
are recognized: classification, association, (class) 
generalization and aggregation. Class generalization and 
aggregation are directly related to changes in the level of 
definition of objects when the mapping scale changes. 
Aggregation is the combination of elementary objects to 
build composite objects and will be based on two types 
of rules: 
a rules specifying the classes of elementary objects 
building a composite object and 
b rulesspecifying the geometric characteristics (such 
as minimum size) and topological relationships of 
these elementary objects (i.e. adjacency, 
connectivity, proximity, etc.). 
The syntactic structure of a data model for handling 
topologic and hierarchical relationships between spatial 
objects will be explained in this article. Processes for 
database generalization will be formulated with this data 
model. 
2. A SPATIAL DATA MODEL FOR MULTI-SCALE 
APPROACHES 
2.1 Topologic Structures for the Representation of 
Spatial Objects 
Entity Types for Spatial Data 
The spatial structure of an area can be expressed in terms 
of point-, line- and area objects. Their spatial extend and 
their topologic relationships will be expressed by means 
of a set of geometric elements. (Frank ea 1986) showed 
that the geometric structure of a vector map can be 
described by means of cell complexes. For a two dimen- 
sional map these consist of O-cells, 1-cells and 2-cells. 
The O-cells and 1-cells play similar roles as respectively 
the nodes and edges when the geometry of the map is 
interpreted as a planar graph. The 2-cells can then be 
compared to the faces related to the planar graph through 
Eulers formula (Gersting 1993). The terminology of the 
planar graph interpretation will be used here, but their 
relationships will be formulated as those for cells according 
to the concepts presented in (Molenaar 1994). This 
formulation is then based on 
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