. Istanbul 2004 
SPATIAL DATA MODELLING, DUAL PARTITIONS 
AND THE SPECIFICATION OF SEMANTICS 
Martien Molenaar 
International Institute for Geo-Information Science and Earth Observation (ITC) 
PO. Box 6, 7500AA Enschede 
The Netherlands 
e-mail: rector@itc.nl 
Phone: 31 - 53 - 4874 269 
Fax: 31 - 53 - 4874 355 
Key note WG IV/4 
KEY WORDS: 
Hierarchies. 
ABSTRACT: 
Spatial Data Modelling, Semantics, Spatial Objects, Spatial Partition, Thematic Partition, Object Aggregation, Class 
The main objective of GSDI is data sharing and integration. This requires the formulation of standards for data exchange. Most standards 
developed to date take mainly care of issues like the technical specification of spatial data structures, spatial operators and meta data. 
Even with these standards the user community will face significant problems in data sharing because hardly any standards are provided 
yet with respect to the semantic aspects of geo-information. Semantics is generally embedded in specific application contexts so that 
knowledge of such a context is a prerequisite for understanding the semantics of data. Yet some of the formal and theoretical aspects of 
spatial data modelling will be guiding the specification of data semantics, so that a proper understanding of these aspects will be essential 
in this respect. These issues will be discussed in this presentation. A mathematical formalization allows the formulation of rules for 
specifying spatial data models relating thematic and geometric data, based on the combination of spatial and thematic partitions. This 
dual partition structure can be seen as a constraint for unambiguous semantic specifications; this constraint implies the direct relationship 
between thematic and spatial object descriptions. Furthermore if we require that semantic specification of spatial data should always 
comply with this constraint then it should be maintained under the process of object aggregation or data generalization. This implies that 
semantic specifications of spatial objects can (or should) generally be understood in a multi aggregation (or multiscale) context. 
1. INTRODUCTION 
Data sharing and integration in a GSDI context requires the 
formulation of standards for data exchange. Presently 
organizations like OGC, ISO and other national and international 
working groups are working hard to develop such standards for 
data formats, data structures, data type definitions, operators and 
for the specifications of meta data. Systems developers and data 
providers make sure their products comply with these standards. 
These standards take mainly care of the technical aspects of data 
exchange and are of great importance for the development of geo- 
informatics. But even with these standards the user community 
will face significant problems in data sharing because no 
standards are provided yet with respect to the semantic aspects of 
geo-information. Question is whether this is possible or even 
desirable. The semantics of spatial representations is generally 
embedded in specific application contexts so that knowledge of 
such a context is a prerequisite for understanding the semantics of 
data. Yet some of the formal and theoretical aspects of spatial data 
modelling will be guiding the specification of data semantics, so 
that a proper understanding of these aspects will be essential in 
this respect. These issues will be discussed in this paper. 
Starting from some fundamental aspects of the spatial 
representation of geo-objects we can formulate a mathematical 
model for the interrelationships of thematic and geometric 
descriptions, see (Molenaar 1998). This model is fundamental for 
the specifications of unambiguous terrain descriptions, based on 
the combination of thematic and geometric partitions which 2e 
will call the dual partition structure. 
This dual partition structure can be seen as a constraint for 
unambiguous semantic specifications; this constraint implies the 
direct relationship between thematic and spatial object 
31 
descriptions. Furthermore if we require that semantic 
specification of spatial data should always comply with this 
constraint then it should be maintained under the process of object 
aggregation or data generalization. This implies that semantic 
specifications of spatial objects can (or should) generally be 
understood in a multi aggregation (or multiscale) context. 
We will discuss several aspects of this model emphasising the 
relationship between the thematic specification and spatial 
resolution. Two approaches will be discussed: 
1. The first approach is based on the relationship between the 
generalization levels of thematic class hierarchies and the 
related aggregation levels of spatial objects, the so called 
class driven object aggregation. 
The second approach is based on functional aggregation 
hierarchies for spatial objects. Spatial objects are aggregated 
to form new functional units at a higher level. Each level 
will have its own thematic classification system. 
From both approaches we will discuss how the semantics of 
objects is embedded in a multi scale or multi resolution setting. 
For both approaches we will give two examples: 
a — Wewill see how each approach supports data generalization 
processes through aggregation procedures. 
b We will see how each approach can be used to develop 
methods for information extraction from remote sensing 
data. 
N 
2. THE SPATIAL EXTENT AND BOUNDARY OF OBJECTS 
We will follow the line of thought developed in (Molenaar 1998). 
Let M be a spatial database containing a terrain description and let 
Um be the collection of all terrain objects represented in this