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TRANSFORMATION OF SPATIAL REPRESENTATION IN SCALE DIMENSION: 
A NEW PARADIGM FOR DIGITAL GENERALIZATION OF SPATIAL DATA 
Dr. Zhilin Li 
Assistant Professor in GIS 
Dept. of Surveying and Geo-Informatics 
Hong Kong Polytechnic University 
Hong Kong 
Iszlli@hkpucc.polyu.edu.hk 
ISPRS Commission III, Working Group IWG III/IV 
KEY WORDS: Generalization, Scale, Digital, Transformation, Digital generalization, Scale dimension, spatial representation. 
ABSTRACT 
Generalization is a fundamental functionality in a geographical information system (GIS). It has recently become a major 
international research theme in cartography and GIS. 
This paper describes a scale-driven paradigm for the generalization process. In this paradigm, scale is considered as the only factor 
which directly drives the transformation of spatial representation from a larger scale to a smaller scale. It is illustrated that such a 
transformation follows a natural principle and that this natural principle can be best depicted by the operators developed in 
mathematical morphology, which is a science dealing with shape, form and structure of spatial objects. 
In this paper, the concept of scale dimension is introduced and generalization is considered as the transformation of spatial 
representation in scale dimension. Such a transformation simplifies the shape, form and structure of spatial data so as to bring the 
spatial representation from a larger scale to a smaller scale. This transformation is an objective process. The subjective aspects of 
generalization may be dealt with using rule-based systems. Rules can be applied before, during and after this scale-driven 
transformation. This paradigm allows the seemingly subjective and complex process of generalization to be greatly simplified so 
that a mathematical basis may be laid down. 
1. INTRODUCTION 
Spatial data (including map data) are usually associated with 
scales. At large scales, detailed information about spatial 
variations of a given area can be represented. If this 
representation is to be made at a smaller scale, then graphic 
space is reduced. Thus, not the same amount of detailed 
information can be represented due to the requirements for the 
clarity of graphic symbols. In this case, the contents of large 
scale spatial data need to be modified to suit the smaller space 
available on smaller scale representations, i.e. some needs to be 
omitted, some simplified, some displaced, some exaggerated, 
and so on. This modification process is referred to as 
generalization. In the context of this paper, generalization is 
considered as being a process of transforming spatial 
representation from a larger scale to a smaller scale. 
Generalization is a vital function in spatial data handling, e.g. 
for geographical modelling, for efficient derivation and 
updating of small-scale maps and spatial databases from large 
scale sources, and for real-time visualisation and analysis of 
spatial data in a GIS. 
Indeed, generalization is so important and difficult a topic that 
it has nowadays become a major international research theme 
in cartography and GIS. Over the last decade, many projects 
have been initiated internationally, in Canada, China, Britain, 
France, Germany, the Netherlands, Sweden, Switzerland, and 
the USA. 
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In the last three decades, a few conceptual frameworks have 
been developed by researchers (e.g. Brassel and Weibel, 1988; 
McMaster and Monmonier, 1989), based on which, a number 
of generalization operations have been identified. However, 
most of these operations remain at a conceptual level. In other 
words, there is a lack of mathematical models or algorithms to 
transform spatial representation from a larger scale to a smaller 
scale. 
This paper aims to offer a new paradigm for digital 
generalization of spatial data. It is a scale-driven paradigm. It 
considers that 
(a) generalization is a process of transforming spatial 
representation in scale dimension; 
(b) this transformation process follows a natural principle, and; 
(c) this natural principle can be best depicted by operators 
developed in mathematical morphology. 
Based on this new paradigm, a mathematical (or an algebraic) 
basis could then be established for digital generalization of 
spatial data. 
This introduction is followed by a scale-driven framework. In 
this section, the motivations of generalization are classified and 
scale is considered as the only direct factor which drives this 
transformation. In Section 3, the concept of scale dimension is 
introduced and the transformation in scale dimension is 
illustrated. Section 4 demonstrates that the transformation in 
scale dimension follows the natural principle for objective 
generalization proposed by Li and Openshaw (1993). Section