**TOWARDS A FORMAL CLASSIFICATION OF GENERALIZATION OPERATORS**

T. Foerster, J. Stoter

*International Institute for Geo-Information Science and Earth
Observation (ITC), the Netherlands*

*foerster@itc.nl*

Within the last decades, research about generalization operators proposed different classifications based on different characteristics of generalization operators as for instance within the Agent project (Lamy et al. 1999) or others (e.g. McMaster & Shea 1992; Yaolin et al. 2001; Han-Sze-Chuen et al. 2002). These classifications are project-driven, i.e. they are based on one specific application such as cartographic generalization. Therefore these classifications lack of generality, transparency, and consistency.

However a comprehensive, unambiguous classification of operators is essential in the context of generalization processes embedded in a loose-coupled environment such as the Web. In this paper we describe first a distinct set of operators, based on an inventory of existing operators extracted from published research on generalization, where we will try to be as complete as possible.

The proposed set of operators is carried out by harmonizing the different descriptions and operator names. The operators will then be classified based on the well-known and broadly-accepted model for generalization of Gruenreich (1992). We chose Gruenreich’s model as it describes the generalization process completely. Gruenreich identifies two types of generalization, namely model generalization used to obtain a data model at a higher level of detail and cartographic generalization used to obtain a readable map taking cartographic constraints into account. Using these models allows us to classify the operators and to define the effect of the operators.

The effects of model generalization operators will be described using the formal ISO 19109 General Feature Model (ISO 2003). This commonly used model provides a valid basis to describe the effects of model generalization in a generic way. The effects of cartographic generalization operators will be defined using the constraint model proposed by Ruas (1998), as it allows classifying the operators towards cartographic constraints.

Describing the effects of the operators in such models allows us to check the operators for consistency. This is important as the determination of generalization operators is known to be highly subjective (Rieger & Coulson 1993).

This paper contributes to generalization research, as it links the operators to the popular model of Gruenreich and as it introduces these operators described by two formal models (ISO and constraint) in a consistent way. Finally as the operators are defined consistently and linked to a formal model, the formalization of the operators is the next step.

**References**

Gruenreich, D. (1992), ATKIS - a
topographic information system as a basis for GIS and digital cartography in
Germany *From digital map series to geo-information systems, *1992*, Geologisches Jahrbuch Reihe A*,
207 - 16.

Han-Sze-Chuen, D.; Mustiere, S. & Moulin, B. (2002), Formalising the
geographic database generalization process by means of a conflicts/operations
graph *Symposium on Geospatial Theory, Processing and Applications*.

ISO 2003, Geographic information - Rules
for application schema *ISO.*

Lamy, S.; Ruas, A.; Demazeu, Y.; Jackson,
M.; Mackaness, W. & Weibel, R. (1999), The Application of Agents in
Automated Map Generalization, *19th International Cartographic Conference*.

Li, Z. (2006), Algorithmic foundation of
multi-scale spatial representation, *CRC*.

McMaster, R.B. & Shea, S.K. (1992), Generalization in Cartography.

Rieger, M.K. & Coulson, M.R.C. (1993),
Consensus or confusion: cartographers' Knowledge of Generalization, *Cartographica,
30*, 69-80.

Ruas, A. (1998), OO-constraint modelling to
automate urban generalization process *SDH 98*.

Yaolin, L.; Molenaar, M. & Tinghua, A.,
D. (2001), Frameworks for Generalization Constraints and Operations Based on
Object-Oriented Data Structure in Database Generalization, *20th ICC,* Du,
H.L. *(ed.), 3*, 2000-12.