SPATIO-TEMPORAL GENERALIZATION: THE CHRONOGRAPH APPLICATION George Panopoulos, Antonis Stamatopoulos and Marinos Kavouras Cartography Laboratory Faculty of Rural and Surveying Engineering National Technical University of Athens 9, Heroon Polytexneiou St., 15780 Zographou Campus, Athens – Greece Tel: +3 210 772 2731, Fax: +3 210 772 2670 [gpani, mkav, astamato]@survey.ntua.gr ABSTRACT This paper describes research conducted in order to introduce traditionally static spatial concepts, like generalisation, into a temporal schema and study their aspects concerning Change over time. Temporal generalisation regards the representation of each object and its Changes over different time scales. It is within the logic of the proposed model to contain strict formalizations of the objects, their domains, their attributes and their Changes. Time scales can be defined at different granularities, according to the map application, as a part of the model. The model treats both objects and changes equivalently, classifying them as Essential or Non-Essential and creating class hierarchies for both. Expanding the notion of cartographic information abstraction, we term Temporal Information Abstraction as the process of transferring a spatio-temporal schema into a new schema of different spatial and temporal detail. Therefore, the four basic operators of conceptual map generalisation are utilised, thus defining four new temporal information abstraction operators: temporal selection, temporal class generalisation, change aggregation and temporal topology association. To check the operators’ efficiency and the proposed model’s suitability, an application has been developed. Its purpose is to facilitate the study of temporal generalisation, by accessing the modelled spatio-temporal schema and producing a generalised version of its objects and Changes. The four operators are applied, according to specific user needs. The final result is visualised through a variation of methods and a fidelity ratio is calculated to express the soundness of the temporally generalised schema. 1. INTRODUCTION Cartographic generalisation has been identified over the years, not only as a visualisation problem, but also as an issue of representing the entities at a modelling level. Different levels of detail, as dictated by map scale, correspond to different conceptual descriptions of the attributes and relations of entities. Conceptual modelling, in reference to spatial databases and cartography, makes an effort to express an infinitely complex world through a particular view, which suits specific user and application needs. Generalisation is considered essential to such modelling procedures, as a representation issue of entities at different scale levels. These data models may well represent the variation of scale through variations of levels in the hierarchical classification schema. This modelling of entities can be extended further from their spatial, static properties, to include their dynamic behaviour and interactions as well. Such spatio-temporal modelling presents difficulties, mainly due to the problematic combination of spatial models with the temporal Change of objects. It is Change that will eventually allow the study of phenomena’s dynamic nature. By representing Changes, the system records “cause” and “effect” of events, and such information leads to cognition and learning. This paper encompasses research conducted in order to expand the concept of information abstraction to include the temporal behaviour of objects. The basic principle to bear in mind is that both space and time are treated simultaneously, as identical notions. A coherent spatio-temporal framework was created, able to sustain the representation of Change. The study originated four basic temporal information abstraction operators from their normal, static equivalents. Finally, an application was developed, implementing those temporal generalisation operators into the spatio-temporal model, in order to study their effectiveness and capabilities. Section 2 focuses on the representation of time and eventually, Change. The effort is to formalize a way to describe and record temporal metric “units” – referred as Intervals. Temporal Change is classified and a spatio-temporal conceptual model is described, suitable for accommodating the temporal scale of objects. The third section of the paper presents the Proceedings of the 21st International Cartographic Conference, Durban, South Africa, 10-16 August 2003.