Geospatial Vagueness in Representations & Modeling

1. Geospatial Research Interests Antony Galton, University of Exeter Exeter UK

2. Vague or Uncertain Location • Schemes for representing indeterminate locations typically require one to go beyond what is actually known, e.g. by • Assigning fuzzy membership values • Assigning precise ‘inner’ and ‘outer’ boundaries • My student James Hood and I have developed a theory of anchoring, which allows one to say just what is known about something’s location and what can be inferred with certainty from this. • Spatial data can be provided in this form, but the user can, if desired, extend the data by using fuzzy values, egg-yolk theory, etc.

3. Spatial aggregates • Given a finite set of points, how can we characterise the region that they occupy (their ‘footprint’)? • Two conflicting requirements: • To describe the region as simply as possible • To do justice to the overall configuration of the points. • Simply giving the convex hull would satisfy the first requirement; and the points themselves, or some ‘skeleton’ formed by joining up the dots, would satisfy the second. • What we want is something between these (a possibly non-convex ‘hull’).

4. Multi-resolution representations • Under different granularities, a spatial object may require different representations (e.g., a 2D blob may become a point). • But different types of object may behave differently (compare: a city, a forest). • Aggregates may fuse to become a texture (field-like rather than object-like). • It would be useful to have a way of representing geospatial features to capture the behaviour of their representations at different granularities.

5. Processes and Events • Processes are generally treated as being essentially similar to events, but somehow different. • But they actually possess many of the properties of objects, persisting as identities from moment to moment while undergoing change of character. • Events, by contrast, are discrete entities occupying temporal intervals and possessing temporal parts – they do not undergo change, although their constituent processes and participating objects may do so. • We need a way of modelling processes and events which does justice to this difference of character.

6. Escaping the ‘layer’ metaphor • Classic GIS conceptualises geospatial phenomena in terms of thematic layers, each of which is a copy of the underlying coordinate frame populated by features pertaining to the theme of the layer. • But this won’t work for features whose location is indeterminate or non-existent – such features can still be spatial by virtue of close relation to physically located features (e.g., a business and its premisses). • We propose the notion of ‘thematic realms’ in which a wider variety of relationships is possible than those which arise from exact location in a layered model.