Abstract
The article presents a qualitative region-based approach to the representation of extension. A geometry of incidence and ordering is taken as a basis to characterize the concept of extension founded on the congruence of certain regions (called places) which have equal extension into all directions. The notion of extension of regions is derived from the sizes of places—not from the distance between points as in classical geometry—and represented by size intervals. A geometric specification of granular or scale-specific spatial contexts and of the local extension of a region is then derived. Extension relative to a spatial context is used to formally specify conditions under which object regions can be classified e.g. as punctual, linear, or planar in the context.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bennett, B.: Application of supervaluation semantics to vaguely defined spatial concepts. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 108–123. Springer, Heidelberg (2001)
Bennett, B.: A categorical axiomatisation of region-based geometry. Fundamenta Informaticae 46, 145–158 (2001)
Borgo, S., Guarino, N., Masolo, C.: A pointless theory of space based on strong connection and congruence. In: Aiello, L.C., Doyle, J., Shapiro, S. (eds.) KR 1996: Principles of Knowledge Representation and Reasoning, pp. 220–229. Morgan Kaufmann, San Francisco (1996)
Carnap, R.: Philosophical Foundations of Physics. Basic Books, New York (1966)
Casati, R., Varzi, A.C.: Parts and Places: the Structure of Spatial Representations. MIT Press, Cambridge (1999)
Cohn, A.G., Hazarika, S.M.: Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae 46(1-2), 1–29 (2001)
Eschenbach, C., Habel, C., Kulik, L., Leßmöllmann, A.: Shape nouns and shape concepts: A geometry for ‘corner’. In: Freksa, C., Habel, C., Wender, K.F. (eds.) Spatial Cognition 1998. LNCS (LNAI), vol. 1404, pp. 177–201. Springer, Heidelberg (1998)
Frank, A.: Qualitative spatial reasoning about distances and directions in geographic space. Journal of Visual Languages and Computing 3, 343–371 (1992)
Galton, A.: Space, time and movement. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 321–352. Kluwer, Dordrecht (1997)
Goodchild, M.: A geographer looks at spatial information theory. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 1–13. Springer, Heidelberg (2001)
Goyal, R., Egenhofer, M.: Consistent queries over cardinal directions across different levels of detail. In: Tjoa, U., Wagner, R., Al-Zobaidie, A. (eds.) 11th International Workshop on Database and Expert Systems Applications, pp. 876–880 (2000)
Herskovits, A.: Language, spatial cognition, and vision. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 155–202. Kluwer, Dordrecht (1997)
Hilbert, D.: Grundlagen der Geometrie. Teubner, Stuttgart (1956)
Kulik, L., Klippel, A.: Reasoning about cardinal directions using grids as qualitative geographic coordinates. In: Freksa, C., Mark, D. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 205–220. Springer, Heidelberg (1999)
Ligozat, G.: Reasoning about cardinal directions. Journal of Visual Languages and Computing 9, 23–44 (1998)
Schmidtke, H.R.: The house is north of the river: Relative localization of extended objects. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 414–430. Springer, Heidelberg (2001)
Suppes, P., Zinnes, J.: Basic measurement theory. In: Luce, R., Bush, R., Galanter, E. (eds.) Handbook of Mathematical Psychology, John Wiley & Sons, New York (1963)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmidtke, H.R. (2003). A Geometry for Places: Representing Extension and Extended Objects. In: Kuhn, W., Worboys, M.F., Timpf, S. (eds) Spatial Information Theory. Foundations of Geographic Information Science. COSIT 2003. Lecture Notes in Computer Science, vol 2825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39923-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-39923-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20148-9
Online ISBN: 978-3-540-39923-0
eBook Packages: Springer Book Archive