A Geometry for Places: Representing Extension and Extended Objects

  • Hedda R. Schmidtke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2825)


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.


Representation of extension extended objects spatial granularity spatial context qualitative spatial reasoning incomplete spatial knowledge 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hedda R. Schmidtke
    • 1
  1. 1.Department for InformaticsUniversity of HamburgHamburgGermany

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