Refining Topological Relations between Regions Considering Their Shapes

  • Roland Billen
  • Yohei Kurata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5266)


Topological relations are sometimes insufficient for differentiating spatial configurations of two objects with critical difference in their connection styles. In this paper, we present the projective 9  +  -intersection model, which refines topological relations into projective binary relations by considering projective properties of the objects’ shapes. This is indeed a reformulation of projective concepts of the Dimensional Model within the framework of the 9  +  -intersection. Thirty projective binary relationsare established between two regions in R 2, one of which has a multi-order boundary (region + mob). These relations are identified computationally by applying to all theoretical relations the existing constraints for topological region-region relations and seven new specific constraints. After defining the concept of continuous neighbours between two projective binary relations, a conceptual neighbourhood graph of the 30 projective region + mob-region relations is developed.


Spatial Relation Spatial Object Topological Relation Projective Relation Supporting Hyperplane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roland Billen
    • 1
  • Yohei Kurata
    • 2
  1. 1.Geomatics UnitUniversity of LiegeLiegeBelgium
  2. 2.SFB/TR 8 Spatial CognitionUniversität BremenBremenGermany

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