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The Family of Conceptual Neighborhood Graphs for Region-Region Relations

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Geographic Information Science (GIScience 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6292))

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Abstract

This paper revisits conceptual neighborhood graphs for the topological relations between two regions, in order to bridge from the A-B-C neighborhoods defined for interval relations in R1 to region relations in R2 and on the sphere S2. A categorization of deformation types—built from same and different positions, orientations, sizes, and shapes—gives rise to four different neighborhood graphs. They include transitions that are constrained by the regions’ geometry, yielding some directed, not undirected neighborhood graphs. Two of the four neighborhood graphs correspond to type B and C. The lattice of conceptual neighborhood graphs captures the relationships among the graphs, showing completeness under union and intersection.

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Author information

Authors and Affiliations

  1. National Center for Geographic Information and Analysis,  

    Max J. Egenhofer

  2. Department of Spatial Information Science and Engineering Department of Computer Science, University of Maine, Boardman Hall, Orono, ME, 04469-5711, USA

    Max J. Egenhofer

Authors
  1. Max J. Egenhofer
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Editor information

Editors and Affiliations

  1. University of Zurich, 8057, Zurich, Switzerland

    Sara Irina Fabrikant  & Tumasch Reichenbacher  & 

  2. Utrecht University, 3508, Utrecht, The Netherlands

    Marc van Kreveld

  3. University of Bamberg, 96047, Bamberg, Germany

    Christoph Schlieder

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Egenhofer, M.J. (2010). The Family of Conceptual Neighborhood Graphs for Region-Region Relations. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds) Geographic Information Science. GIScience 2010. Lecture Notes in Computer Science, vol 6292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15300-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-15300-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15299-3

  • Online ISBN: 978-3-642-15300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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