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Three-Valued 9-Intersection for Deriving Possible Topological Relations from Incomplete Observations

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Advances in GIScience

Part of the book series: Lecture Notes in Geoinformation and Cartography ((LNGC))

Abstract

Topological relations, which concern how two objects intersect, are one of the most fundamental and well-studied spatial relations. Typically, topological relations are distinguished by the presence or absence of pairwise intersections between several parts of two objects. However, when an observation is not complete, it is often impossible to determine the presence or absence of some intersections. In order to support such uncertain situations, this paper introduces three-valued 9- intersection matrix (3-9i matrix), which records the presence, absence, or indeterminate state of the nine types of intersections between the objects. We can use the 3-9i matrix to describe the spatial arrangement of objects in various scenarios of incomplete observations. In addition, from the pattern of the 3-9i matrix we can computationally determine a set of topological relations that may hold between the objects. We assess the degree of topological information derived from the 3-9i matrix for 14 sets of topological relations between simple lines, regions, and bodies embedded in R1, R2, R3, R1, and S2.

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Authors and Affiliations

  1. SFB/TR 8 Spatial Cognition, Universität Bremen, Postfach 330 440, 28334, Bremen, Germany

    Yohei Kurata

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  1. Yohei Kurata
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Correspondence to Yohei Kurata .

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Editors and Affiliations

  1. Leibniz Universität Hannover Inst. Kartographie und Geoinformatik, Appelstraße 9a, 30167, Hannover, Germany

    Monika Sester  & Volker Paelke  & 

  2. TU Dresden Fak. Forst-, Geo- und Hydrowissenschaften, Helmholtzstr. 10, 01069 , Dresden, Germany

    Lars Bernard

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Kurata, Y. (2009). Three-Valued 9-Intersection for Deriving Possible Topological Relations from Incomplete Observations. In: Sester, M., Bernard, L., Paelke, V. (eds) Advances in GIScience. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00318-9_15

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