Encyclopedia of GIS

Living Edition
| Editors: Shashi Shekhar, Hui Xiong, Xun Zhou

Directional Relations

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DOI: https://doi.org/10.1007/978-3-319-23519-6_1539-1
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Synonyms

Cardinal direction relations; Direction relations; Orientation relations

Definition

Directional relations are qualitative spatial relations that describe how an object or a region is placed relative to other objects or regions. This knowledge is expressed using symbolic (qualitative) and not numerical (quantitative) terms. For instance, north, southeast, front, and back-right are directional relations. Such relations are used to describe and constrain the relative positions of objects or regions and can be used to pose queries such as “Find all objects/regions a, b, and c such that a is north of b and b is southeast of c.”

Historical Background

Qualitative spatial relations (QSRels) approach commonsense knowledge and reasoning about space using symbolic and qualitative rather than numerical and quantitative terms and methods (Hernández, 1994) (see also reference to Qualitative Spatial Reasoningentry). QSRels have found applications in many diverse scientific areas such as...

Keywords

Reference Object Geographic Information System Cardinal Direction Model Partition Exact Shape 
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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References

  1. Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11):832–843CrossRefMATHGoogle Scholar
  2. Chang S-K, Jungert E (eds) (1996) Symbolic projection for image information retrieval and spatial reasoning. Academic Press, LondonGoogle Scholar
  3. Cicerone S, Di Felice P (2004) Cardinal directions between spatial objects: the pairwise-consistency problem. Inf Sci 164(1–4):165–188MathSciNetCrossRefMATHGoogle Scholar
  4. Clementini E, Billen R (2006) Modeling and computing ternary projective relations between regions. IEEE Trans Knowl Data Eng 18(6):799–814CrossRefGoogle Scholar
  5. Clementini E, Di Felice P, Hernandez D (1997) Qualitative representation of positional information. Artif Intell 95(2):317–356MathSciNetCrossRefMATHGoogle Scholar
  6. Clementini E, Skiadopoulos S, Billen R, Tarquini F (2010) A reasoning system of ternary projective relations. IEEE Trans Knowl Data Eng 22(2):161–178CrossRefGoogle Scholar
  7. Frank AU (1996) Qualitative spatial reasoning: cardinal directions as an example. Int J Geogr Inf Sci 10(3):269–290CrossRefGoogle Scholar
  8. Freksa C (1992) Using orientation information for qualitative spatial reasoning. In: Proceedings of COSIT’92, Piza. LNCS, vol 639, pp 162–178. http://dblp.uni-trier.de/rec/bibtex/conf/gis/Freksa92
  9. Glasgow J, Papadias D (1992) Computational imagery. Cogn Sci 16:355–394CrossRefGoogle Scholar
  10. Goyal R (2000) Similarity assessment for cardinal directions between extended spatial objects. Ph.D. thesis, Department of Spatial Information Science and Engineering, University of MaineGoogle Scholar
  11. Hernández D (1994) Qualitative representation of spatial knowledge. LNCS, vol 804. Springer, BerlinGoogle Scholar
  12. Ligozat G (1993) Qualitative triangulation for spatial reasoning. In: Proceedings of COSIT’93, Elba Island. LNCS, vol 716, pp 54–68Google Scholar
  13. Ligozat G (1998) Reasoning about cardinal directions. J Vis Lang Comput 9:23–44CrossRefGoogle Scholar
  14. Liu W, Li S (2011) Reasoning about cardinal directions between extended objects: the NP-hardness result. Artif Intell 175(18):2155–2169MathSciNetCrossRefMATHGoogle Scholar
  15. Liu W, Zhang X, Li S, Ying M (2010) Reasoning about cardinal directions between extended objects. Artif Intell 174(12–13):951–983MathSciNetCrossRefMATHGoogle Scholar
  16. Mukerjee A, Joe G (1990) A qualitative model for space. In: Proceedings of AAAI’90, Boston, pp 721–727. http://dblp.uni-trier.de/rec/bibtex/conf/aaai/MukerjeeJ90
  17. Papadias D (1994) Relation-based representation of spatial knowledge. Ph.D. thesis, Department of Electrical and Computer Engineering, National Technical University of AthensGoogle Scholar
  18. Papadias D, Sellis TK (1994) Qualitative representation of spatial knowledge in two-dimensional space. VLDB J 3(4):479–516CrossRefGoogle Scholar
  19. Peuquet DJ, Ci-Xiang Z (1987) An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane. Pattern Recognit 20(1):65–74CrossRefGoogle Scholar
  20. Schlieder C (1995) Reasoning about ordering. In: Proceedings of COSIT’95, Semmering. LNSC, vol 988, pp 341–349Google Scholar
  21. Scivos A, Nebel B (2001) Double-crossing: decidability and computational complexity of a qualitative calculus for navigation. In: Proceedings of COSIT’01, Morro Bay. LNCS, vol 2205, pp 431–446. http://dblp.uni-trier.de/rec/bibtex/conf/cosit/ScivosN01
  22. Skiadopoulos S, Koubarakis M (2004) Composing cardinal direction relations. Artif Intell 152(2):143–171MathSciNetCrossRefMATHGoogle Scholar
  23. Skiadopoulos S, Koubarakis M (2005) On the consistency of cardinal directions constraints. Artif Intell 163(1):91–135MathSciNetCrossRefMATHGoogle Scholar
  24. Skiadopoulos S, Giannoukos C, Sarkas N, Vassiliadis P, Sellis T, Koubarakis M (2005) Computing and managing cardinal direction relations. IEEE Trans Knowl Data Eng 17(12):1610–1623CrossRefGoogle Scholar
  25. Skiadopoulos S, Sarkas N, Sellis T, Koubarakis M (2007) A family of directional relation models for extended objects. IEEE Trans Knowl Data Eng 19(8):1116–1130CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of PeloponneseTripoliGreece