Abstract
Conceptual neighborhood graphs form the foundation for qualitative spatial-relation reasoning as they capture the relations’ similarity. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundary lines, roughly at the same degree as it increases for crisp lines that are transformed from R1 into R2.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alexandroff P (1961) Elementary concepts of topology. Dover: Mineola, NY
Allen J (1983) Maintaining knowledge about temporal intervals. Communications of the ACM 26(11): 832-843
Bruns HT, Egenhofer M (1996) Similarity of spatial scenes. In: Kraak MJ, Molenaar M (eds), Seventh international symposium on spatial data handling pp 173-184
Chrisman N (1982) A theory of cartographic error and its measurement in digital data bases. Fifth international symposium on computer-assisted cartography. Bethesda, MD, pp 159-68
Clementini E (2005) A model for uncertain lines, Journal of Visual Languages and Computing 16: 271-288
Clementini E, Di Felice P (1996) An algebraic model for spatial objects with indeterminate boundaries. In: Burrough P, Frank A (eds) Geographic objects with indeterminate boundaries. Taylor & Francis, London, pp 155-169
Clementini E, Di Felice P (1997) Approximate topological relations. International journal of approximate reasoning 16: 173-204
Cohn A, Gotts N (1996) The ‘egg-yolk’ representation of regions with indeterminate boundaries. In: Burrough P, Frank A (eds) Geographic objects with indeterminate boundaries. Taylor & Francis, London, pp 171-187
Dutton G (1992) Handling positional uncertainty in spatial databases. Spatial data handling symposium. Charleston, SC, vol 2, pp 460-469
Egenhofer M (1993) Definitions of line-line relations for geographic databases. IEEE data engineering bulletin 16(3): 40-45
Egenhofer M (1997) Query processing in Spatial-Query-by-Sketch. Journal of visual languages and computing 8(4): 403-424
Egenhofer M (2005) Spherical topological relations. Journal of data semantics III: 25-49
Egenhofer M (2007) Temporal relations of intervals with a gap, 14th international symposium on temporal representation and reasoning (TIME 2007). Alicante, Spain, IEEE Computer Society, pp 169-174
Egenhofer M, Al-Taha K (1992) Reasoning about gradual changes of topological relationships. In: Frank A, Campari I, Formentini U (eds) Theory and methods of spatio-temporal reasoning in geographic space. Lecture Notes in Computer Science vol 639, pp 196-219
Egenhofer M, Franzosa R (1991) Point-set topological spatial relations, International journal of geographical information systems 5(2): 161-174
Egenhofer M, Herring J (1991) Categorizing binary topological relationships between regions, lines, and points in geographic databases. Technical Report, Department of Surveying Engineering, University of Maine, Orono, ME, (http://www.spatial.maine.edu/∼ max/9intreport.pdf)
Egenhofer M, Mark D (1995) Modeling conceptual neighborhoods of topological line-region relations, International journal of geographical information systems 9(5): 555-565
Egenhofer M, Sharma J (1993) Topological relations between regions in R2 and Z2. In: Abel D, Ooi BC (eds) Advances in spatial databases-third international symposium on large spatial databases, SSD’93. Lecture Notes in Computer Science vol 692, pp 316-336
Freksa C (1992) Temporal reasoning based on semi-intervals. Artificial intelligence 54: 199-227
Hornsby K, Egenhofer M, Hayes P (1999) Modeling cyclic change. In: Chen P, Embley D, Kouloumdjian J, Liddle S, Roddick J (eds) ER workshops. Lecture Notes in Computer Science vol 1727, pp 98-109
Kurata Y, Egenhofer M (2006) The head-body-tail intersection for spatial relations between directed line segments. In: Raubal M, Miller H, Frank A, Goodchild M. (eds) GIScience 2006. Lecture Notes in Computer Science vol 4197, pp 269-286
Kurata Y, Egenhofer M (2007) The 9+-intersection for topological relations between a directed line segment and a region, In: Gottfried B (ed.) Workshop on behaviour monitoring and interpretation, University Bremen, TZI Technical Report 42, pp 62-76
Mark D, Egenhofer M (1994) Modeling spatial relations between lines and regions: combining formal mathematical models and human subjects testing. Cartography and geographic information systems 21(4): 195-212
Papadias D, Theodoridis Y, Sellis T, Egenhofer M (1995) Topological relations in the world of minimum bounding rectangles: a study with R-Trees, SIGMOD record 24(2): 92-103
Reis R, Egenhofer M, Matos J (2006) Topological relations using two models of uncertainty for lines. In: Caetano M, Painho M (eds), Accuracy 2006 (http://www.spatial-accuracy.org/2006/PDF/Reis2006accuracy.pdf)
Stevens S (1946) On the theory of scales of measurement. Science 103: 677-680.
Schlieder C (1995) Reasoning about ordering. In: Frank A, Kuhn W (eds), COSIT’95, Spatial information theory. Lecture Notes in Computer Science vol 988, pp 341-350
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reis, R.M., Egenhofer, M.J., Matos, J.L. (2008). Conceptual Neighborhoods of Topological Relations Between Lines. In: Ruas, A., Gold, C. (eds) Headway in Spatial Data Handling. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68566-1_32
Download citation
DOI: https://doi.org/10.1007/978-3-540-68566-1_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68565-4
Online ISBN: 978-3-540-68566-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)