Abstract
This paper describes the geometric and statistical properties of areal object under randomness. In order to describe formally such a uncertain topological relation, a new formal model (i. e. 4ID model) is proposed. On the basis of this, the effects of positional uncertainty on topological relations between areal objects are investigated in detail. Some possibility function for the determination of relations are constructed based on the assumption that, randomness of point location complies with a normal distribution, and the concept of uncertain sets of topological relations under randomness is introduced.
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References
Egenhofer M, Franzosa R (1991) Point-set topological spatial relations.International Journal of Geographical Information Systems, 5(2):161–174
Egenhofer M, Mark D (1995) Modeling conceptual neighborhoods of topological line-region relations.International Journal of Geographical Information Systems, 9 (5): 555–565
Goodchild M F, Gopal S (1989) Accuracy of spatial databases. London: Tayloy & Francis.
Guptill S C, Morrison J L (1995) Elements of spatial data quality. Oxford: Elsevier Scientific.
Burrough P A, Frank A U (1996) Geographic objects with indeterminate boundaries. London: Taylor and Francis.
Shi W Z, Liu W B (2000) A stochastic process-based model for positional error of line segments in GIS.International Journal of Geographic Information Sciences, 14 (1): 51–66.
Chen X (1996) Spatial relation between uncertain sets. International Archives of Photogrammetry and Remote Sensing, XVIII Congress, Vienna.
Winter S (2000) Uncertain topological relations between imprecision regions.International Journal of Geographical Information Systems, 14 (5): 411–430
Liu W B, Dai H L, Xu P L, et al. (1998) Models of positional error donut for planar polygon in GIS.Acta Geogdaetica et Cartographica Sinica, 27 (4): 338–344 (in Chinese)
Chen X, Deng M (2003) Complete description of topological relations between spatial regions. The 2nd International Symposium on Spatial Data Quality, Hong Kong.
Deng M (2003) Extended models of topological relations in vector GIS: theories and methods. [Ph. D disertation]. Wuhan: Wuhan University (in Chinese)
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Funded by the National Natural Science Fundation of China(No. 4010122, 49801016) and Doctor Discipline Fund (No. 20010284011).
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Min, D., Xuesong, Z. & Wenbao, L. An approach to reasoning topological relations between areal objects under randomness. Geo-spat. Inf. Sci. 7, 255–261 (2004). https://doi.org/10.1007/BF02828548
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DOI: https://doi.org/10.1007/BF02828548