, Volume 8, Issue 1, pp 71–98 | Cite as

A Probability-based Uncertainty Model for Point-in-Polygon Analysis in GIS

  • Chui Kwan Cheung
  • Wenzhong Shi
  • Xian Zhou


In a geographical information system (GIS), a conventional point-in-polygon analysis is used to determine whether a point is located inside a polygon with a Boolean result. Due to positional uncertainties existing with both the point and the polygon, the Boolean answer cannot describe the relationship of closeness between the point and the polygon. This paper aims to develop a model and to provide a continuous index—the probability value—to indicate the extent of the uncertain point located inside the uncertain polygon based upon existing research development. This probability index is derived based on probability and statistical theories considering the statistical uncertainty distributions of the point and the polygon's vertices. The associated mathematical expressions for the probability index are addressed in cases depending on the intersection between the polygon and the error ellipse of the point. The proposed probability index can provide an objective description of the relationship of closeness between an uncertain point and an uncertain polygon.

positional uncertainty point-in-polygon analysis error propagation GIS 


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  1. 1.
    P.A. Burrough. Principles of Geographical Information Systems for Land Resources Assessment. Clarendon Press: Oxford, 1986.Google Scholar
  2. 2.
    P.A. Burrough and R.A. McDonnell. Principles of Geographical Information Systems. Oxford University Press, 1998.Google Scholar
  3. 3.
    P.V. Bolstad, P. Gessler, and T.M. Lillesand. “Positional uncertainty in manually digitised map object,” International Journal of Geographical Information Systems, Vol. 4(4):399-412, 1990.Google Scholar
  4. 4.
    C.K. Cheung and W.Z. Shi. “Measuring uncertainty of spatial features in a three-dimensional geographical information system based upon numerical analysis,” Geographic Information Sciences, Vol. 7(2):124-130, 2001.Google Scholar
  5. 5.
    M.M. Desu and D. Raghavarao. Sample Size Methodology. Academic Press Inc., 1990.Google Scholar
  6. 6.
    R. Dunn, A.R. Harrison, and J.C. White. “Positional accuracy and measurement error in digital databases of land use: An empirical study,” International Journal of Geographical Information System, Vol. 4:385-398, 1990.Google Scholar
  7. 7.
    G.B.M. Heuvelink. Error Propagation in Environmental Modelling with GIS. Taylor and Francis Ltd., 1998.Google Scholar
  8. 8.
    B.J. Keefer, J.L. Smith, and T.G. Gregoire. “Simulating manual digitising error with statistical models,” in GIS/LIS'88, 475-483, 1988.Google Scholar
  9. 9.
    B.J. Keefer, J.L. Smith, and T.G. Gregoire. “Modelling and evaluating the effects of stream mode digitising errors on map variables,” Photogrammetric Engineering & Remote Sensing, Vol. 57(7):957-963, 1991.Google Scholar
  10. 10.
    G. Maffini, M. Arno, and W. Bityterlich. “Observations and comments on the generation of error in digital GIS data,” in Accuracy of Spatial Databases, edited by M.F. Goodchild and S. Gopal, 55-67, 1989.Google Scholar
  11. 11.
    Y. Leung and J.P. Yan. “Point-in-polygon analysis under certainty and uncertainty,” GeoInformatica, Vol. 1:93-114, 1997.Google Scholar
  12. 12.
    X.L. Meng, D.J. Liu, and Z.H. Zhu. “NL distribution test of map digitisation errors,” Journal of Tongji University, Vol. 24(5):525-529, 1996.Google Scholar
  13. 13.
    X.L. Meng, W.Z. Shi, and D.J. Liu. “Statistical tests of the distribution of errors in manually digitised cartographic lines,” Geographic Information Science, Vol. 4(1–2):52-58, 1998.Google Scholar
  14. 14.
    W.Z. Shi. Modelling Positional and Thematic Uncertainty in Integration of GIS and Remote Sensing. ITC Publication, Enschede, No. 22, 1994.Google Scholar
  15. 15.
    W.Z. Shi, “A generic statistical approach for modeling errors of geometric features in GIS,” International Journal of Geographical Information Science, Vol. 12(2):131-143, 1998.Google Scholar
  16. 16.
    W.Z. Shi and W.B. Liu, “A stochastic process-based model for positional error of line segments in GIS,” International Journal of Geographical Information Science, Vol. 14(1):51-66, 2000.Google Scholar
  17. 17.
    L.E. Stanfel, M. Conerly, and C. Stanfel. “Reliability of polygonal boundary of land parcel,” Journal of Surveying Engineering, Vol. 121(4):163-176, 1995.Google Scholar
  18. 18.
    X.H. Tong, W.Z. Shi, and D.J. Liu. “Error distribution, error tests and processing of digitised object in GIS,” in Proc.: Accuracy 2000, Amsterdam, July, 642-646, 2000.Google Scholar
  19. 19.
    J.C. Walsby. “The causes and effects of manual digitising on error creation in object input to GIS,” in Innovations in GIS 2, edited by P. Fisher, 113-122, 1995.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Chui Kwan Cheung
    • 1
  • Wenzhong Shi
    • 1
  • Xian Zhou
    • 2
  1. 1.Advanced Research Center for Spatial Information Technology, Department of Land Surveying and Geo-InformaticsThe Hong Kong Polytechnic UniversityHunghom, KowloonHong Kong
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic University, c[Hunghom, KowloonHong Kong

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