A Vector Approach to the Analysis of (Patterns with) Spatial Dependence

  • Andrés Molina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


It is evident that the utility of an image or map will depend on the quantity of the information we can extract from it by the analysis of the spatial relationships of the phenomenon represented. For it, tools that describe aspects such as spatial dependence or autocorrelation in patterns are used. The statistic techniques that measure the spatial dependence are very varied, but all of them provide only scalar information about the variation of spatial properties in the pattern, without analyzing the possible directedness of the dependence mentioned. In this work, we make a vector approach to the analysis of spatial dependence, therefore, given a pattern, besides quantifying its autocorrelation level, we will determinate if statistics evidence of directedness exists, calculating the angle where the direction appears. For this we will use a parametric method when the normality of population can be assumed, and a non-parametric method for uniform distribution.


Spatial Dependence Anisotropy Directional Trend Circular Statistics 


  1. [1]
    Getis, A.: Homogeneity and Proximal Databases. In Fotheringham, S., Rogerson, P. (eds.): Spatial Analysis and GIS. Taylor&Francis, London (1994) 105–120Google Scholar
  2. [2]
    Bailey, T.C., Gattrel, A.C.: Ineractive Spatial Data Analysis. Longman, Edinburgh (1995)Google Scholar
  3. [3]
    Wackernagel, H.: Multivariate geostatistics. Springer, Berlin Heidelberg New York (1995)zbMATHGoogle Scholar
  4. [4]
    Batschelet, E.: Recent statistical methods for orientation data. U.S. Government Printing Office, Washington (1965)Google Scholar
  5. [5]
    Chow, Y,H.: Spatial Patern and Spatial Autocorrelation In: Frank, A.U., Kuhn, W. (eds.): Spatial Information Theory. Lectures Notes in Computer Science, Vol. 988. Springer, Berlin Heidelberg New York (1995) 365–376Google Scholar
  6. [6]
    Cox, D.R., Hinkley, D.V.: Theoretical Statistics. Chapman and Hall, London (1974)zbMATHGoogle Scholar
  7. [7]
    Batschelet, E.: Circular statistics in biology. Academic Press, London (1981)zbMATHGoogle Scholar
  8. [8]
    Molina, A., Feito, F.R.: Design of Anisotropic Functions Within Analysis of Data. In: Wolter, F.E., Patrikalakis, N.M. (eds.): Proc. IEEE Computer Graphics International (1998) 726–729Google Scholar
  9. [9]
    Moore, F.R.: A modification of the Rayleigh test for vector data. Biometrika 67 (1980) 175–180CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andrés Molina
    • 1
  1. 1.Dpto. de Informática, Escuela Politécnica SuperiorUniversidad de JaénJaénSpain

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