Linear Models in Spatial Discriminant Analysis

  • J. Haslett
  • G. Horgan
Part of the NATO ASI Series book series (volume 30)


This paper reports on developments of a linear model, proposed in Haslett and Horgan (1985), for the reconstruction of binary (2 colour) images corrupted by additive Gaussian noise. The proposed method involved constructing a simple linear filter of the image, and thresholding the result. This very simple method was competitive with others, much more complicated, in terms of accuracy and speed. Further, by virtue of its close affinities with classical statistical methods of multivariate linear discriminant analysis, it yielded important and easily interpretable qualifications to any given reconstruction, notably (a) an estimated value for the proportion of pixels correctly classified and (b) posterior probabilities for the colour of each pixel.


Linear Discriminant Analysis Discriminant Function Neighbourhood Size Noisy Image Additive Gaussian Noise 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Besag, J., “On the Statistical Analysis of Dirty Pictures”, read to the Royal Statistical Society, May 1986, and to appear in JRSS(B).Google Scholar
  2. [2]
    Besag, J. and P.A.P. Moran, “On the Estimation and Testing of Spatial Inter- Action in Gaussian Lattice Processes” Biometrika 62, pp. 555- 562, 1975.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Flury, B.N. and H. Riedwyl, “ T2-Tests, the Linear Two-Group Discriminant Function and their Computation by Linear Regression”, The American Statistician 39, pp. 20–25, 1985.MATHCrossRefGoogle Scholar
  4. [4]
    Geman, S. and D. Geman, “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images”, IEEE Trans. PAMI-6, pp. 271–741, 1984.CrossRefGoogle Scholar
  5. [5]
    Haslett, J., “Maximum Likelihood Discriminant Analysis on the Plane, Using a Markovian Model of Spatial Context”, Pattern Recognition 18 3/4, pp. 287–296, 1985.MATHCrossRefGoogle Scholar
  6. [6]
    Haslett, J. and G. Horgan, “Spatial Discriminant Analysis — A Linear Function for the Black/White Case”, presented to SERC Workshop “Statistics and Pattern Recognition”, Edinburgh 1985, and submitted for publication.Google Scholar
  7. [7]
    Kent, J.T. and K.V. Mardia, “Spatial Classification Using Fuzzy Membership Models”, preprint, 1986.Google Scholar
  8. [8]
    Mardia, K.V., “Spatial Discrimination and Classification Maps, Comm. Statist. Theor. Meth. 13(18), pp. 2181–2197, 1984.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Mardia, K.V., J.T. Kent and J.M. Bibby, “Multivariate Analysis”, Academic Press,Google Scholar
  10. [10]
    Rosenfeld, A., “Interactive Methods in Image Analysis”, Pattern Recognition 10, pp. 181–187, 1978.CrossRefGoogle Scholar
  11. [11]
    Saebo, H.V., K. Braten, N.L. Hjort, B. Llewellyn and E. Mohn, “Contextual Classification of Remotely Sensed Data: Statistical Methods and Development of a System”, Rept. 768, Norwegian Computing Centre, 1985.Google Scholar
  12. [12]
    Seber, G.A.F., “Multivariate Observations, Wiley, 1984.MATHCrossRefGoogle Scholar
  13. [13]
    Switzer, P., “Extensions of Linear Discriminant Analysis for Statistical Classification of Remotely Sensed Imagery”, J. Int. Ass. Math. Geol. 12, pp. 367–376, 1980.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • J. Haslett
    • 1
  • G. Horgan
    • 1
  1. 1.Department of StatisticsTrinity CollegeDublin 2Ireland

Personalised recommendations