Nonlinear variance measures in image data

  • Carolyn J. Evans
  • Imants D. Svalbe
Shape Representation and Image Segmentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1451)


The homogeneity of regions in images can be measured in terms of the variation of local image values, or in terms of the local variation of ranks assigned to those image values. Previously proposed measures of nonlinear, or rank variance are shown in this paper to be insufficient measures of rank variation, especially when applied to discrete image data. A more useful measure of rank variance for image analysis, called diversity, is presented and characterised here. The dependence of diversity on the size of the data set involved and on the number of possible data values is discussed. The measure provides a very concise summary of the rank structure about each point and is sensitive to ‘ties’ in the local rank distribution.


rank variance non-parametric statistics order statistics robust estimation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Carolyn J. Evans
    • 1
  • Imants D. Svalbe
    • 1
  1. 1.Department of PhysicsMonash UniversityClaytonAustralia

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