Advertisement

Nonlinear covariance for multi-band image data

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

Abstract

Multi-band data is often (unavoidably) pre-processed by nonlinear mappings, or is comprised of measurements taken across non-commensurate bands. We treat such cases using rank order statistics, avoiding problems of dimensionality and nonlinearity. Our aim is to reduce multi-band data to two images; one showing inhomogeneous image regions common to all of the image bands and another image which reflects the differences. The measure used is a nonlinear analog of linear covariance, the ‘co-diversity’, which responds to the relative homogeneity of local image regions in terms of rank. Algorithms to determine the ‘co-diversity’ are presented and applied to the interpretation of edges in multispectral data and to the combination of information from different sources, for example, binary and greyscale data. The method is robust to contrast variations across the data, but relies on some prior morphologic smoothing to ensure the local rank order is not dominated by noise.

Keywords

nonlinear statistics multivariate techniques mathematical morphology 

References

  1. 1.
    Barnett V.. The Ordering of Multivariate Data. J. R. Statist. Soc. A., 139 part 3. (1976),318–344.Google Scholar
  2. 2.
    Jones R. and Talbot H.. Morphological Filtering for Colour Images with No New Colours. IVCNZ '96, 149–154, Lower Hutt, New Zealand, 1996.Google Scholar
  3. 3.
    Evans C.J. and Svalbe I.D.. Nonlinear Variance Measures in Image Data. To be presented at SPR 98.Google Scholar
  4. 4.
    Kendall M.G.. Rank Correlation Methods, 4th ed.. Griffin, London, 1970.Google Scholar
  5. 5.
    Draper D.. Rank-Based Robust Analysis of Linear Models.I. Exposition and Review. Statistical Science, 3(2) (1988), 239–271.Google Scholar
  6. 6.
    Chung L. and Marden J.L. Use of Nonnull Models for Rank Statistics in Bivariate, Two-Sample, and Analysis of Variance Problems. J. American Statistical Association, 86(413) (1991), 188–200.Google Scholar
  7. 7.
    Serra, J.. Image Analysis and Mathematical Morphology. volume 2: Theoretical Advances. Academic Press, London, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

Personalised recommendations