Autocorrelation Function

  • Renée Heilbronner
  • Steve Barrett


In this chapter, as in the previous one, we look at images directly—we do not try to segment the images, we do not look for objects that are represented on the image. Instead, we will again take the gray values for what they are, and we will think of the image matrix as a map of measurements that are coded as gray values. We will then look at the statistics of these measurements, and we will be concerned with describing the spatial correlation between them. The two-dimensional (2-D) autocorrelation function is an ideal tool for describing such maps or ‘visual textures’. As will become apparent, the calculation of the autocorrelation (ACF) is easy and it is fast because no prior segmentation is necessary. The difficult part of the ACF analysis is to interpret the ACF and relate its geometrical characteristics to the image for which it was calculated (Heilbronner 1992).


Software Downloads

  1. Lazy ACF Tiling – click on ‘software’ link


  1. Panozzo Heilbronner R (1992) The autocorrelation function: an image processing tool for fabric analysis. Tectonophysics 212:351–370CrossRefGoogle Scholar


  1. De Ronde AA, Heilbronner R, Stünitz H, Tullis J (2004) Spatial correlation of deformation and mineral reaction in experimetnally deformed plagioclase-olivine aggregates. Tectonophysics 389:93–109CrossRefGoogle Scholar
  2. Heilbronner R (2002) Analysis of bulk fabrics and microstructure variations using tesselations of autocorrelation functions. Comput Geosci 28:447–455CrossRefGoogle Scholar
  3. Heilbronner R (2010) Mapping of texture domains in quartzite microstructures. J Geol Soc India 75: 160–170CrossRefGoogle Scholar
  4. McGrath R, Leung L, Barrett SD, Ledieu L (2005) Imaging quasicrystal surfaces using scanning tunnelling microscopy. Proc R Microsc Soc 40:215–220Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Renée Heilbronner
    • 1
  • Steve Barrett
    • 2
  1. 1.Geologisch-Paläontologisches InstitutUniversität BaselBaselSwitzerland
  2. 2.Department of PhysicsUniversity of LiverpoolLiverpoolUK

Personalised recommendations