December 2001
Volume 1, Issue 3
Vision Sciences Society Annual Meeting Abstract  |   December 2001
Why correlation, energy and gradient motion models are not equivalent
Author Affiliations
  • A. Johnston
    University College London, London, UK
  • C. W. G. Clifford
    Macquarie University, Sydney, Australia
  • C. P. Benton
    University College London, London, UK
  • P. W. McOwan
    Queen Mary University of London, London, UK
Journal of Vision December 2001, Vol.1, 240. doi:
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      A. Johnston, C. W. G. Clifford, C. P. Benton, P. W. McOwan; Why correlation, energy and gradient motion models are not equivalent. Journal of Vision 2001;1(3):240.

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      © ARVO (1962-2015); The Authors (2016-present)

  • Supplements

Claims that some instantiations of generic low-level motion models are mathematically equivalent have led to a widely held view that differences between models are minor and of little significance. The question of equivalence is addressed at a number of levels. We first identify the computational principle by which motion is extracted in each case. Each model is defined by the computational theory implemented. Questions about equivalence relate to the algorithmic and implementation levels. The units of measurement of the models cannot be equated; this alone guarantees that they are not mathematically equivalent. The output of a gradient motion model encodes speed directly (e.g. in pixels per frame), whereas a correlation or energy model encodes the degree of match between the stimulus and the tuned detector. Speed is not computed. Arguments for the equivalence of correlation and energy detectors [1] ignore contrast normalisation whereas contrast normalisation is essential to the argument for an equivalence between gradient and energy models [2,3]. In the latter case the inner product in the gradient model is expanded (4a·b=|a+b|^2-|a-b|^2) to generate terms, e.g.|a+b|, that might be synthesised from linear space-time oriented filters. However in an energy model space-time oriented filters in quadrature phase are combined to deliver phase invariance. In the expanded gradient model these filters are not in quadrature phase and are not phase invariant. Phase invariance specifically from the combination of space-time filters in spatiotemporal quadrature is considered the defining property of an energy model and this is not shared with any implementation of the gradient model.

(1) AdelsonE. H.BergenJ. R.J. Opt. Soc. Am. A 2. 284– 299 (1985)

(2) AdelsonE. H.BergenJ. R.Motion: Representation & Analysis (IEEE Proc), 151– 155, (1986).

(3) BruceV.GreenP. R.GeorgesonM. A.Visual Perception. Hove: Psychology Press (1996).

Johnston, A., Clifford, C.W.G., Benton, C.P., McOwan, P.W.(2001). Why correlation, energy and gradient motion models are not equivalent [Abstract]. Journal of Vision, 1( 3): 240, 240a,, doi:10.1167/1.3.240. [CrossRef]

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