Abstract

   Natural  time-varying   images   possess  substantial  spatiotemporal
   correlations.  We measure these correlations ---  or equivalently the
   power spectrum --- for an ensemble of more  than  a thousand segments
   of  motion  pictures,  and  we  find  significant regularities.  More
   precisely, our measurements show  that  the  dependence  of the power
   spectrum on the spatial frequency,  f , and  temporal frequency,  w ,
   is in general nonseparable and is given  by   f^{-m-1} F(w/f) , where
    F(w/f)  is a nontrivial function  of  the  ratio   w/f .   We give a
   theoretical derivation of this  scaling  behaviour  and  show that it
   emerges from objects  with  a  static  power  spectrum    ~  f^{-m} ,
   appearing at a wide range of depths and moving with a distribution of
   velocities relative to the observer.  We show that  in  the regime of
   relatively  high  temporal  and  low  spatial  frequencies, the power
   spectrum  becomes  independent  of  the   details   of  the  velocity
   distribution and it is  separable  into  the  product  of spatial and
   temporal power spectra with the temporal part given  by the universal
   power-law    ~  w^{-2} .   Making  some  reasonable assumptions about
   the  form  of  the  velocity  distribution  we  derive an  analytical
   expression  for  the  spatiotemporal  power  spectrum   which  is  in
   excellent agreement with the data for the entire range of spatial and
   temporal frequencies of our measurements.  The results  in this paper
   have direct implications to neural processing  of time-varying images
   in the visual pathway.

   (Network: Computation in Neural Systems. Vol 6(3): page 345-358. 1995)

   (Papers' Index of Dawei Dong)