Re: 1D autocorrelation function

Posted by Gluender-2 on Apr 06, 2009; 2:32pm
URL: http://imagej.273.s1.nabble.com/1D-autocorrelation-function-tp3692494p3692497.html

>HI
>     The correlation function is not a projection of the image.

I didn't state this. (Please read carefully!)

>[...]
>
>1) let's describe the binary image by a phase function (Z(r)), which takes
>the values zero or one, depending on whether what pixel is white (a grain)
>or black (a pore)
>
>2)The structure of a statistically homogeneous medium can be described by
>the first two statistical moments of this function, the porosity (f) -
>actually phi, but I've no idea how to put such symbols in an e-mail, and the
>Autocorrelation function R(u) these are given by the averages <>
>
>F = <Z(r)>
>
>R(u) = ( <Z(r) - f>*<Z(r+u)-f> )/ abs(f - f^2)
>
>So what does all this mean for a plugin programmer and a two-dimensional
>image

????

>One first calculates f for the image
>Then one starts at the first pixel (0,0) and finds its Z(r) value and,
>Or each of the other pixels relative to that one, finds the distance (u),
>The Z(r) value for the second pixel (called Z(r+u) above, and calculates
>The value of R.  One does this for all pairs of pixels in the image, and
>sums the results for each value of (u) to get R(u).  (I'm not 100% sure, but
>I think Ioannidis et al. only actually do this along x-and y-directions from
>each pixel, not radially)
>
>Does this make any sense ? Can anyone help ?

Sorry no, not for me.
Before you are going to tackle the ij-macro problem, you should have
understood the theory.

Best Herbie

>--larry
>
>--
>Dr. Lawrence M. Anovitz
>MS 6110 PO Box 2008
>Aqueous and Geochemistry Group
>Oak Ridge National Laboratory
>Oak Ridge, Tennessee 37831-6110
>
>865-574-5034 : phone
>865-574-4961 : fax
>
>[hidden email]
>
>
>
>
>
>On 4/4/09 7:58 AM, "Gluender" <[hidden email]> wrote:
>
>>  Larry,
>>
>>  without reading the papers (not my job)...
>>
>>  Could you please explain what happens with the second coordinate of
>>  an image during the 1-D autocorrelation? Is the image projected in
>>  one direction or is the desired result a series of 1-D
>>  autocorrelation functions?
>>
>>  As far as I know imagej does'nt provide neither 1-D
>>  Fourier-transformation nor 1-D autocorrelation which in general is
>>  computed by Fourier-retransformation of the power spectrum.
>>
>>  However there are numerous applications for data/signal analyses that
>>  allow the computation of both, autocorrelation and power spectrum of
>>  1-D signals. Hence you may export the 1-D data from imagej to one of
>>  these applications and then perform the desired computations.
>>
>>
>>>  Hi
>>>    I am looking for a plug-in for ImageJ that will calculate the 1-D
>>>  autocorrelation function from a binary image.
>>>
>>>  As per
>>>
>>>  Journal of Petroleum Science and Engineering 16 (1996) 251-261
>>>  Statistical analysis of the porous microstructure as a method for
>>>  estimating reservoir permeability
>>>  M.A. Ioannidis, M.J. Kwiecien, I. Chatzis
>>>
>>>  A fourier transform of this curve will then be used to extend my neutron
>>>  scattering data to
>>>  Lower Q values as per
>>
>>  Because the Fourier transform of the autocorrelation function is the
>>  power spectrum, I don't quite grasp why the latter isn't directly
>>  computed, but I think I'm missing some essential information that you
>>  may perhaps kindly provide.
>>
>>>  Radlinski et al. (2004) Angstron-to-millimeter characterization of
>>>  sedimentary rock microstructure.
>>>  J Colloid and Interface Sci. 247, 607-612.
>>>
>>>  Can anyone suggest what the correct  plug-in might be ?
>>>  Thanks.
>>>
>>>  --Larry
>>>  --
>>>  Dr. Lawrence M. Anovitz
>>>  MS 6110 PO Box 2008
>>>  Aqueous and Geochemistry Group
>>>  Oak Ridge National Laboratory
>>>  Oak Ridge, Tennessee 37831-6110
>>>
>>>  865-574-5034 : phone
>>>  865-574-4961 : fax
>>>
>>>  [hidden email]
>>
>>  HTH

--

                   Herbie

          ------------------------
          <http://www.gluender.de>