Posted by
LMAnovitz on
Apr 06, 2009; 1:35pm
URL: http://imagej.273.s1.nabble.com/1D-autocorrelation-function-tp3692494p3692496.html
HI
The correlation function is not a projection of the image.
Rather, it is a measure of the spatial distribution of, and within
particles in it. It is sometimes called a pair distribution function
Or a radial distribution function. You may have seen these in various
types of computation chemistry or X-ray measurements where one plots
concentration as a function of distance, and there a peaks in the curves
That correspond to, say, in water, the average H-H, O-H and O-O distances.
In this case of a sample with pore space, this gives the correlations of
distances within a given pore, and between pores.
Summarizing from Ioannidis et al (I tried to attach it, just fyi, in case my
description is not clear enough, but the system won't let me. Please contact
Me directly at the address below, and I'll forward the paper if anyone needs
it)
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 ?
--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