Posted by
Michael Schmid on
Oct 29, 2010; 3:30pm
URL: http://imagej.273.s1.nabble.com/Calculating-specific-surface-area-of-2D-image-tp3686537p3686539.html
Hi Neil,
for the point-point correlation function, you can use my macro
http://imagejdocu.tudor.lu/doku.php?
id=macro:radially_averaged_autocorrelation
In contrast to the 'raw' correlation function S2 often used in the
'rock porosity' community, the macro gives you a normalized
autocorrelation, such that the correlation function is zero for no
correlation and 1 for perfect correlation (aka the 'one-point
correlation function'). There is a linear relationship between the
'raw' and the 'normalized' correlation function. You can use the
following two cases to get the linear scaling:
S2(0) = phi
S2(uncorrelated) = phi^2
with phi being the pore fraction.
Thus,
S2 = phi^2 + (phi-phi^2) * a
where a is the autocorrelation from my macro.
My macro uses the Fourier transform to calculate the correlation
function, but it uses a function equivalent to the denominator of Eq.
9 in the Torabi et al. J. Geophys. Res. 113, B08208 paper to correct
for the finite image size.
Hope this helps,
Michael
________________________________________________________________
On 29 Oct 2010, at 12:49, Neil Bishop wrote:
> Just noticed the link doesn't work.
>
> The address is
http://www.jongant.co.uk/
> spatial_correlation_functions.pdf
>
> There are also a couple of other papers here that go more into the
> detail of how tah equations used are generated
>
>
http://www.jongant.co.uk/berryman_1988.pdf>
>
http://www.jongant.co.uk/berryman_and_blair_1986.pdf>
> Thanks,
> Neil.
>
> --- On Mon, 25/10/10, Neil Bishop <
[hidden email]> wrote:
>
>
> From: Neil Bishop <
[hidden email]>
> Subject: Calculating specific surface area of 2D image
> To:
[hidden email]
> Date: Monday, 25 October, 2010, 15:45
>
>
> Hi,
> We have come across a paper where the authors calculate the
> permeability of a rock sample from a 2D backscattered SEM image. In
> order to do this they calculate Specific Surface Area using a
> binary image (rock is black, pores are white). To do this they
> first calculate a two-point correlation function. Apparantly this
> is the probability that two points separated by a line (r) are both
> in the pore space. Firstly in a Cartesian Coordinate system. They
> then convert this to a Polar Coordinate system. Then from this they
> calculate the Specific Surface Area.
>
> I should probably mention that the two-point correlations equations
> that they are using in this paper are a little bit beyond me, so if
> you would like to look at the paper for yourself you can download
> it from here. The equations in question are 9, 10 and 12 on pages 3-4.
>
> According to the paper they have done these calculations using a
> function that is written in MATLAB. I just wondered if such a
> function existed in ImageJ already? I have downloaded and installed
> the ImageJ for Microscopy version and I have been through all the
> menus, but nothing seems to obviously be it. If not could anyone
> advise me how I could go about getting this function into ImageJ?
>
> Any advice will be gratefully received,
> Neil.
>
>
>
>
>
>
>