Calculating specific surface area of 2D image

[Neil Bishop]

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.

[Neil Bishop]

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.

[Michael Schmid]

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.
>
>
>
>
>
>
>