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I am working towards my degree thesis in image processing, and I'm using the Matlab Image Processing toolbox. I'm calculate the correlation of an image with the co-occurrence matrix using the Matlab function graycoprops. My problem is that I can't understand the meaning of the formula that defines the correlation property (see the previous link):

Correlation

In particular, what are \mu_i, \mu_j, \sigma_i, \sigma_j ,if i and j are graylevels of the image?

Tonechas
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Elettra
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  • I agree that the definitions are not very clear. Traditionally mu and sigma refer to the mean and standard deviation, respectively. That appears to be the case in this formula as well. It is not clear to me what they mean by "i" and "j", though. – Jim Clay Nov 16 '11 at 17:17

2 Answers2

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I would imagine it's the mean and standard deviation in the x and y directions. i probably corresponds to x, and j to y. That's just a guess, though.

EDIT: This is supported by looking at the function code. I highly recommend you check it out yourself (simply type edit graycoprops), but here's the relevant part:

function Corr = calculateCorrelation(glcm,r,c)
...
% Calculate the mean and standard deviation of a pixel value in the row
% direction direction. e.g., for glcm = [0 0;1 0] mr is 2 and Sr is 0.
mr = meanIndex(r,glcm);
Sr = stdIndex(r,glcm,mr);

% mean and standard deviation of pixel value in the column direction, e.g.,
% for glcm = [0 0;1 0] mc is 1 and Sc is 0.
mc = meanIndex(c,glcm);
Sc = stdIndex(c,glcm,mc);
eykanal
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  • It makes sense, thanks a lot! I'll check out the function code, as you recommended, thanks. – Elettra Nov 16 '11 at 22:15
  • No prob. Thats one of the awesome things about matlab; you can always just look at the function code and see what it does. Highly useful! – eykanal Nov 16 '11 at 23:56
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I have had the same question, and the paper "Statistical Texture Measures Computed from Gray Level Coocurrence Matrices" by Fritz Albregtsen (2008) was of great help, as it gives a precise definition of all the formulas.

Tisys
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