Correlation formula Matlab

Question

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):

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

Answer 1

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.

Answer 2

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);