How to calculate the energy and correlation of an image

Question

I think you are looking for graycomatrix and graycoprops. From the graycoprops documentation, two properties that can be computed:

'Correlation'   statistical measure of how correlated a pixel is to its 
                neighbor over the whole image. Range = [-1 1]. 
                Correlation is 1 or -1 for a perfectly positively or
                negatively correlated image. Correlation is NaN for a 
                constant image.

'Energy'        summation of squared elements in the GLCM. Range = [0 1].
                Energy is 1 for a constant image.

To compute these properties, first compute the graylevel co-occurrence matrix via graycomatrix, then call graycoprops. For example,

I = imread('circuit.tif');
GLCM = graycomatrix(I,'Offset',[2 0;0 2]);
stats = graycoprops(GLCM,{'correlation','energy'})

You just need to decide on the Offset parameter for graycomatrix. A thorough choice would be offset = [0 1; -1 1; -1 0; -1 -1];

To compute entropy for the GLCMs, you can't use graycoprops, so you'll have to do it yourself:

p = bsxfun(@rdivide,GLCM,sum(sum(GLCM,1),2)); % normalize each GLCM to probs

numGLCMs = size(p,3);
entropyVals = zeros(1,numGLCMs);
for ii=1:numGLCMs,
    pi = p(:,:,ii);
    entropyVals(ii) = -sum(pi(pi>0).*log(pi(pi>0)));
end