glcm_features2.m

segmentation code in image processing

glcm_mean = zeros(size_glcm_3,1);
glcm_var  = zeros(size_glcm_3,1);

% http://www.fp.ucalgary.ca/mhallbey/glcm_mean.htm confuses the range of 
% i and j used in calculating the means and standard deviations.
% As of now I am not sure if the range of i and j should be [1:Ng] or
% [0:Ng-1]. I am working on obtaining the values of mean and std that get
% the values of correlation that are provided by matlab.
u_x = zeros(size_glcm_3,1);
u_y = zeros(size_glcm_3,1);
s_x = zeros(size_glcm_3,1);
s_y = zeros(size_glcm_3,1);

% checked p_x p_y p_xplusy p_xminusy
p_x = zeros(size_glcm_1,size_glcm_3); % Ng x #glcms[1]  
p_y = zeros(size_glcm_2,size_glcm_3); % Ng x #glcms[1]
p_xplusy = zeros((size_glcm_1*2 - 1),size_glcm_3); %[1]
p_xminusy = zeros((size_glcm_1),size_glcm_3); %[1]
% checked hxy hxy1 hxy2 hx hy
hxy  = zeros(size_glcm_3,1);
hxy1 = zeros(size_glcm_3,1);
hx   = zeros(size_glcm_3,1);
hy   = zeros(size_glcm_3,1);
hxy2 = zeros(size_glcm_3,1);

corm = zeros(size_glcm_3,1);
corp = zeros(size_glcm_3,1);

for k = 1:size_glcm_3
    
    glcm_sum(k) = sum(sum(glcm(:,:,k)));
    glcm(:,:,k) = glcm(:,:,k)./glcm_sum(k); % Normalize each glcm
    glcm_mean(k) = mean2(glcm(:,:,k)); % compute mean after norm
    glcm_var(k)  = (std2(glcm(:,:,k)))^2;
    
    for i = 1:size_glcm_1
        
        for j = 1:size_glcm_2
            p_x(i,k) = p_x(i,k) + glcm(i,j,k); 
            p_y(i,k) = p_y(i,k) + glcm(j,i,k); % taking i for j and j for i
            if (ismember((i + j),[2:2*size_glcm_1])) 
                p_xplusy((i+j)-1,k) = p_xplusy((i+j)-1,k) + glcm(i,j,k);
            end
            if (ismember(abs(i-j),[0:(size_glcm_1-1)])) 
                p_xminusy((abs(i-j))+1,k) = p_xminusy((abs(i-j))+1,k) +...
                    glcm(i,j,k);
            end
        end
    end
    
end

% marginal probabilities are now available [1]
% p_xminusy has +1 in index for matlab (no 0 index)
% computing sum average, sum variance and sum entropy:


%Q    = zeros(size(glcm));

i_matrix  = repmat([1:size_glcm_1]',1,size_glcm_2);
j_matrix  = repmat([1:size_glcm_2],size_glcm_1,1);
% i_index = [ 1 1 1 1 1 .... 2 2 2 2 2 ... ]
i_index   = j_matrix(:);
% j_index = [ 1 2 3 4 5 .... 1 2 3 4 5 ... ]
j_index   = i_matrix(:);
xplusy_index = [1:(2*(size_glcm_1)-1)]';
xminusy_index = [0:(size_glcm_1-1)]';
mul_contr = abs(i_matrix - j_matrix).^2;
mul_dissi = abs(i_matrix - j_matrix);
%div_homop = ( 1 + mul_contr); % used from the above two formulae
%div_homom = ( 1 + mul_dissi);

for k = 1:size_glcm_3 % number glcms
    
    out.contr(k) = sum(sum(mul_contr.*glcm(:,:,k)));
    out.dissi(k) = sum(sum(mul_dissi.*glcm(:,:,k)));
    out.energ(k) = sum(sum(glcm(:,:,k).^2));
    out.entro(k) = - sum(sum((glcm(:,:,k).*log(glcm(:,:,k) + eps))));
    out.homom(k) = sum(sum((glcm(:,:,k)./( 1 + mul_dissi))));
    out.homop(k) = sum(sum((glcm(:,:,k)./( 1 + mul_contr))));
    % [1] explains sum of squares variance with a mean value;
    % the exact definition for mean has not been provided in 
    % the reference: I use the mean of the entire normalized glcm     
    out.sosvh(k) = sum(sum(glcm(:,:,k).*((i_matrix - glcm_mean(k)).^2)));
    out.indnc(k) = sum(sum(glcm(:,:,k)./( 1 + (mul_dissi./size_glcm_1) )));
    out.idmnc(k) = sum(sum(glcm(:,:,k)./( 1 + (mul_contr./(size_glcm_1^2)))));
    out.maxpr(k) = max(max(glcm(:,:,k)));
    
    u_x(k)       = sum(sum(i_matrix.*glcm(:,:,k))); 
    u_y(k)       = sum(sum(j_matrix.*glcm(:,:,k))); 
    % using http://www.fp.ucalgary.ca/mhallbey/glcm_variance.htm for s_x
    % s_y : This solves the difference in value of correlation and might be
    % the right value of standard deviations required 
    % According to this website there is a typo in [2] which provides
    % values of variance instead of the standard deviation hence a square
    % root is required as done below:
    s_x(k)  = (sum(sum( ((i_matrix - u_x(k)).^2).*glcm(:,:,k) )))^0.5;
    s_y(k)  = (sum(sum( ((j_matrix - u_y(k)).^2).*glcm(:,:,k) )))^0.5;
    
   corp(k) = sum(sum((i_matrix.*j_matrix.*glcm(:,:,k))));
   corm(k) = sum(sum(((i_matrix - u_x(k)).*(j_matrix - u_y(k)).*glcm(:,:,k)))); 
   
   out.autoc(k) = corp(k);
   out.corrp(k) = (corp(k) - u_x(k)*u_y(k))/(s_x(k)*s_y(k));
   out.corrm(k) = corm(k) / (s_x(k)*s_y(k)); 
   
   out.cprom(k) = sum(sum(((i_matrix + j_matrix - u_x(k) - u_y(k)).^4).*...
                glcm(:,:,k))); 
   out.cshad(k) = sum(sum(((i_matrix + j_matrix - u_x(k) - u_y(k)).^3).*...
                glcm(:,:,k)));        
    
            

    

   out.savgh(k) = sum((xplusy_index + 1).*p_xplusy(:,k));
   % the summation for savgh is for i from 2 to 2*Ng hence (i+1)
   out.senth(k) =  - sum(p_xplusy(:,k).*...
            log(p_xplusy(:,k) + eps));
   
    % compute sum variance with the help of sum entropy
    out.svarh(k) = sum((((xplusy_index + 1) - out.senth(k)).^2).*...
        p_xplusy(:,k));
        % the summation for savgh is for i from 2 to 2*Ng hence (i+1)    
    
    % compute difference variance, difference entropy,
    % out.dvarh2(k) = var(p_xminusy(:,k));
    % but using the formula in 
    % http://murphylab.web.cmu.edu/publications/boland/boland_node26.html
    % we have for dvarh
    out.denth(k) = - sum((p_xminusy(:,k)).*...
        log(p_xminusy(:,k) + eps));
    out.dvarh(k) = sum((xminusy_index.^2).*p_xminusy(:,k));
    
    % compute information measure of correlation(1,2) [1]
    hxy(k) = out.entro(k);
    glcmk  = glcm(:,:,k)';
    glcmkv = glcmk(:);
    
    hxy1(k) =  - sum(glcmkv.*log(p_x(i_index,k).*p_y(j_index,k) + eps));
    hxy2(k) =  - sum(p_x(i_index,k).*p_y(j_index,k).*...
        log(p_x(i_index,k).*p_y(j_index,k) + eps));
     hx(k) = - sum(p_x(:,k).*log(p_x(:,k) + eps));
     hy(k) = - sum(p_y(:,k).*log(p_y(:,k) + eps));   
    
    out.inf1h(k) = ( hxy(k) - hxy1(k) ) / ( max([hx(k),hy(k)]) );
    out.inf2h(k) = ( 1 - exp( -2*( hxy2(k) - hxy(k) ) ) )^0.5;
    
    %     eig_Q(k,:)   = eig(Q(:,:,k));
    %     sort_eig(k,:)= sort(eig_Q(k,:),'descend');
    %     out.mxcch(k) = sort_eig(k,2)^0.5;
    % The maximal correlation coefficient was not calculated due to
    % computational instability 
    % http://murphylab.web.cmu.edu/publications/boland/boland_node26.html    
    
              
end



%       GLCM Features (Soh, 1999; Haralick, 1973; Clausi 2002)
%           f1. Uniformity / Energy / Angular Second Moment (done)
%           f2. Entropy (done)
%           f3. Dissimilarity (done)
%           f4. Contrast / Inertia (done)
%           f5. Inverse difference    
%           f6. correlation
%           f7. Homogeneity / Inverse difference moment
%           f8. Autocorrelation
%           f9. Cluster Shade
%          f10. Cluster Prominence
%          f11. Maximum probability
%          f12. Sum of Squares
%          f13. Sum Average
%          f14. Sum Variance
%          f15. Sum Entropy
%          f16. Difference variance
%          f17. Difference entropy
%          f18. Information measures of correlation (1)
%          f19. Information measures of correlation (2)
%          f20. Maximal correlation coefficient
%          f21. Inverse difference normalized (INN)
%          f22. Inverse difference moment normalized (IDN)