glcm_features1.m

glcm examples in matlab

hx   = zeros(size_glcm_3,1);
hy   = zeros(size_glcm_3,1);
hxy2 = zeros(size_glcm_3,1);

%Q    = zeros(size(glcm));

for k = 1:size_glcm_3 % number glcms

    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

            out.contr(k) = out.contr(k) + (abs(i - j))^2.*glcm(i,j,k);
            out.dissi(k) = out.dissi(k) + (abs(i - j)*glcm(i,j,k));
            out.energ(k) = out.energ(k) + (glcm(i,j,k).^2);
            out.entro(k) = out.entro(k) - (glcm(i,j,k)*log(glcm(i,j,k) + eps));
            out.homom(k) = out.homom(k) + (glcm(i,j,k)/( 1 + abs(i-j) ));
            out.homop(k) = out.homop(k) + (glcm(i,j,k)/( 1 + (i - j)^2));
            % [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) = out.sosvh(k) + glcm(i,j,k)*((i - glcm_mean(k))^2);
            
            %out.invdc(k) = out.homom(k);
            out.indnc(k) = out.indnc(k) + (glcm(i,j,k)/( 1 + (abs(i-j)/size_glcm_1) ));
            out.idmnc(k) = out.idmnc(k) + (glcm(i,j,k)/( 1 + ((i - j)/size_glcm_1)^2));
            u_x(k)          = u_x(k) + (i)*glcm(i,j,k); % changed 10/26/08
            u_y(k)          = u_y(k) + (j)*glcm(i,j,k); % changed 10/26/08
            % code requires that Nx = Ny 
            % the values of the grey levels range from 1 to (Ng) 
        end
        
    end
    out.maxpr(k) = max(max(glcm(:,:,k)));
end
% glcms have been normalized:
% The contrast has been computed for each glcm in the 3D matrix
% (tested) gives similar results to the matlab function

for k = 1:size_glcm_3
    
    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
    
%     % consider u_x and u_y and s_x and s_y as means and standard deviations
%     % of p_x and p_y
%     u_x2(k) = mean(p_x(:,k));
%     u_y2(k) = mean(p_y(:,k));
%     s_x2(k) = std(p_x(:,k));
%     s_y2(k) = std(p_y(:,k));
    
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:
for k = 1:(size_glcm_3)
    
    for i = 1:(2*(size_glcm_1)-1)
        out.savgh(k) = out.savgh(k) + (i+1)*p_xplusy(i,k);
        % the summation for savgh is for i from 2 to 2*Ng hence (i+1)
        out.senth(k) = out.senth(k) - (p_xplusy(i,k)*log(p_xplusy(i,k) + eps));
    end

end
% compute sum variance with the help of sum entropy
for k = 1:(size_glcm_3)
    
    for i = 1:(2*(size_glcm_1)-1)
        out.svarh(k) = out.svarh(k) + (((i+1) - out.senth(k))^2)*p_xplusy(i,k);
        % the summation for savgh is for i from 2 to 2*Ng hence (i+1)
    end

end
% compute difference variance, difference entropy, 
for k = 1:size_glcm_3
% 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
    for i = 0:(size_glcm_1-1)
        out.denth(k) = out.denth(k) - (p_xminusy(i+1,k)*log(p_xminusy(i+1,k) + eps));
        out.dvarh(k) = out.dvarh(k) + (i^2)*p_xminusy(i+1,k);
    end
end

% compute information measure of correlation(1,2) [1]
for k = 1:size_glcm_3
    hxy(k) = out.entro(k);
    for i = 1:size_glcm_1
        
        for j = 1:size_glcm_2
            hxy1(k) = hxy1(k) - (glcm(i,j,k)*log(p_x(i,k)*p_y(j,k) + eps));
            hxy2(k) = hxy2(k) - (p_x(i,k)*p_y(j,k)*log(p_x(i,k)*p_y(j,k) + eps));
%             for Qind = 1:(size_glcm_1)
%                 Q(i,j,k) = Q(i,j,k) +...
%                     ( glcm(i,Qind,k)*glcm(j,Qind,k) / (p_x(i,k)*p_y(Qind,k)) ); 
%             end
        end
        hx(k) = hx(k) - (p_x(i,k)*log(p_x(i,k) + eps));
        hy(k) = hy(k) - (p_y(i,k)*log(p_y(i,k) + eps));
    end
    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

corm = zeros(size_glcm_3,1);
corp = zeros(size_glcm_3,1);
% using http://www.fp.ucalgary.ca/mhallbey/glcm_variance.htm for s_x s_y
for k = 1:size_glcm_3
    for i = 1:size_glcm_1
        for j = 1:size_glcm_2
            s_x(k)  = s_x(k)  + (((i) - u_x(k))^2)*glcm(i,j,k);
            s_y(k)  = s_y(k)  + (((j) - u_y(k))^2)*glcm(i,j,k);
            corp(k) = corp(k) + ((i)*(j)*glcm(i,j,k));
            corm(k) = corm(k) + (((i) - u_x(k))*((j) - u_y(k))*glcm(i,j,k));
            out.cprom(k) = out.cprom(k) + (((i + j - u_x(k) - u_y(k))^4)*...
                glcm(i,j,k));
            out.cshad(k) = out.cshad(k) + (((i + j - u_x(k) - u_y(k))^3)*...
                glcm(i,j,k));
        end
    end
    % 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) = s_x(k) ^ 0.5;
    s_y(k) = s_y(k) ^ 0.5;
    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));
%     % alternate values of u and s
%     out.corrp2(k) = (corp(k) - u_x2(k)*u_y2(k))/(s_x2(k)*s_y2(k));
%     out.corrm2(k) = corm(k) / (s_x2(k)*s_y2(k));
end
% Here the formula in the paper out.corrp and the formula in matlab
% out.corrm are equivalent as confirmed by the similar results obtained

% % The papers have a slightly different formular for Contrast
% % I have tested here to find this formula in the papers provides the 
% % same results as the formula provided by the matlab function for 
% % Contrast (Hence this part has been commented)
% out.contrp = zeros(size_glcm_3,1);
% contp = 0;
% Ng = size_glcm_1;
% for k = 1:size_glcm_3
%     for n = 0:(Ng-1)
%         for i = 1:Ng
%             for j = 1:Ng
%                 if (abs(i-j) == n)
%                     contp = contp + glcm(i,j,k);
%                 end
%             end
%         end
%         out.contrp(k) = out.contrp(k) + n^2*contp;
%         contp = 0;
%     end
%     
% 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)