analysis metrics

analysis_metrics_in_paper/analysis_MI.m

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+function MI = analysis_MI(A,B,F)
+
+% MI_A = nmi(A,F);
+% MI_B = nmi(B,F);
+
+% MI_A = mutual_information_images(A,F);
+% MI_B = mutual_information_images(B,F);
+
+MI_A = MutualInformation(A,F);
+MI_B = MutualInformation(B,F);
+
+MI = MI_A + MI_B;
+
+end
+
+% by soleimani h.soleimani@ec.iut.ac.ir
+%input---> im1 and im2... they should be in gray scale,[0 255], and have the same size
+function MI=mutual_information_images(im1, im2)
+im1=double(im1)+1;
+im2=double(im2)+1;
+
+% find joint histogram
+joint_histogram=zeros(256,256);
+
+for i=1:min(size(im1,1),size(im2,1))
+    for j=1:min(size(im1,2),size(im2,2))
+       joint_histogram(im1(i,j),im2(i,j))= joint_histogram(im1(i,j),im2(i,j))+1;
+    end
+end
+
+
+ JPDF=joint_histogram/sum(joint_histogram(:)); % joint pdf of two images
+ pdf_im1=sum(JPDF,1); % pdf of im1
+ pdf_im2=sum(JPDF,2); % pdf of im2
+
+ % find MI
+ MI=0;
+ for i=1:256
+     for j=1:256
+         if JPDF(i,j)>0
+             MI=MI+JPDF(i,j)*log2(JPDF(i,j)/(pdf_im1(i)*pdf_im2(j)));
+         end
+     end
+ end
+end
+
+% MutualInformation: returns mutual information (in bits) of the 'X' and 'Y'
+% by Will Dwinnell
+%
+% I = MutualInformation(X,Y);
+%
+% I  = calculated mutual information (in bits)
+% X  = variable(s) to be analyzed (column vector)
+% Y  = variable to be analyzed (column vector)
+%
+% Note: Multiple variables may be handled jointly as columns in matrix 'X'.
+% Note: Requires the 'Entropy' and 'JointEntropy' functions.
+%
+% Last modified: Nov-12-2006
+
+function I = MutualInformation(X,Y)
+
+if (size(X,2) > 1)  % More than one predictor?
+    % Axiom of information theory
+    I = JointEntropy(X) + entropy(Y) - JointEntropy([X Y]);
+else
+    % Axiom of information theory
+    I = entropy(X) + entropy(Y) - JointEntropy([X Y]);
+end
+
+
+% God bless Claude Shannon.
+
+% EOF
+end
+
+
+% JointEntropy: Returns joint entropy (in bits) of each column of 'X'
+% by Will Dwinnell
+%
+% H = JointEntropy(X)
+%
+% H = calculated joint entropy (in bits)
+% X = data to be analyzed
+%
+% Last modified: Aug-29-2006
+
+function H = JointEntropy(X)
+
+% Sort to get identical records together
+X = sortrows(X);
+
+% Find elemental differences from predecessors
+DeltaRow = (X(2:end,:) ~= X(1:end-1,:));
+
+% Summarize by record
+Delta = [1; any(DeltaRow')'];
+
+% Generate vector symbol indices
+VectorX = cumsum(Delta);
+
+% Calculate entropy the usual way on the vector symbols
+H = entropy(VectorX);
+
+
+% God bless Claude Shannon.
+
+% EOF
+end