MATLAB: Please help me implement the equations: Pij = (f(i,j))/(​∑_(i=1)^M∑​_(j=1)^N〖f​(i,j)〗) and H = ─∑_(i=1)^M​∑_(j=1)^NP​ijlog2Pij

Image Processing Toolboximage segmentation

Can someone please explain how to implement these equations in MATLAB?
 Pij = (f(i,j))/(∑_(i=1)^M∑_(j=1)^N〖f(i,j)〗)
 H = ─∑_(i=1)^M∑_(j=1)^NPijlog2Pij

Best Answer

It would be something like (provide your own functions for f, and set up the values of M and N),
clc;clear;close; % set up, clean up.. 
% start of Pij part: Pij = (f(i,j))/(∑_(i=1)^M∑_(j=1)^N〖f(i,j)〗) 
M=...; N=...; % give values
function f=functionF(x,y)
% ... how to find f for x (x is imported i) and y (it is j ) 
end % function 
Pij_single=zeros(M,N); P_of_J=zeros(1,M); % initialize P's  
for i=1:M 
     for j=1:N
         Pij_single(i,j)=functionF(i,j);
     end 
   P_of_J(i)=sum(Pij_single(i,:));
end  
Pij_sumOnly=sum(P_of_J); % it must be a single value
for i=1:M
   for j=1:M
     P(i,j)=functionF(i,j)./Pij_sumOnly;
   end 
end
% End of Pij part
% Start of H part: H = ─∑_(i=1)^M∑_(j=1)^NPijlog2Pij 
clear P_single, P_of_J; % in case you need to save memory
H_of_J=zeros(1,M);Hij=zeros(N,M);
% Mark 1   
% Note: if you need  H = ─∑_(i=1)^M∑_(j=1)^NPijlog2Pij  use the code in mark2.
% If you mean H = ─∑_(i=1)^(M-1)∑_(j=1)^(N-1)Pij*log2(Pij) use below: 
H=entropy(Pij);
disp('H is:  '); H
% Mark 2. Delete the lines below if not needed
for i=1:M;
    for j=1:N
      Hij(i,j)=P(i,j).*log2(P(i,j));
    end 
    H_of_J(i)=sum(Hij(:,1));
  end 
  H=-sum(H_of_J);
  disp('H is:  '); H
  % End of the code. Double check initial indices of M, N please.
Related Question