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

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

Answer 1

[Ahmed A. Selman]

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.

Answer 2

[Image Analyst]

Try to construct a pair of nested for loops over i and j. See the getting started section if you don't know how to program in MATLAB yet. The latter formula is the entropy and there are functions for that, such as entropyfilt() in the Image Processing Toolbox.