I m currently working on fuzzy based approach in image segmentation using an ultrasound image. I hv already generated the membership function. I m having a difficulty to generate the function which expresses entropy of the fuzzy set.

H(x) = 1/(M*N) ΣΣ Sn(μ(g(i,j))

(i=1,2,...M; j=1,2,....N)

How to execute this function? Pls provide me the code. Also I would like to ask about the mapping of ultrasound image from intensity space domain (g(i,j)) to fuzzy domain (μ(g(i,j))?

[Image Analyst]

List the toolboxes you have in the Products section below, for example Fuzzy Logic or Image Processing.

[Seetharaman]

I m using both fuzzy logic and Image processing toolbox. I hv used Fuzzy logic toolbox for generatins S-membership function using 'smf' command.

Answer 1

[Youssef Khmou]

hi, try this function :

 function h = fuzzy_entropy(x,n) 

 % FUZZY_ENTROPY : Computes the first order estimate of the entropy matrix 
%
% H = FUZZY_ENTROPY( X, N ) returns the first order estimate of matrix X 
% with N symbols  ( N =256 if omitted) in bits /symbol . The estimate assume
% statistically independant source caracterized by the relative frequency
% of the occurance of the element in X

 error(nargchk(1,2,nargin)) % Check Input Arguments
 if nargin < 2
    n=256;                  % default n
end

 x=double(x);
 xh=hist(x(:),n);             % Compute N-bin histogram

 xh=xh /sum(x(:));            % Compute probablities

 %  Make mask to eliminate zeros since log2(0)=-Inf
i=find(xh);
h=-sum(xh(i).*log2(xh(i))+((1-xh(i)).*log2(1-xh(i)))); % Compute entropy