estimation/measure of entropy

How to calculate entropy of an image without using the inbuilt functions? Entropy is the measure of loss of information.

-summation(P.*log2 P)

P is the count of histogram..but not getting the proper result!Anyone plz help.

Answer 1

[Thorsten]

Make sure you run log2 only on values > 0. Otherwise you would get NaN.

I = im2double(rgb2gray(imread('peppers.png')));
P = hist(I(:), linspace(0, 1, 256)); P = P(:); P = P(P(:)>0);
E = -sum(P.*log2(P))

[Youssef Khmou]

a minus sign as remark to the code, this method can be sensitive to the number of bins used in function Hist.

[Thorsten]

I've added the minus. And, yes, this method is sensitive to the number of bins:

for b = 1:512
  P = hist(I(:), linspace(0, 1, b)); P = P(:); P = P(P(:)>0); 
  E(b) = -sum(P.*log2(P));
end
plot(E)

So use the minimum number of bins where the entropy does not change anymore

Nbins = min(find(diff(E) == 0))
Nbins =

   256

I've changed the number of bins in the code above accordingly.

[Youssef Khmou]

that is an efficient technique for controlling the histogram.

[Durga]

Thanks a lot for helping me to understand.

Answer 2

[Behrang Mehrparvar]

this link might be useful in setting the bin size [ link ]