Shanon entropy of a matrix

I defined a matrix like A and I want to calculate its entropy and when I use the entropy function it returns zero :

A = [2,3,4;4,5,6;10,12,1]
entropy(A)

ans =

     0

but when I read the matlab entropy help, it mentioned that this funtion will return the entropy of a grayscale image, so I have decided to apply mat2gray to convert my matrix into the grayscale, and now it returns 2.9477.

b= mat2gray(A)

b =

    0.0909    0.1818    0.2727
    0.2727    0.3636    0.4545
    0.8182    1.0000         0

entropy(b)

ans =

    2.9477

so, could you please help to find is this way correct?

Answer 1

[Jan]

As the documentation tells, the input is expected to be a gray scale image. Then value over 1.0 are limit to 1.0 and you matrix is interpreted as [1, 1, 1; 1, 1, 1; 1, 1, 1] with zero entropy.

Converting the matrix by mat2gray divides the values by the larges element after subtracting the smalles element:

A  = [2,3,4; 4,5,6; 10,12,1]
mA = min(A(:));
B  = (A - mA) / (max(A(:)) - mA)  % same as MAT2GRAY

As far as I understand, this is the correct way to determine the entropy.