Taking the median of the same matrix index over a series of matrices

I am trying to calculate the median of each matrix index over multiple matrices. For example:

A = [1 2 3; 4 5 6; 7 8 9];
B = [9 8 7; 6 5 4; 3 2 1];
C = [3 3 5; 6 7 4; 8 6 5];

All are 3x3 matrices and what I would like to do is to calculate the median of A(i,j), B(i,j), and C(i,j).

What I was thinking is to convert all matrices into an array, and compose a large matrix out of the strings. Like this:

A = A'; A = A(:)'
B = B'; B = B(:)'
C = C'; C = C(:)'
X = [A; B; C];
Med = median(X,'c');

Is there is a better way to do this? I am trying to do this to a series of 2048x2048 images and I would like to avoid unnecessarily large matrix operations.

Thanks in advance!

Answer 1

[Geoff Hayes]

Manu - consider using cat to concatenate the three matrices into a 3D array as

 D = cat(3,A,B,C);

where D(:,:,1) == A, D(:,:,2) == B and D(:,:,3) == C.

Now compute the median of D along the third dimension as

 median(D,3)

which returns

     3     3     5
     6     5     4
     7     6     5

which should be the median for A(i,j), B(i,j), and C(i,j).

[Manu]

That's a much more elegant way of doing this! Thanks!