Average every n*n elements in a two dimensional matrix

8 views (last 30 days)
Peter on 10 May 2013
I have a two dimensional matrix, and create a second matrix with the averages of every n*n elements. So, say I have a 100*100 matrix; I would want a 10*10 matrix where each single element is the average of the 10*10 elements in the original matrix at that location.
So far I have tried splitting the matrix into n separate row vectors, averaging each of those every n elements, concatenating and re averaging ever n of the averaged vectors. Then I concatenate each of those vectors. Is there a more efficient way to do this this, without using so many loops? It is very inefficient and inelegant for such a large matrix.

Accepted Answer

Sean de Wolski
Sean de Wolski on 10 May 2013
Edited: Sean de Wolski on 10 May 2013
If you have the Image Processing Toolbox, you can use blockproc
blockproc(magic(100),[10 10],@(bs)sum(bs.data(:)))
And for more info:
doc blockproc
Otherwise just use a double for-loop.
OR if you're curious to learn about vectorizing and speed is a top priority:
G = reshape(sum(reshape(sum(reshape(A,sz(1),blk(2),[]),2),blk(1),[]),1),sz./blk);
And broken into pieces:
A = magic(100);
blk = [10 10];
sz = size(A);
B = reshape(A,sz(1),blk(2),[]); %reshape so every blk column is a page
C = sum(B,2); %sum blocks across rows
D = reshape(C,blk(1),[]); %reshape so each column is a block
E = sum(D,1); %sum columns
F = reshape(E,sz./blk); %reshape to final size.
  1 Comment
Peter on 10 May 2013
Yes, that's perfect. That give the sum of those elements, and to get the mean I just divided by the number of elements.

Sign in to comment.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!