How to change 4x4 matrix to 2x2 matrix

I have a 4x4 matrix A = [1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7]

Now, I'd like to change the matrix size from 4x4 to 2x2 and have the average of 4 cells for new cell.

To visualize,

*1 2* 3 4
*2 3* 4 5
 3 4  5 6      2 4
 4 5  6 7 -->  4 6

Any input would be appreciated,

Answer 1

[Orion]

A = [1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7]

B = cellfun(@mean,cellfun(@mean,mat2cell(A,[2 2],[2 2]),'UniformOutput',false))

A =

       1     2     3     4
       2     3     4     5
       3     4     5     6
       4     5     6     7

B =

       2     4
       4     6

Note : you can simplify by decomposing in several steps if you prefer.

[Jan]

This is surprisingly slow: it needs about 100 times longer than the other M-versions posted here.

Answer 2

[James Tursa]

Yet another way (not necessarily any better than other posts), generalized:

kr = 2; kc = 2; % Row and Column sizes of sub-block
[m n] = size(A); mk = m/kr; nk = n/kc; % Size of input and result
B = reshape(sum(reshape(reshape(sum(reshape(A,kr,[])),mk,[]).',kc,[])),nk,mk).'/(kr*kc);

Answer 3

[Matt J]

It was for this kind of thing that I wrote SEPBLOCKFUN ( Download ).

    Anew = sepblockfun(A,[2,2],@mean);

Answer 4

[Jan]

And if speed matters, FEX: BlockMean.mex will help.

Answer 5

[Image Analyst]

Did you try the straightforward:

out = [A(1,1)+A(1,2)+A(2,1)+A(2,2),...
  A(1,3)+A(1,4)+A(2,3)+A(2,4);...
  A(3,1)+A(3,2)+A(4,1)+A(4,2),...
  A(3,3)+A(3,4)+A(4,3)+A(4,4)]/4

Answer 6

[Azzi Abdelmalek]

A = [1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7]
[n,m]=size(A)
[ii1,jj1]=ndgrid(1:2:n,1:2:m)
out=arrayfun(@(x,y) mean(mean(A(x:x+1,y:y+1))),ii1,jj1)

Answer 7

[Jan]

Some timings for a 1024*768 image, 100 iterations (Matlab R2011b, Win7/64, Core2Duo):

 BlockMean:      0.35 sec
 CELLFUN:      784.0  sec    (wow!)
 SUM(RESHAPE):   8.37 sec
 SUM(RESHAPE) 2: 5.70 sec
 ARRAYFUN:       9.74 sec
 SEPBLOCK:       7.50 sec
 (BLOCKPROC:    Undefined function, I do not have the required toolbox)

function SpeedTest(A)

A = rand(1024, 768);
n = 100;

tic;
for k = 1:n
   r = BlockMean(A, 2, 2);
end
fprintf('BlockMean: %.4g sec\n', toc);

tic;
for k = 1:1
   [m, n] = size(A);
   r = cellfun(@mean, ...
      cellfun(@mean, ...
      mat2cell(A, repmat(2, 1, m/2), repmat(2, 1, n/2)),'UniformOutput',false));
end
fprintf('CELLFUN: %.4g sec\n', toc * 100);

tic;
for k = 1:n
   kr = 2;
   kc = 2;
   [m, n] = size(A);
   mk = m/kr;
   nk = n/kc;
   B  = reshape(sum(reshape( ...
      reshape(sum(reshape(A,kr,[])), mk,[]).', kc, [])), nk, mk).' / (kr*kc);
end
fprintf('SUM(RESHAPE): %.4g sec\n', toc);

tic;
for k = 1:n
   V = 2;
   W = 2;
   [M, N] = size(A);
   AM = reshape(A, V, M/V, W, N/W,  []);
   r  = sum(sum(AM, 1), 3) .* (1.0 / (V * W));
end
fprintf('SUM(RESHAPE) 2: %.4g sec\n', toc);

tic;
for k = 1:1
   [n,m]      = size(A);
   [ii1, jj1] = ndgrid(1:2:n,1:2:m);
   r          = arrayfun(@(x,y) mean(mean(A(x:x+1,y:y+1))),ii1,jj1);
end
fprintf('ARRAYFUN: %.4g sec\n', toc);

tic;
for k = 1:n
   r = sepblockfun(A, [2,2], @mean);
end
fprintf('SEPBLOCK: %.4g sec\n', toc);

tic;
for k = 1:n
   r = blockproc(A,[2,2], @(x) mean(x.data(:)) )
end
fprintf('BLOCKPROC: %.4g sec\n', toc);

[Image Analyst]

Why did you run the cellfun and arrayfun tests only 1 iteration instead of n iterations like the other tests? By the way, 1 iteration of blockproc took 12 seconds.