Clever Geek Handbook

Sum Blocks in 3D Matrix - MATLAB

For a 3N by 3N by 3N matrix A, I would like to get an N by N over N matrix B whose entries are taken from the block summation in A.

For example, B (1,1,1) = the sum of all elements of A (1: 3,1: 3,1: 3).

Basically, A is a kind of high resolution matrix and B is a low resolution matrix from summation in A.

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3 answers


reshape

+ sum

and as such should be quite efficient -

sumrows = sum(reshape(A,3,[]),1);                      %// Sum along rows
sumcols = sum(reshape(sumrows,N,3,[]),2);              %// Sum along cols
B = reshape(sum(reshape(sumcols,N*N,3,[]),2),N,N,N);   %// Sum along 3rd dim


If you are crazy about one-liners, here's what brings all the steps into one -

B = reshape(sum(reshape(sum(reshape(sum(reshape(A,3,[]),1),N,3,[]),2),N*N,3,[]),2),N,N,N);
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If memory is not a concern, you can use the "tagging" approach: construct a three-way label to group the elements A

and use that label as the first input argument for accumarray

to make the sum. The label uses integers from 1

to N

, so the result accumarray

already has the desired shape ( N

x N

x N

).



N = 5;
F = 3; %// block size per dimension
A = rand(15,15,15); %// example data. Size FN x FN x FN
[ii jj kk] = ind2sub(size(A), 1:numel(A));
label = ceil([ii.' jj.' kk.']/F);
result = accumarray(label, A(:));
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For a 2D matrix, this will work:

B = reshape(sum(im2col(A, [3 3], 'distinct')), [N N]);

Note. You need an imaging toolbar.

But for 3D matrices, I don't know of any built-in function equivalent im2col

. You may need to use a loop. Left as an exercise for the reader;)

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