MATLAB: Summing within an array to change the size

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I have an array that has dimensions of 111x46x2. I want to sum the values in the first 3×3 block to become the first value of the next matrix repeating this until the last column is summed together. The dimensions of the new matrix should be 37x16x2.

I could make the dimensions of the original matrix 111x48x2 if that makes the calculations easier and more efficient. The 9×9 blocks will have values only in certain locations such as [ 0 0 #; # 0 0; 0 # 0]; and the last column will have values in each row.

Best Answer

If you have the Image Processing Toolbox:

x = rand(111,46,2);
y = blockproc(x,[3 3],@(s)sum(sum(s.data,1),2));

Or if you don't:

z = convn(x,ones(3),'valid');
z = z(1:3:end,1:3:end,:); %may need to crop differently depending on last edges

Related Solutions

MATLAB: How to divide image into non-overlapping blocks?

What do you want to do with the blocks? Would using blockproc be sufficient already?

If not, what should happen with the margins if M is not a multiple of m or n?

Creating a loop is not hard:

X   = rand(1000, 1000);
m   = 21;
n   = 17;
siz = size(X);
vm  = 1:m:siz(1) - m + 1;
vn  = 1:n:siz(2) - n + 1;
B   = cell(numel(vm), numel(vn));
for im = 1:numel(vm)
  for in = 1:numel(vn)
     B{im, in} = X(vm(im):vm(im)+m-1, vn(in):vn(in)+n-1);
  end
end

Now you have a cell matrix containing the blocks. Maybe a multi-dimensional numerical array is much better:

X   = rand(1000, 1000);
m   = 21;
n   = 17;
% Crop not matching right and bottom margin:
siz = size(X);
M   = siz(1) - mod(siz(1), m);
N   = siz(2) - mod(siz(2), n);
X   = X(1:M, 1:N);
% Reshape the matrix:
C   = reshape(X, m, M/m, n, N/n);
C   = permute(C, [1, 3, 2, 4]);

Now C(:, :, i, j) is the block in row i and column j.

MATLAB: Finding average of every nth row

This is the mean over 6 subsequent rows:

x  = rand(9985, 1);
S  = numel(x);
xx = reshape(x(1:S - mod(S, 6)), 6, []);
y  = sum(xx, 1).' / 6;

The trailing rows are ignored.

[EDITED] General method for matrices:

x  = rand(9985, 14);
p  = 6;
n  = size(x, 1);          % Length of first dimension
nc = n - mod(n, p);       % Multiple of p
np = nc / p;              % Length of result
xx = reshape(x(1:nC, :), p, np, []); % [p x np x size(x,2)]
y  = sum(xx, 1) / p;      % Mean over 1st dim
y  = reshape(y, np, []);  % Remove leading dim of length 1

Best Answer

Related Solutions

MATLAB: How to divide image into non-overlapping blocks?

MATLAB: Finding average of every nth row

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