# Coarsening a 2D or 3D grid in Matlab

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Sai Prasanth on 14 Sep 2020
Commented: Sai Prasanth on 17 Sep 2020
Hello,
I have several fields/arrays that are either 2D or 3D. I am looking for a method in which I coarsen the resolution by a factor of 3^2. For example, if I had 699*699 pixels in the old array, I would like to reconstruct that variable such that each pixel in the new array is an average of 3x3 pixels in the old array. What is the best way to do this for 2D as well as 3D arrays?
Thanks.

Vinai Datta Thatiparthi on 17 Sep 2020
Hi Sai,
"..each pixel in the new array is an average of 3x3 pixels in the old array.."
Use the conv2 function:
inputData = reshape(1:25,5,5);
kernel = ones(3,3);
outputData = conv2(inputData, kernel, 'valid')
% From your description, I felt it is best to set the shape parameter to 'valid'.
% If this doesn't work for you, explore other shape options ['full' & 'same'] as well.
For N-D matrices, use the nconv function:
inputData3D = reshape(1:125,5,5,5);
kernel = ones(3,3);
outputData3D = convn(inputData3D, kernel, 'valid')
Hope this helps!

#### 1 Comment

Sai Prasanth on 17 Sep 2020
Thank you, I wrote the following function using convolution to help me coarsen an array of 2 or 3 dimensions (not a 3D convolution but only 2D).
Using this function, say, if W were a 3D array and lat were a 2D array and I want a 3 x 3 moving average, I could simply use:
coarse_W = coarse(W,3);
coarse_LAT = coarse(XLAT,3);
function Z = coarse(X,squaredim)
Y = ones(squaredim,squaredim)/squaredim^2;
if(length(size(X)) == 2)
Z = conv2(X,Y,'same');
elseif (length(size(X)) == 3)
Z = ones(size(X));
for lev = 1:size(X,3) % Works only if the third dimension is vertical levels
Z(:,:,lev) = conv2(squeeze(X(:,:,lev)),Y,'same');
end
end
end