Reducing a matrix size by averaging blocks within the matrix.

I have a 1024x1280 matrix. I want to reduce this to a smaller matrix of 512x640 by taking an average of 2x2 blocks and making that a 1x1 block.

e.g. say the first 2x2 block within the large matrix is [1,3; 7,9]

then this would average that 2x2 block to a 1x1 block of [5]

I have no idea how to do this so any help would be greatly appreciated.

Answer 1

[Stephen23]

You could use conv2 and select every second element of its output:

>> X = [1,3,5,6,7,8;7,9,5,3,1,0;9,8,7,6,5,4;0,1,2,3,4,5]
X =
   1   3   5   6   7   8
   7   9   5   3   1   0
   9   8   7   6   5   4
   0   1   2   3   4   5
>> Y = conv2(X,[1,1;1,1],'valid');
>> Z = Y(1:2:end,1:2:end)/4
Z =
   5.0000   4.7500   4.0000
   4.5000   4.5000   4.5000

[F S]

Could you do that also for blocks with other shapes than just 2x2, e.g. if I need the mean of 10x10 or 35x4 sized blocks?

[Image Analyst]

Yes, you just need to figure out where to pluck the output values from - and that could be tricky but it IS possible.

Answer 2

[Thorsten]

 fun = @(block_struct) mean(block_struct.data(:));
 Y = blockproc(X, [2 2], fun)

[Stephen23]

Note: blockproc requires the Image Processing Toolbox.

Answer 3

[Image Analyst]

I just answered this 2 days ago in http://www.mathworks.com/matlabcentral/answers/252349#answer_198175 where I said:

If you have the Image Processing Toolbox (use "ver" to check), then you can use blockproc():

myData = rand(1024,1280); % Sample data
% Define the mean function to be used with blockproc.
myMeanFunction = @(block_struct) mean(block_struct.data);
% Get the means by each 2-by-2 block.
blockMeans = blockproc(myData, [2, 2], myMeanFunction)

You can also use

smallArray = imresize(bigArray, 0.5);