3-Dimensional Matrix and Standard Deviation

Hi there,

I have a 3-Dimensional matrix (sizeX, sizeY, 700 Frames). I would like to group the "frames" in groups of 10, so that I can take the standard deviation of each of these groups of frames. E.g. -- Since I have 700 frames (z values), I would like to take the standard deviation of 1:10, then 11:20, then 21:30. For mean, I could just bin them in groups of ten (using for loop and mean function) and get my 70 values. But for standard deviation, I'm not sure how to do this.

[Sami Case]

**Similar to the Grouped-Z Project function in ImageJ where you can do Standard Deviation of your data with a group size of 10.

[Sami Case]

See DGM’s comment below for answer help.

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is a relatively simple solution for the standard deviation calculation:

D = DATA;   % DATA of size: X-by-Y-Zs, where Zs = 1:700;
IND = 1:10:700;
for ii=2:numel(IND)
    S_D(ii-1) = std2(D(:,:,IND(ii-1):IND(ii)));       % Standard deviation
    M_D(ii-1)=mean2(D(:,:, IND(ii-1):IND(ii)));       % Mean values
end

Good luck.

[Sami Case]

This is returning a 1x70 vector, I was wanting to have a standard deviation for each pixel (160 x 160) based on 10 frame bins. So the dimensions of the output would be 160x160x70. Any help?

[Sulaymon Eshkabilov]

It is quite simple:

...
IND = 0:10:700;
IND(1)=1;
for ii = ... % the rest is the same
...

Good luck.

[Sami Case]

This is still showing a 1x70 vector. My goal it to have a standard deviation from 1-70 for each cell in the matrix. So my matrix is 160-by-160 and the z is 700. I would like to have a standard deviation of the cell in column 1, row 1 for every z. And for column 2, row 2 for every z. The output should be 160 by 160 by 70 matrix.

[DGM]

Try this:

D = rand(10,10,100); % random sample data
blocksize = 10; % how many pages to collapse?

npages = size(D,3);
IND = 1:blocksize:npages;
stdpict = zeros(size(D,1),size(D,2),numel(IND));
meanpict = zeros(size(D,1),size(D,2),numel(IND));
for ii=1:numel(IND)
    idxrange = IND(ii):(IND(ii)+blocksize-1);
    % Standard deviation of block along dim 3
    stdpict(:,:,ii) = std(D(:,:,idxrange),0,3); 
    % Mean of block along dim 3
    meanpict(:,:,ii) = sum(D(:,:,idxrange),3)/blocksize;       
end
% the indexing will break if npages is not integer-divisible by blocksize

This does operations along dim3 of each block of pages. That sounds like what you're after.

Prior code was also indexing 1:11, 11:21, 21:31, etc, and dropping the last sample block.