How to calculate standard deviation of nonzero elements along the third dimension of a 3D Array

Hi,

I have a 3D-Array called A1, with dimensions 576x640x100.

I want to calculate the standard deviation of elements along the third axis, without taking into account the elements which are equal to 0.

The result would be a 576x640 matrix.

What I have tried :

Since I haven't found a way to use the default function std() in this case, I have tried using 3 loops and calculating the standard deviation using another formula (see figure below)

% Pre-allocate the final result Ds
Ds=zeros(576,640);
% Loop through all lines and columns
for i = 1:576
  for j = 1:640
%     m is the sum of elements, 'summcar' is the sum of squares m^2
    m=0;
    summcar=0;
    n=100;
    for k = 1:100
%       if an element = 0 --> substract 1 from number of total elements,
      if A1(i,j,k)==0 
          n=n-1;
      else      
      m = m+A1(i,j,k);
      summcar = summcar+m^2;
      end
    end 
    if n==0
%         if all elements along the third axis are equal to 0 --> assign value 0
        Ds(i,j)=0;
    else
%         np is the sum of all elements that are different than 0
        np=sum(A1(i,j,:)~=0);
        Ds(i,j)=sqrt(double((summcar-(m^2/np))/np-1));
    end
  end
end

Formula used for standard deviation (on the right) :

Any help is much appreciated.

Thank you.

Answer 1

[Image Analyst]

@hamza lafkiri, did you try the std() function this way:

a = randi(9, 576,640, 100); % Create sample data.
a(a==0) = nan; % Set to nan wherever there is a 0.
stDev = std(a, 0, 3, 'omitnan'); % Compute st dev along the third dimension, ignoring nans.
imshow(stDev, []); % Display resulting image.

[Cris LaPierre]

Moving my answer here since it is essentially the same.

See the example in the documentation Standard Deviation of 3-D Array.

You would use this syntax to specify which dimension to calculate the standard deviation.

S = std(A,w,dim)

As for ignoring zeros, look at all the synta options. I see there is a syntax for handling NaNs.

S = std(___,nanflag)

So if I can turn the zeros into NaNs, I can ignore them.

The final code might look something like this.

A = data; % 3D array
B = A; % create a copy of matrix
B(A==0) = nan;
stdA = std(B,[],3,'omitnan')

[hamza lafkiri]

@Image Analyst

Thank you!. This seems to be the right answer.

I have also tried this code right after I posted the question.

Ds(i,j)=std(double(A1(i,j,A1(i,j,:)~=0)),0,3);

The two methods seem to be yielding the same result so I guess it's the right one.

@Cris LaPierre

Thank you. That is indeed it but I guess we first need to convert the zeros to NaN since they're not treated the same way in Matlab, or so I think (please correct me if I'm wrong).

[Cris LaPierre]

That is what the 3rd line of code in my answer does.

[Image Analyst]

Cris's answer also makes a copy of the original array, unlike mine, in case you don't want to change your original array. However you don't need two copies of data (A & B) -- just one will do. You can then clear it if you want to save memory.

A = data; % Create a copy of original 3-D array
A(A==0) = nan;
stdA = std(A, [], 3, 'omitnan'); % A 3-D array.
clear('A'); % Get rid of temporary variable.