Why my calculation of standard deviation of an image is different from the built-in function

1 view (last 30 days)
ZhG
ZhG on 28 Jun 2013
Hello,
My code is shown below, and I opened the built-in function. I found it just calculates the square root or variance. So, the method is the same. I don't know why.
function ret = yStdDeva(im)
tic;
[tR, tC] = size(im);
mean1 = mean(im(:));
% Calculate square of difference between pixels and mean
sdpm = (double(im) - mean1).^2;
sum_sdpm = sum(sdpm(:));
% Calculate variance
imvar = (1/(tR*tC ))*sum_sdpm;
% Calculate Standard deviation
ret = (imvar)^(1/2);
toc;

Sign in to answer this question.

Answers (4)

Jan
Jan on 28 Jun 2013
Edited: Jan on 28 Jun 2013
You simply use a wrong formula: You have to normalize by the number of elements minus 1. In addition there can be a difference between SQRT and ^0.5 due to the different numerical implementations.
d = double(im);
C = d(:) - mean(d(:));
S = sqrt(sum(C .* C, 1) ./ (numel(d) - 1)):
  4 Comments
Show 2 older comments
ZhG
ZhG on 28 Jun 2013
Actually, it is the same after I had modified my program as your answer. I am confused. The result obtained by built-in function is only 9.6938. But a result of 72.0412 was obtained by my program.
Jan
Jan on 28 Jun 2013
Edited: Jan on 28 Jun 2013
I have converted the image to the type double to avoid saturation effects with integer types. So please try my code and not a program modified like my code.

Sign in to comment.

ZhG
ZhG on 28 Jun 2013
However, I found where the problem happens. If I calculate standard deviation of an image without converting it into double, it will generate a result of 9.6938. However, it will does return 72.0412 afte I transformed it to double.
Is there anyone know what the problem is?
  3 Comments
Show 1 older comment
Jan
Jan on 28 Jun 2013
Edited: Jan on 28 Jun 2013
Operations on integer types are affected of the saturaion:
uint8(250) + uint8(250) == uint8(255) !!

Sign in to comment.

Image Analyst
Image Analyst on 28 Jun 2013
I don't see much difference - just a really slight difference (less than a thousandth of a gray level):
im=imread('cameraman.tif');
% Your way:
[tR, tC] = size(im);
mean1 = mean(im(:));
% Calculate square of difference between pixels and mean
sdpm = (double(im) - mean1).^2;
sum_sdpm = sum(sdpm(:));
% Calculate variance
imvar = (1/(tR*tC ))*sum_sdpm;
% Calculate Standard deviation
ret = (imvar)^(1/2)
% Standard, built-in way:
std(double(im(:)))
In the command window:
ret =
62.3412396872523
ans =
62.3417153186086
Why are you wanting to do it yourself anyway? Why not just use std()?
ZhG
ZhG on 28 Jun 2013
thank you all, guys.

Categories

Find more on Image Arithmetic in Help Center and File Exchange

Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!