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Standard deviation from discrete values

asked 2014-01-13 03:18:37 -0500

updated 2014-01-13 07:34:05 -0500

Adi gravatar image

I want to calculate standard deviation for every pixel in image, that I will get from web camera. So I will have many samples for every pixel.

Is possible to calculate the standard deviation of discrete values, without knowing the probabilities of the values (without keeping the last 100 frames into the memory)?

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answered 2014-01-13 07:33:09 -0500

Adi gravatar image

Yes.
Std-dev is the root of the variance. The variance can be defined as:
the-mean-of-square-values minus the-square-of-the-value-mean.

Thus, you can keep 3 running values:

  1. The number of processed pixels: n;
  2. The sums of all the pixels - m_x;
  3. The sum of the squares of all the pixels m_xx.

The variance is then: float var = (m_xx - m_x)/n;
The std-dev is thus: float stddev = sqrt(var);.

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Asked: 2014-01-13 03:18:37 -0500

Seen: 177 times

Last updated: Jan 13 '14