# Standard Deviation of an histogram

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Pedro Silva le 7 Déc 2022
Commenté : Abdelaaziz le 5 Oct 2023
Hello,
I am trying to obtain histogram parameters from an image. I’ve also ran this image through ImageJ’s histogram function to know the correct values to expect.
I’ve transformed the image to a gray-scale image (using rgb2gray), plotted the histogram (using imshow), obtained the values for the histogram using [COUNTS,X] = imhist(Sample).
For the mean, multiplying each bin number per its frequency I am able to correctly obtain the mean value of the histogram ((bin vs frequency)/nr of pixels), but when trying to calculate the standard deviation I am unable to get the correct value.
I’ve already tried to use the bult in standard deviation of matlab, and also calculating the standard deviation manually (calculating intensity (bin vs frequency), calculating the mean, and applying the usual standard deviation formula), but the results is orders of magnitude higher than what is expected,
What function/code should I be using to obtain the standard deviation?
Any suggestions?
Example of sample attached, and also the imageJ histogram:
Thanks!
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Abdelaaziz le 5 Oct 2023
Hi Pedro. I have the Same Projekt. Did you finde hier to lose this Problem ?

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### Réponses (1)

Bjorn Gustavsson le 7 Déc 2022
You don't want the standard deviation of the histogram. You want the standard deviation of the pixel intensities in the image. You can calculate that as simply as:
meanSample = mean(Sample(:));
stdSample = std(Sample(:));
You can also estimate these characteristics from the histogram:
[COUNTS,X] = imhist(Sample);
mS = sum(COUNTS.*X)/sum(COUNTS); % Identical to how you calculate the centre of mass.
stdS = sqrt(sum(COUNTS.*(X-mS).^2)/sum(COUNTS));
That would also give you an estimate of the standard deviation - you could compare this to the second moment of any distribution (or square-root of that). But here you might have lost some precision in that estimate since you have discretized the intensities - to the centres of the bins.
HTH
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Bjorn Gustavsson le 8 Déc 2022
Good. You can also use the 'all' flag to mean and std, I forgot about that "new" capabillity...
Image Analyst le 8 Déc 2022
Like @Bjorn Gustavsson says, the standard deviation of the histogram bin counts is an entirely different thing than the standard deviation of the actual individual pixel gray levels. I hope you realize that now. One is the stdev of counts while the other is stdev of gray levels - totally different.

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