...three slides specified...

Michael Cammer, Sr Research Scientist, DART Microscopy Laboratory

NYU Langone Health, 540 First Avenue, SK2 Microscopy Suite, New York, NY 10016

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________________________________

From: Cammer, Michael

Sent: Saturday, July 27, 2019 6:29:41 PM

To:

[hidden email]
Subject: Re: Query to understand standard deviation of an image

The standard deviation has nothing to do with the geometry of the pixels. Each image has a discrete number of pixels each with a value (usually intensity, but it may represent some other quality). The variance of the pixel values is calculated using standard statistics formula. How the pixels are arranged to look like a picture is not part of this calculation. For instance, the pixels in the gradient image below could be displayed as speckled noise or the black half and white half of the image at the right could be shown as interlaced narrow stripes; the mean and stdev would be unchanged.

I think your question is addressed in slides 61, 62, 63 at

http://microscopynotes.com/draft_image_analysis_presentation_20130716_1511.pdf(This is an old lecture that needs updating, so maybe stick to the two slides specified.)

Cheers-

Michael Cammer, Sr Research Scientist, DART Microscopy Laboratory

NYU Langone Health, 540 First Avenue, SK2 Microscopy Suite, New York, NY 10016

[hidden email]<mailto:

[hidden email]>

http://nyulmc.org/micros http://microscopynotes.com/Voice direct only, no text or messages: 1-914-309-3270 and 1-646-501-0567

________________________________

From: anusuya pal <

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Sent: Saturday, July 27, 2019 5:20:17 PM

To:

[hidden email]
Subject: Query to understand standard deviation of an image

Dear all,

I am trying to understand the standard deviation of an image. I have made 5

gray images, all contain the same area. Then I made horizontal and vertical

lines with black and white colors, to understand the definition of the

standard deviation (SD) with the image. Please see the attached files.

As per the definition of the standard deviation, it means how much

variation exists from

the mean. A low SD indicates that the points are very close to the mean,

whereas high SD means these points are spread out.

I calculated the mean and standard deviation of each image given. The SD of

the image named 'gray' makes sense to me. SD is 0 because there are no

points to deviate from the mean. Now, when I draw a horizontal line in

white color (see the image, gray+w_h) and then horizontal and vertical

lines in white color (see the image gray+w_hv), the SD values changes from

5 to 6. I have found a similar trend when I did the same with black color.

The only difference is the individual values are more,18 to 21. Please find

the attached results.

What I don't understand or trying to understand looking at the images is

how the definition of SD makes sense by just comparing the images? Any

thoughts would be much appreciated.

Thanks,

Anu

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