Query to understand standard deviation of an image

[anusuya pal]

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

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

[Cammer, Michael-2]

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 <[hidden email]>
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

--
ImageJ mailing list: https://urldefense.proofpoint.com/v2/url?u=http-3A__imagej.nih.gov_ij_list.html&d=DwIBaQ&c=j5oPpO0eBH1iio48DtsedeElZfc04rx3ExJHeIIZuCs&r=E0xNnPAQpUbDiPlC50tp7rW2nBkvV7fujQf0RknE5bU&m=m1gOQX7xIXcsq0BVJM2cXOLTCfKURvzk4B7MahTZoAk&s=TMnSv9Y_Cj2IUJuEtDXoyujlGLy-CD5M9M8gEVO7J00&e=

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[Cammer, Michael-2]

...three slides specified...


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: 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 <[hidden email]>
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

--
ImageJ mailing list: https://urldefense.proofpoint.com/v2/url?u=http-3A__imagej.nih.gov_ij_list.html&d=DwIBaQ&c=j5oPpO0eBH1iio48DtsedeElZfc04rx3ExJHeIIZuCs&r=E0xNnPAQpUbDiPlC50tp7rW2nBkvV7fujQf0RknE5bU&m=m1gOQX7xIXcsq0BVJM2cXOLTCfKURvzk4B7MahTZoAk&s=TMnSv9Y_Cj2IUJuEtDXoyujlGLy-CD5M9M8gEVO7J00&e=

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html