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I am working on digital image correlation and want to figure out the noise in my data. In a book, I read "many digital cameras record intensity values using 8 bits with Gaussian noise in the intensity values having a standard deviation of 2 gray levels".

How can I translate 2 gray levels in a unit, say, milimeter?

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    \$\begingroup\$ how can you translate grey to millimeters?? you can't \$\endgroup\$ Commented Jan 18, 2023 at 12:45
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    \$\begingroup\$ Welcome to Stack Exchange. Please note that this site is specifically about photography rather than imaging in a general sense; could you please edit your question to explain the photographic issue you are trying to solve? \$\endgroup\$
    – Philip Kendall
    Commented Jan 18, 2023 at 12:46

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A "deviation of 2 gray levels" is the same as saying an intensity value 2 numbers away... i.e. 120 - 122.

You can use Photoshop (or similar) to evaluate the noise levels in an image. Here I created a 50% gray layer; the level is 128, the mean (average) and median are 128, the standard deviation is 0, and 100% of the image pixels are at that level.

enter image description here

If I then apply a filter to add monochromatic gaussian noise at .77% it results in a standard deviation of 2. If I select the 128 level in the histogram the count (number of pixels) at that value is less, and the percentage of the image at that value decreases correspondingly.

But because the noise is somewhat random it is not dispersed entirely evenly; the mean and median values are no longer 128, nor are they the same value. The standard deviation of 2 doesn't mean that is the minimum/maximum deviation; in this case that was 7 grey levels (121-135).

enter image description here

If you then wanted to do some kind of conversion/evaluation by area, you could crop the image to the desired area and use the statistics for what remains.

But it would be very difficult to evaluate an image that contains detail in the same way. What was being referred to as gaussian noise is (probably) the typical photosite read error of a sensor at that time... i.e. the sensor should read/write 128 from a photosite at a given exposure, but sometimes it reads/writes 126 or 130 instead. In an image with detail that error doesn't cause visible noise; a detail where a detail doesn't belong... it just causes a detail (photosite/pixel) to be more/less distinct.

The read error does contribute significantly to color noise from the demosaicing process... you can change the histogram channel from luminosity (RGB) to any of the individual colors. I.e. are you concerned with noise of the input data (photosite luminance) or the output data (image).


note that the "percent noise" added to reach a standard deviation of 2 varies with the initial value; and the results will vary slightly every time.

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"Level" here is very likely to be the value corresponding to 1-bit in the encoding (so more related to luminosity)

I'm a bit worried about your book though because:

  • Most modern cameras do more than 8 bits in the sensor. 8-bit is the output image format (typically JPEG).

  • Furthermore the 8-bit image is usually gamma-encoded (middle gray is around 180 and not 128), so the same value of sensor noise doesn't produce the same difference in the encoding (more sensor noise in the shadows after encoding).

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