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I am trying to detect patterns in a raw image file where each pixel has an intensity. I can imagine fitting a 2D surface to the image (or to a portion of it) using a chi2, but for that, I need the intensity fluctuations in each pixel. How does one generally obtain those?

I have thought of taking a picture of a uniform field and looking at the distribution of intensities, assuming that the distribution of intensities between pixels is the same as the distribution in a pixel. A drawback of this method is that it would become complicated if the fluctuations depend on the intensity level itself (ie Poisson noise).

I should add that in practice I am working with data that have R, G and B info for each pixel, so I might be carrying out a fit on each color.

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    $\begingroup$ The noise in an image is a combination of Poisson (caused by how many photons hit the pixel), uniform (caused by quantization), and shot noise (caused by thermal fluctuations in the chip). How each of these balance against each other, and whether you can model the combination as Gaussian noise or not, depends on the imaging modality, the amount of light coming in, etc. If you're dealing with regular (daytime) photography, you can assume a Gaussian distribution. You can estimate the noise from a flat region in the image, or from the difference of the image with a blurred version of the image. $\endgroup$
    – Cris Luengo
    Commented Jun 25 at 20:45
  • $\begingroup$ @CrisLuengo, Shot Noise is the Poisson Noise. I think you meant Thermal Noise / A/D Noise. $\endgroup$
    – Royi
    Commented Jun 28 at 17:34
  • $\begingroup$ @Royi You’re right! Shot noise is caused by electrical currents starting and stopping. And there’s als impulse noise that can happen because of subatomic particles visiting from outer space. $\endgroup$
    – Cris Luengo
    Commented Jun 28 at 18:53
  • $\begingroup$ @CrisLuengo How would one proceed with the blurred image? Determine the difference at each pixel and then? $\endgroup$
    – Mister Mak
    Commented Jun 30 at 0:46
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    $\begingroup$ Take the difference with the blurred image, then compute the variance in some small region that is away from any edges in the input image (or multiple such regions). $\endgroup$
    – Cris Luengo
    Commented Jun 30 at 1:25

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There is a concept called ergodicity. If a signal were ergodic you could use one realization of signal to estimate some of its statistical properties otherwise you have to obtain multiple realization of this signal, in your case taking multiple pictures of single object.

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