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3

Gamma Correction is Pixel Wise operation. Hence what you can do is estimate it per pixel and then average it per local area.

3

Yes, using a non-linear mapping function on the intensity. Let us for the moment suppose you have a grayscale image (because of the words "black and white", "shadings"), with luminance $0\leq p_{i,j} <1$. The piecewise linear mapping: $f( p_{i,j}) = \frac{p_{i,j}}{2}$ if $p_{i,j}<\frac{1}{2}$, and \$f( p_{i,j}) = \frac{3}{2} (p_{i,j}-\frac{1}{2})+\...

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I assume you mean Binnning at the Pixel Level before Demosaicing (Bayer Pattern) and resizing image after Demosaicing. The main difference has to do with the properties of the Noise. Demosaicing creates spatially correlated noise which means "Averaging" becomes less effective in reducing it. At RAW level noise is much whiter hence averaging is more ...

1

I would assume that I1 and I2 are of the same scene/same lighting conditions/same camera position. In the ideal world images I1 and I2 would have been related by a constant scale factor (+ random noise) so in this case the way to go would be to determine an optimal scale factor that maps I1 into I2 and then estimating noise variance from the difference. ...

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If you have access to the raw pixel data, you can implement binning in software too. They should be identical upto the step-size of the ADC, by which the quantized analog sum of pixels may differ from sum of quantized pixels. Hardware binning has the advantage that it has to transfer less number of pixels, hence can operate at high fps compared to raw data ...

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