There are no underexposed digital pictures

[spid (Sami)]

@anon41087856

@CarVac

The photodiodes will (have a probability to) respond to single photons falling upon them, so no matter how low the light is, if there is any light at all it will respond.

When signal < uncertainty(signal), having a sensor photonic response is not the matter anymore, or signal processing has changed a lot since I was in school. Every pixel whose intensity is below noise variance goes to the garbage bin and gets a 0.

@anon41087856

Every non-zero intensity of light that is below noise variance/measurement uncertainty is non-data. That’s Metrology 101. There is no discussing this.

As mentioned by other people in the thread, when you combine n pixels of approximately equal values, you increase SNR by a factor of \sqrt n (since the signal adds linearly and the noise in quadrature, as explained here).

That means that if you have a 80 MP camera with a per-pixel SNR of 0.75, and you downsample its output to 20 MP, you get a per-pixel SNR of 1.5 in the downsampled image. And yet, you would consider that data as garbage, but not the output of a native 20 MP camera that would directly have a per-pixel SNR of 1.5? Am I getting this right?

There is nothing special about SNR=1, especially at the pixel level.

To quote a comment from Jim Kasson’s blog (please read the article, by the way):

Just a comment from a (bio-)statistician: SNR is of course related to the r² metric (proportion of variance explained) in a regression. If we stopped at SNR=1 (r²=0.5) biomedical research would pretty much stop overnight

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@anon41087856

@nosle

But you don’t add any data in software. In hardware more exposure means more data until it clips

You don’t add data either by changing exposure settings in hardware, you make data brighter until they reach saturation threshold, or darker until they hit the noise threshold.

However, exposure still means log2(luminance), and the technicalities of your imaging device don’t change that.

Photon shot noise is roughly the square root of the average signal. That’s an intrinsicality of light, independent of any capture device, as you say. That means that in the shot-noise-limited part of the dynamic range (i.e. most of it), if you double the photoelectrons recorded at capture time, you double the signal but only multiply the shot noise by \sqrt 2, therefore the SNR is multiplied by \sqrt 2. Does that count as “more data”? I would say so.

As an illustration, here is the SNR curve of an iPhone 7 (red), based on data from PhotonsToPhotos.net, compared to the “ideal” SNR curve with just photon noise. The abscissa is the number of stops relative to sensor saturation, and the ordinate is the SNR in dB after normalizing to 8 MP (thus corresponding to DxOMark’s “print SNR” metric). The iPhone’s curve deviates from the ideal curve in the shadows because of read noise, and in the highlights because of photo response non-uniformity. Together, read noise, shot noise and photo response non-uniformity are the three relevant sources of noise in digital cameras in the visible spectrum. (At very short wavelengths, for example in X-ray imaging, Fano noise becomes relevant too.)