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For one clean image, one person can identify every details at first. Then white Gaussian noise is added to the image.
With low noise level, one person can still identify every details even though noise is present.
With a litter higher noise level, small details and low contrast edges will be not be identified.
With much higher noise level, only strong edges can be identified.
Is there any data or theory about relationship between noise level and characterization of identificable features in the image?

enter image description here

This figure is from one paper about video denoising.
The first image is from one noisy video. The other three are obtained by different video deniosing methods. The details above the soldier is not observable because the noise level is high. After video denoising applied, the noise level is reduced and the details can be identified. Is there any data or theory about relationship between noise level and characterization of identificable features in the image?

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    $\begingroup$ Are you talking about human visual system itself? $\endgroup$ Jun 24, 2022 at 11:04
  • $\begingroup$ I'm not sure. I just hope to know the relationship between noise level and characterization of identificable features in the image. $\endgroup$ Jun 24, 2022 at 11:18
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    $\begingroup$ also note that white additive noise is very rarely what the human visual system gets exposed to by nature or through technology. But sure, you should be able to directly translate your SNR to what is usually called PSNR, and I bet there's plenty of work relating that to the human ability to detect things, for codec research. The question is whether this "detour" through PSNR is fair, because, as said, the noise caused by e.g. video codes or camera sensors in low-light condition is typically either not white or not additive, or both, in practice! $\endgroup$ Jun 24, 2022 at 11:20
  • $\begingroup$ So, I'm not an expert on image distortion, but would probably be wise to talk a bit (in your question, not in the comments, if possible) about what you want to model as white additive noise, or why you chose white additive noise as "penalty". $\endgroup$ Jun 24, 2022 at 11:22
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    $\begingroup$ I'm new to the community, but I notice that noise/artifacts tend to vanish if the image is scaled down enough bilinearly(eg a low res jpg can seem high res if scaled down enough(compared to the original at the same size), even if dead pixels are added). Also our vision tends to build up a general image non-instantly with details only being observable at the last stage, which is also why we can't see details if the object is moving fast enough as we do not have the time to focus onto any particular details. $\endgroup$
    – Dmytro
    Jun 24, 2022 at 12:35

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The phenomenon of the perceptibility of a one stimulus in the presence of the another is typically called "masking". The amount of "masking" varies greatly with the differences in the stimuli properties: spectral, temporal, spatial, energy, envelopes, etc. This leads quickly to "combinatorial explosion" and hence makes the science complicated.

For example Auditory Masking has been studied extensively (many thousands of scientific experiments and articles) and that knowledge base has (amongst many other things) been the foundation for lossy encoders such as MP3, OGG, AAC, OPUS, etc.

I'm not an expert visual perception, but it stands to reason that the same applies for visual perception as well and a quick Google search seems to confirm this. The term "visual masking" appears to have been established in 1925, so there is about 100 years worth of science available. A starting point could be: https://psychology.fandom.com/wiki/Visual_masking

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