How is DxOMark’s “SNR 18%” defined and calculated?
Asked 11/13/2013
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I’m trying to understand the precise meaning of DxOMark’s “SNR 18%” measurement. Mathematically, how is signal-to-noise ratio defined for an image of a uniform 18% gray target? If a grayscale image is represented by pixel values a_ij over a flat gray patch, what quantities correspond to the signal and the noise, and how would the SNR be computed? Also, is this typically based on linear sensor data or processed/perceptual pixel values?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
12y ago
2 Answers
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SNR is the ratio of the log of power of the Signal to the log of power of Noise. So, it is Signal divided by Noise, but we don't take the amplitude of both but rather its powers. Power contained in a signal is amplitude squared. That is why, if you have the amplitude, you get a factor of 2 in the formula. Then there is an additional factor 10 relating to dB being the deci-Bell.
SNR = 2 * 10 * log(signal/noise)
Here signal and noise are defined to be the mean and standard deviation. This assumes that we are taking a picture of a smooth, unicoloured surface. Thus we would expect the same lightness value across the image (or region of interest). This means our mean is the signal. Any deviation from that mean means that the camera measured the "wrong" value, i.e. added noise. Thus the standard deviation is taking to be the noise.
Finally, we get:
SNR = 20 * log10(mean/std dev)
Originally by user7718. Source · Licensed CC BY-SA 4.0
user7718
12y ago
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Generated from our catalog & community — verify before relying on it.
For a uniform gray patch, SNR is typically computed from a region of interest by treating:
- signal = the mean pixel value
- noise = the standard deviation of the pixel values
So for pixel values a_ij on a flat target:
- compute the mean μ of the patch
- compute the standard deviation σ of the patch
- then SNR = μ / σ
If expressed in decibels, the common form is:
- SNR_dB = 20 log10(μ / σ)
This is equivalent to 10 log10 of a power ratio, since power is proportional to amplitude squared.
The basic idea is that, for a perfectly uniform target, all variation away from the mean is treated as noise.
One community answer also notes that when comparing sensors after downsizing to the same output size, SNR scales with the square root of the resolution ratio:
- SNR_downsized,A / SNR_downsized,B = sqrt(R_A / R_B) × (SNR_A / SNR_B)
As for linear vs perceptual values: SNR measurements of sensor performance are generally most meaningful on linear data, not tone-mapped perceptual values, because gamma/tone curves change the relationship between signal and noise.
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