more pixels are better!

Started Dec 14, 2008 | Discussions thread
ejmartin Veteran Member • Posts: 6,274
Re: Are those figures for "print" or "screen"? (nt)

Les Olson wrote:

ejmartin wrote:

Noise is properly characterized not by a single number; it has a
spectral power distribution as a function of spatial frequency. It
is therefore important to take into account when comparing images
from cameras with different pixel counts, that one has image data out
to higher spatial frequencies than the other.

Don't you mean "has image data at higher spatial frequencies if there
are higher spatial frequencies in the image"? But a uniform tonality
patch has zero modulation - that is what uniform tonality means. An
image of such a patch does not contain data out to higher spatial
frequencies, and it has only one SNR. If you want to argue that SNR
at zero modulation is not the metric we need that's fine, but it is
the current standard.

How pedantic do you want me to be? I do not mean "has image data at higher spatial frequencies if there are higher spatial frequencies in the image"; there is always data up to the Nyquist frequency in an image. The amplitude of the signal at high spatial frequency can be small if there is no fine scale detail. Such is the case for a region of uniform tonality.

No photographic image of any scene has zero modulation, due to statistical fluctuations in the flux of light during an exposure. This is true even when an object being imaged has absolutely uniform reflectivity. The phenomenon is often called photon shot noise. Photon shot noise is uncorrelated from pixel to pixel in the RAW data, and therefore its spatial frequency distribution is entirely governed by this statistical randomness. So even if the signal has no high frequency content, the noise does (unless of course noise reduction filtering has been applied).

To illustrate some of the issues involved in characterizing the noise by the std dev of the pixel values, here are some patches having what are typically described as uniform tonality (the left one is an image of a square of a GM colorchecker, the other two are upsamplings of the left one by factors of 1.5 and 2); the contrast of each patch was adjusted so that the std dev of tonal values is the same for each:

Here are the noise power spectra (128 is Nyquist for each):

They look quite different, because the power distribution of noise is quite different for each -- the upsampled ones have little or no noise power above the original Nyquist frequency (2/3 of 128 for the 3/2 upsampling, 1/2 of 128 for the 2x upsampling), and they arrange for the std dev to be the same by having more noise power at lower frequencies. The original (fine-grained) patch has the characteristic noise power spectrum of uncorrelated noise, linearly rising toward the Nyquist frequency.

Noise reduction has an effect very similar to the above -- it acts locally on the image, and therefore removes noise power only at the highest frequencies, resulting in a "blotchy" appearance, as it is unable to remove strong noise power at low frequencies.

If one is going to state which image has more noise, one should state what spatial frequency is being referred to. The coarse grained images have less noise at high frequency, and more noise at low frequency. Similar issues exist when comparing cameras of different pixel count, as I demonstrated in an earlier post in this subthread.

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