# Pixel density - can the playing field be leveled???

Started Jun 6, 2009 | Discussions thread

Graystar wrote:

So there are two parts to this question. The first is what happens
when you lower the resolution of the image from 15MP to 10MP. The
second question is, essentially, what happens when you compare
sensors of similar size but different densities.

On resizing...
I said that resizing an image doesn’t change the noise level. It
simply makes the noise smaller, as with everything else in the image.
When said image is printed at the same size as the original, it will
have the same noise.

This depends on what you mean by "change the noise level". Noise is not one number, it has a frequency spectrum. If by "noise level" one means pixel standard deviation, then downsampling reduces the pixel standard deviation, because the new pixels are aggregates of the old ones, and the noise averages out. However the amount by which the noise is lowered depends on the noise power spectrum of the original, and the downsampling method. Assuming that the downsampling method does not alias the noise, the noise power of the source image at frequencies beyond the Nyquist frequency of the target image is filtered out; then there will be less noise power in the target image.

Aliasing reduces the amount of noise power that is filtered out. Discrete sampling of the source image can shift frequencies beyond the Nyquist frequency of the sampling to frequencies below Nyquist; in that case, noise power that should be absent makes its way into the target image. Since there can be no true detail beyond the Nyquist frequency, any image data beyond the target Nyquist (including noise at those frequencies) that makes its way into the downsampled image is spurious.

For example, suppose one has image detail at the source Nyquist frequency; a sequence of pixel values along a row is thus

a b a b a b a b a b a b

Now suppose one downsamples by a factor 3; sampling every third pixel, the downsampled sequence is

a b a b

Which is what naively would have come from a sequence

a a a b b b a a a b b b

in the source image. This many-to-one frequency map is called aliasing. If there is noise at high frequencies and one allows it to be aliased upon downsampling, it gets lumped in with lower frequency noise and is not filtered out.

You’re saying that’s not the case. You’re saying that a “proper”
downsampling process starts with a low-pass filter, and you provide
images to that effect.

The problem I have with this is that a low-pass filter is a noise
reduction process that has nothing to do with resolution reduction.

On the contrary, it is there to guarantee that there will be no aliasing of high-frequency noise into the target image that shouldn't be there.

I consider the application of the low-pass filter prior to image
reduction to be unjustified when the intent is to perform a
qualitative comparison to the original image. I could just as easily
apply the low-pass filter to the original image and have matching
noise levels but more detail than the reduced image.

No, a low-pass filter will remove both noise and detail beyond the cutoff frequency of the filter. Perhaps you are thinking of noise reduction filters; these are not strictly low-pass filters, since they retain high-frequency detail.

What is the
justification to not do so? There is none. There’s no reason to
say, “Applying a low pass filter to the original is unfair to the
upcoming comparison.”

The only thing you can say about your processing is that the end
result may have less noise (at the expense of detail) than an
untouched original. But it’s not going to be better than the
original with matching noise reduction applied. At best the noise
levels will be the same, which is what I’m saying.

Jay's processing will have less high frequency noise, since it has less high frequencies, provided that aliasing has been tamed, which is why he applied the blur prior to downsampling. Agreed though that this sort of processing is throwing the baby out with the bath water; use of a sophisticated noise filter will retain much high frequency detail while decresing high frequency noise.

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