Higher resolution and noise

Higher resolution and noise
Saturday, November 22, 2008

I'm often complaining about the megapixel race. For example I had wished that the Canon 5D mark II had only had 14MP instead of 21, and thus could have had even better low-light performance. And the same goes for recent Canon compacts. But there's a case to be made for the opposite viewpoint.
This article is about DSLRs, but the same principles applies to compact cameras. It seems that higher resolution will compensate for higher noise, so it will even out because the total light gathering area of the sensor is the same. And then you can always downsample the higher resolution image, but you can't invent data from the lower resolution image.
Of course, if you never intend to make prints bigger than, say, 8x10" (20x25cms), then 6MP will do you. But try and find a 6MP camera today.

Posted by Eolake Stobblehouse

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improbable · 854 weeks ago

Very nice. It's good to see some hard analysis from people who aren't scared of numbers. The answer seems to be that more pixels on a sensor from the same year doesn't cost you anything in terms of noise, once you compare correctly i.e. accounting for the fact that downsampling averages pixels together and thus reduces the per-pixel noise.

It would be nice to see them re-run that for compact cameras too. I'd bet that the low-noise 6MP cameras whose disappearance people complain about would turn out to be no better than current models.

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crt · 854 weeks ago

One thing I feel needs more explaination is their assupmtion.
They assume per pixel SNR is linearly related to pixel size, well, it may not be, it could be square or even cubic propotional.
another thing is they assume at base ISO level, same sensor size, for example, a 4 megapixel camera captures 3 times more detailthan a 1 megapixel camera captures. putting other issues aside, the higher per pixel noise alone may reduce the detail captured by the higher pixel count camera.
This article provides some food for thoughts, and I believe their results mean something, but I just need more explainations.

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1 reply · active 854 weeks ago

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improbable · 854 weeks ago

I think it's the other way around. They work with actual noise figures from real-world cameras, and then calculate a corrected SNR which accounts for the difference in resolution. This should be equivalent to downsampling, and the easiest case to imagine is binning 4 pixels into 1 new pixel. The noise on that new pixel is easy to work out, it's standard maths, and independent of how the sensor works: you add the signals (4x) and add the variances (4x) but the noise (std dev) is the sqr root of the variance, so it's increased by 2x, and the result is that SNR increases by a factor of 2. That's their sqrt(N/Nref) factor.

Then they observe that, if you do this scaling to the noise figures for real cameras, they do come out to be the same. Which tells you something about the sources of noise in the sensor. In fact I think it tells you exactly that "per pixel SNR is linearly related to pixel size" but this is a result, not an assumption.

I hope I've got the maths right here! (Just saw that they give exactly my 4-pixel example on page 2, I was looking at page 3, shows you how carefully I read on the web doesn't it.)

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oluv · 854 weeks ago

there is an interesting comparison from phil, which actually shows how much your noise is really reduced by downsampling, very interesting read:
http://blog.dpreview.com/editorial/2008/11/downsa...

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improbable · 854 weeks ago

I hadn't seen that. It is odd that he finds so little improvement upon downsampling, but this is, I think, more about what he's doing than that the theory doesn't apply. As he points out, starting with an image which isn't signal + random noise means the simplest calculation doesn't apply. But nor is his measure of noise a good one anymore.

For instance, if you start with an image which has had noise reduction, as the in-camera jpegs certainly have, then some of the tradeoff "less detail but less noise" which you'd expect has already happened, while keeping the pixel count constant. As an extreme example, you could use as your noise reduction algorithm a downsample-upsample sequence, which will smear detail and noise. When you then downsample this, you will see no improvement in noise, and no loss of detail.

Looking at his postage stamps, the one he starts with isn't all that sharply detailed at the 1-pixel level, meaning that some kind of smearing (be it noise reduction, AA filter, by-product of bayer de-interlacing) has already occurred. If he were to apply a similar level of smearing to the lower-resolution output (thus simulating a camera with fewer pixels of similar quality) then I'm sure the drop in noise would be nicely back in line with what you'd expect.