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### AuthorTopic: Noise statistics vs noise visibility  (Read 7982 times)

#### John Sheehy

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##### Noise statistics vs noise visibility
« on: January 18, 2007, 09:06:48 AM »

In other threads I have mentioned that the statistics of noise, as often measured in digital images, is not directly correlated to visibility.  I have constructed a vivid demonstration of this fact.

The following image contains four large squares of noise; 3 of them are 2D random noise at three different frequencies; one is 1D random noise (line noise or banding).  The standard deviation (the statistician's basic measurement of noise) is the same for all the larger squares, but clearly, the difference in frequency content makes the noise very different in visibility.  The line noise is at the same frequency as the finest 2D noise ( pixel), yet is much more visible.  The insets are reductions via bicubic interpolation, and you can see that the noises don't clear up uniformly, either, with downsampling.

Gotta go now, but I'll discuss some of the ramifications later.
« Last Edit: January 18, 2007, 09:08:35 AM by John Sheehy »
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#### Ray

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##### Noise statistics vs noise visibility
« Reply #1 on: January 18, 2007, 10:19:46 AM »

This could be an interesting design for a ceramic tile, John. Have you ever thought of going into graphic design?

I guess the ramifications of this are, as image size is downsampled, the visibility of noise is reduced, eventually to the point where it is invisible. Right?

At present, I'm doing a bit of large format printing up to 24"x36". At those sizes, noise visible on the monitor is usually transferred to the print; very visible in broad daylight. At smaller print sizes the noise tends to get lost, but also the resolution of course.
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#### John Camp

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##### Noise statistics vs noise visibility
« Reply #2 on: January 18, 2007, 10:58:06 AM »

John,
I'll be interested in hearing your discussions of the ramifications. One question: does noise have any characteristic that makes it discernible mathematically? In other words, can it be isolated as noise other than visually?

JC
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#### bjanes

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##### Noise statistics vs noise visibility
« Reply #3 on: January 18, 2007, 12:09:37 PM »

Quote
In other threads I have mentioned that the statistics of noise, as often measured in digital images, is not directly correlated to visibility.  I have constructed a vivid demonstration of this fact.

Gotta go now, but I'll discuss some of the ramifications later.
[{POST_SNAPBACK}][/a]

John,

Your image is an excellent demonstration of how human perception responds differently to high frequency and low frequency noise, being more sensitive to the latter.

[a href=\"http://www.cambridgeincolour.com/tutorials/noise2.htm]Sean McHugh[/url] has a similar demonstration on his web site and also points out that the standard deviation of pixel values as commonly reported in camera tests is not a good measure of perceived noise.

If you take a sensor with a given size and increase the pixel count and assume that shot noise is predominant, the noise pattern shifts to higher frequencies and is less visible as you demonstrate, but one must also consider that the signal to noise ratio is decreasing. If N photons are collected, the shot noise is sqrt(N) and the S:N is N/sqrt(N) or sqrt(N). If the pixel count is increased sufficiently, the S:N will become too low, image quality will suffer and, at some point, the eye can not separate the image detail from the noise and contrast will be very low.

It will be very interesting if you can demonstrate how all these factors interact to determine perceived noise.

Bill
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#### Tim Lookingbill

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##### Noise statistics vs noise visibility
« Reply #4 on: January 18, 2007, 12:50:01 PM »

Interesting topic.

I wonder if these studies of flat patches of noise patterns have gone further in explaining how they affect perception of detail and if it's measureable.

Great that you should post on this topic because I've been playing around yesterday with grainy Kodak HD400 scans of negatives using luminosity layer blending and "blend if" with several applications of blur with USM contrast and detail sharpening to selectively neutralize and smooth out scanner chroma noise, edge blooming and film grain without posterizing shadow detail and still retain sharp haloless hard edges.

Fun and interesting experiment  that yielded interesting and beautiful grain textures that don't look anything like the noise patterns presented.

Can this kind of noise be seen in poster size prints of high end DSLR images?
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#### Eric Myrvaagnes

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##### Noise statistics vs noise visibility
« Reply #5 on: January 18, 2007, 04:36:56 PM »

Quote
This could be an interesting design for a ceramic tile, John. Have you ever thought of going into graphic design?

I guess the ramifications of this are, as image size is downsampled, the visibility of noise is reduced, eventually to the point where it is invisible. Right?

At present, I'm doing a bit of large format printing up to 24"x36". At those sizes, noise visible on the monitor is usually transferred to the print; very visible in broad daylight. At smaller print sizes the noise tends to get lost, but also the resolution of course.
[a href=\"index.php?act=findpost&pid=96359\"][{POST_SNAPBACK}][/a]
That gives me a great idea, Ray. For my next exhibit, I'll print all my photos to a 1 pixel by 1 pixel resolution, so I won't need to worry abotu using either Noise Ninja or Focus Magic.
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-Eric Myrvaagnes

http://myrvaagnes.com  Visit my photo website. New images each season. Also visit my new website: http://ericneedsakidney.org

#### John Sheehy

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##### Noise statistics vs noise visibility
« Reply #6 on: January 18, 2007, 08:03:14 PM »

Quote
Interesting topic.

I wonder if these studies of flat patches of noise patterns have gone further in explaining how they affect perception of detail and if it's measureable.
What they relate most directly to is bokeh, in real images, as there is no detail at those frequencies, generally speaking.  With real detail, I doubt that any equation can be made that would objectively quantify subjective noise.  I have done comparisons of noise vs resolution for detail, and when the trade-off is exact (4x the noise amplitude at the pixel level, same pixel frequencies for 4x the pixels) the higher-res pixels, noisier at the pixels level, give a better view of detail, IMO.

Here's an example:

The upper left is original 100% crop of Canon 20D RAW of a section of a Mockingbird's face, accidently under-exposed by about 3.5 stops at ISO 800 (effectively ISO 8200).  In english-reading order, the other three are the RAW image binned down to 2x2, 4x4, and 8x8, which should reduce noise at the pixel level to 0.5x, 0.25x, and 0.125x of the original.  The noise doesn't even look much better at 2x2, probably because of CFA pattern, but the pattern shouldn't be an issue at 4x4, and the noise, atlthough statistically lower, is still quite visible because of its low frequency.  No matter how far you stand from the monitor, the original still looks the most detailed, and the noise in it isn't even an issue, compared to the others.  The image is very RAW, so that conversion factors don't have much of an influence.  IOW, no noise reduction at all, other than that caused by the binning, is applied.  None of the normal chromatic noise reduction in a standard conversion is applied.  I tried to keep factors to a minimum.

I think this whole "bigger pixels are better" stuff is a lot of nonsense.  It is just a coincidence of current marketing and design pricepointing that results in some high-pixel count cameras with greater *image* noise.  The noise need only increase significantly at the *pixel* level, and that is not directly relevant to the image (or the subject), unless you take the number of them into account.

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Can this kind of noise be seen in poster size prints of high end DSLR images?
[a href=\"index.php?act=findpost&pid=96412\"][{POST_SNAPBACK}][/a]
Digital noise has more patterning to it, so it is more distracting at the same strength and average frequency than grain, IMO.
« Last Edit: January 20, 2007, 08:57:56 AM by John Sheehy »
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#### John Sheehy

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##### Noise statistics vs noise visibility
« Reply #7 on: January 18, 2007, 08:08:07 PM »

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That gives me a great idea, Ray. For my next exhibit, I'll print all my photos to a 1 pixel by 1 pixel resolution, so I won't need to worry abotu using either Noise Ninja or Focus Magic.
[a href=\"index.php?act=findpost&pid=96459\"][{POST_SNAPBACK}][/a]

And if a visitor brings along a good collection of color filters, they can view one piece and see every other piece in it!
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#### Ilya Razmanov

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##### Noise statistics vs noise visibility
« Reply #8 on: January 19, 2007, 07:33:27 AM »

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The standard deviation (the statistician's basic measurement of noise) is the same for all the larger squares

Before we discuss the standard deviation: is it proven that all noise samples are distributed normally? Otherwise referring to standard deviation may appear to be meaningless.
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#### bjanes

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##### Noise statistics vs noise visibility
« Reply #9 on: January 19, 2007, 02:03:55 PM »

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Before we discuss the standard deviation: is it proven that all noise samples are distributed normally? Otherwise referring to standard deviation may appear to be meaningless.
[a href=\"index.php?act=findpost&pid=96548\"][{POST_SNAPBACK}][/a]

Yes, shot noise follows a Poisson distribution where the standard deviation of captured photons is equal to the square room of that number. Read noise and dark noise are close enough to a Gaussian distribution to allow treatment with the normal distribution (remember the central limit theorem). For consideration of the total noise remember that variances (standard deviations squared) are additive, so the total noise is approximately equal to the square root of the above SDs squared.
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#### bjanes

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##### Noise statistics vs noise visibility
« Reply #10 on: January 19, 2007, 02:11:05 PM »

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I think this whole "bigger pixels are better" stuff is a lot of nonsense.  It is just a coincidence of current marketing and design pricepointing that results in some high-pixel count cameras with greater *image* noise.  The noise need only increase significantly at the *pixel* level, and that is not directly relevant to the image (or the subject), unless you take the number of them into account.

Digital noise has more patterning to it, so it is more distracting at the same strength and average frequency than grain, IMO.
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It is true that as the total pixel count increases, the noise becomes finer grained and may not be so visible to the naked eye.

However, if you keep the pixel count the same, the larger pixel has a decided advantage as shown on [a href=\"http://www.clarkvision.com/imagedetail/does.pixel.size.matter2/index.html]Roger Clark's[/url] web site.
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#### Ray

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##### Noise statistics vs noise visibility
« Reply #11 on: January 19, 2007, 03:04:01 PM »

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That gives me a great idea, Ray. For my next exhibit, I'll print all my photos to a 1 pixel by 1 pixel resolution, so I won't need to worry abotu using either Noise Ninja or Focus Magic.
[a href=\"index.php?act=findpost&pid=96459\"][{POST_SNAPBACK}][/a]

No need to go to extremes, old chap   . I merely make the point that the sensor with the greater number of pixels will have a noise advantage at the same print size, even though the individual pixels might be smaller and noisier than those of the smaller sensor with fewer pixels.

Of course, this result depends on just how much noisier the more numerous pixels are and how much more numerous they are. It's difficult to find any clear cut examples because one invariably ends up comparing new technology with old. There's also perhaps too big a gap between the size of P&S pixels and DSLR pixels for any meaningful comparison. As I recall, the dpreview review of the 1Ds showed it as having marginally worse noise than the earlier D60, on a pixel-for-pixel basis, but clearly less noise in the image as a whole as a result of its more numerous pixels.
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#### John Sheehy

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##### Noise statistics vs noise visibility
« Reply #12 on: January 19, 2007, 05:47:58 PM »

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Before we discuss the standard deviation: is it proven that all noise samples are distributed normally? Otherwise referring to standard deviation may appear to be meaningless.
[a href=\"index.php?act=findpost&pid=96548\"][{POST_SNAPBACK}][/a]

I'm not sure what you mean by normally.  A symmetrical gaussian curve?

When blackframe read noise is measured, it is from a totally unexposed "exposure".  Everything should be whatever the black level is for the camera system in the RAW data.  In some cameras, the RAW data maintains the bias of the sensor capture (Canon does this, and gives a full gaussian curve), and some cameras (like Nikons) clip the RAW data at black=0 before the file is written, so half of the noise of a blackframe is clipped away (and you get only a half of a curve).  This makes the noise appear to be about 60% of what it really is in a blackframe, as a standard deviation, but in reality, for infinitessimal signals, the S/N is actually lower.  That's because some of the signal exists below black, so you lose up to 50% of signal for the smallest signals.

The noise in truly exposed levels can be measured by using a flat surface and extremely poor focus, and taking the standard deviation of the noise in a certain exposure level.  You can also subtract a similar exposure, and multiply the results by 0.71, to eliminate any noise that repeats from frame to frame if you're only interested in non-repeating noises. That should almost always give a symmetrical gaussian curve.

If you're talking spatially, then noise varies by luminance, and it has 1-dimensional components like the upper-right square in my first image in this thread.  The significance of the 1-dimensional noise is that it does not disappear much with reduction.  Most people who measure noise seem to ignore this component, but I don't think it should be ignored.  It is a very visible noise for its statistical power, and is something that companies like Canon should be addressing, but seem to be ignoring.  It is also something that people ignore when they declare that the improvement in noise from ISO 1600 to 3200 is too small to be worth doing a real gain-based ISO 3200; the 1-dimensional line noise, as measured in electrons, is still dropping very quickly on recent Canons as you get to the higher ISOs; it certainly seems that even if using a gain-based ISO 3200 or 6400 on a 20D would not result in much less noise statistically, it could very well result in lower 1-dimensional noise, which is highly visible.
« Last Edit: January 19, 2007, 11:04:01 PM by John Sheehy »
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#### John Sheehy

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##### Noise statistics vs noise visibility
« Reply #13 on: January 19, 2007, 11:07:11 PM »

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However, if you keep the pixel count the same, the larger pixel has a decided advantage as shown on Roger Clark's web site.
[a href=\"index.php?act=findpost&pid=96622\"][{POST_SNAPBACK}][/a]

That's a given, with or without his tests.  I don't think anyone would be debating that, but lots of people assume that more pixels crammed into a sensor automatically increases image noise, because of pure photon binning geometry.
« Last Edit: January 19, 2007, 11:20:36 PM by John Sheehy »
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