Down-sampling an image increases DR -- true or false (and why)?

boggis the cat

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Hopefully some people good at explaining this is cat-brain terms can enlighten me.

'Anders W' has a sub-thread starting here where he claims that down-sampling an existing image (e.g. from a raw) will increase the DR.

I don't think that this is true.

So, is Anders correct, and if so, can you explain it?

Thanks.
 
boggis the cat wrote:

Hopefully some people good at explaining this is cat-brain terms can enlighten me.

'Anders W' has a sub-thread starting here where he claims that down-sampling an existing image (e.g. from a raw) will increase the DR.

I don't think that this is true.

So, is Anders correct, and if so, can you explain it?

Thanks.

I think he is saying that because DR is very dependant on how low the noise floor is, and downsampling reduces noise, so therefore the DR must be increased. Of course he has shown it mathematically if I read it right.

Brian
 
boggis the cat wrote: Hopefully some people good at explaining this is cat-brain terms can enlighten me. ...claims that down-sampling an existing image (e.g. from a raw) will increase the DR [Dynamic range]. I don't think that this is true.
Let's say a sensor has a maximum brightness output of 100. And when it's in the dark, the sensor could read out, in the absence of any noise, with a value 2. Sounds like the Dynamic Range of this sensor could be 100 divided by 2, or 50. But whenever you take a real picture with it, when the bright areas read out at, say, 99, 100, 99, 100, because of that +/- 1 noise, the real dark areas read out at 2, 3, 2, 3. So in the highlight areas, things look pretty good, because a brightness of 99 looks pretty much like 100. But in the dark areas, if you map/assign/force a readout of 2 to show up in the final print as pure black, the pure black areas are going to look "speckled" or "noisy". Because some pixels are going to show up as 3 instead of 2 due to the noise bounce. And note at the low end, 3 is 50% brighter than 2. Noticeable. Really to make the picture look clean, you have to print out any value of 3 or less as just black. So because of noise, the real dynamic range is only 100 divided by 3, or 33.

But if you downsample the image small enough, averaging all the pixels, the highlight area pixels settle down to exactly 99.5. And the shadow areas settle down/average out to a steady 2.5. Well 99.5 divided by 2.5 gives you a dynamic range in the downsampled image of about 40 instead of 33.
 
RussellInCincinnati wrote:
boggis the cat wrote: Hopefully some people good at explaining this is cat-brain terms can enlighten me. ...claims that down-sampling an existing image (e.g. from a raw) will increase the DR [Dynamic range]. I don't think that this is true.
Let's say a sensor has a maximum brightness output of 100. And when it's in the dark, the sensor could read out, in the absence of any noise, with a value 2. Sounds like the Dynamic Range of this sensor could be 100 divided by 2, or 50. But whenever you take a real picture with it, when the bright areas read out at, say, 99, 100, 99, 100, because of that +/- 1 noise, the real dark areas read out at 2, 3, 2, 3. So in the highlight areas, things look pretty good, because a brightness of 99 looks pretty much like 100. But in the dark areas, if you map/assign/force a readout of 2 to show up in the final print as pure black, the pure black areas are going to look "speckled" or "noisy". Because some pixels are going to show up as 3 instead of 2 due to the noise bounce. And note at the low end, 3 is 50% brighter than 2. Noticeable. Really to make the picture look clean, you have to print out any value of 3 or less as just black. So because of noise, the real dynamic range is only 100 divided by 3, or 33.

But if you downsample the image small enough, averaging all the pixels, the highlight area pixels settle down to exactly 99.5. And the shadow areas settle down/average out to a steady 2.5. Well 99.5 divided by 2.5 gives you a dynamic range in the downsampled image of about 40 instead of 33.
OK, that looks reasonable. (Although DR should be calculated as a doubling: 3 to 6, 6 to 12, ... 24, ... 48, ... 96, ... 100 so 5.0x EV; and 2.5 to 5, 5 to 10, ... 20, ... 40, ... 80, ... 99, so 5.2x EV. But still yields an increase in 'DR'.)

I guess it comes down to what we are referring to by 'dynamic range'.

If I shoot a scene and can capture a dark area (2, 3, 2, 3) through to a bright area (99, 100, 99, 100), then when I down-sample it to yield 2.5 through 99.5 I don't see this as having resulted in more of the scene becoming perceptible. It would be, on average, unchanged -- just less visible noise.

So, what would be a non-ambiguous term to use for what I am referring to? The range of brightness being captured within the data?

Thanks for your effort.
 
boggis the cat wrote: If I shoot a scene and can capture a dark area (2, 3, 2, 3) through to a bright area (99, 100, 99, 100), then when I down-sample it to yield 2.5 through 99.5 I don't see this as having resulted in more of the scene becoming perceptible. It would be, on average, unchanged -- just less visible noise.
Momento, senor. In the full size original of our example, the darkest thing you dare print at brighter than full black "without" speckling, has a scene-brightness-value of more than 3. With the downsampling, the darkest values you can print are any values above 2.5. So you really can see in a good-looking print, deeper into the shadows with downsampling. Or analogous multi-exposure stacking of a static scene.

A big win is that you get to record and playback darker shadow values, without having to increase the exposure to dig out that greater shadow detail, thus blowing out the highlights to blank white.
So, what would be a non-ambiguous term to use for what I am referring to? The range of brightness being captured within the data?
Dynamic range is fine. Your logic is right that downsampling doesn't exactly elevate or reduce the shadow values in the image file. What it does do it let you set the "black point" darker, i.e. with less dark-value noise you don't have to "pull down" the values of 3, 3.25 etc in post-processing (or indeed JPEG firmware) to pure black, just to bury the shadow noise speckling.
 
RussellInCincinnati wrote:
boggis the cat wrote: If I shoot a scene and can capture a dark area (2, 3, 2, 3) through to a bright area (99, 100, 99, 100), then when I down-sample it to yield 2.5 through 99.5 I don't see this as having resulted in more of the scene becoming perceptible. It would be, on average, unchanged -- just less visible noise.
Momento, senor. In the full size original of our example, the darkest thing you dare print at brighter than full black "without" speckling, has a scene-brightness-value of more than 3. With the downsampling, the darkest values you can print are any values above 2.5. So you really can see in a good-looking print, deeper into the shadows with downsampling. Or analogous multi-exposure stacking of a static scene.
Yes, but then you've dropped the highlights to 99.5 at the other end. Basically, you have 'smoothed out' the photo -- blurred then down-sized it, in effect.

(And printing is a whole different matter, in any case. I am thinking of the captured data and how you can or cannot squeeze more information from it, prior to additional processing or printing. Different strategies such as hardware pixel-binning or multiple-exposures are a different consideration, and can obviously yield benefits in capturing the DR of a scene.)
A big win is that you get to record and playback darker shadow values, without having to increase the exposure to dig out that greater shadow detail, thus blowing out the highlights to blank white.
That's getting a bit more complex. You're now into applying tone curves and such, when you are trying to preserve the highlights and lift the blacks.

All that I wanted to establish was whether you really can get more DR from a captured photo -- the data -- by sacrificing resolution. It appears that this depends on what you mean by 'DR', but you can't 'unhide' actual DR by magically sweeping away noise -- at least not by merely down-sampling. Noise should have an essentially random character (more random that the scene, in almost all cases) and so should be able to be selectively targeted if the underlying signal is able to be teased out (but I would expect this to be a complicated issue).
So, what would be a non-ambiguous term to use for what I am referring to? The range of brightness being captured within the data?
Dynamic range is fine. Your logic is right that downsampling doesn't exactly elevate or reduce the shadow values in the image file. What it does do it let you set the "black point" darker, i.e. with less dark-value noise you don't have to "pull down" the values of 3, 3.25 etc in post-processing (or indeed JPEG firmware) to pure black, just to bury the shadow noise speckling.
I don't see why you'd necessarily want to do that. If you were, for example, putting a 1:1 crop up on a website then yes, it may look bad unless you try to de-noise the shadow areas -- but routinely? I never bother, and haven't had any problems.

What I am really thinking of is how I want to know how much DR of an actual scene a camera can capture, and thus whether it is worth upgrading because, for example, DxO give a camera a larger number. If 'DR' is always a calculated 'engineering' value then that doesn't seem to necessarily help a photographer.
 
hjulenissen wrote:

I am guessing that this thread might be relevant:

http://www.dpreview.com/forums/post/39856801
Well, that seems to show noise reduction by down-sampling and low-pass filtering.

Essentially, you are changing the original photo in an unpredictable manner by doing this. (Don't like that noisy original? Replace it with one that is a facsimile of the original at a lower resolution, but looks cleaner.)

And I am specifically asking about the 'trade resolution for DR in existing data' theory, here.

Interesting thread, though.
 
boggis the cat wrote:
Essentially, you are changing the original photo in an unpredictable manner by doing this. (Don't like that noisy original? Replace it with one that is a facsimile of the original at a lower resolution, but looks cleaner.)
I see it slightly differently. If your image contains flat (ish) spectrum noise and low frequency dominated signal, then some lowpassfilter will increase your SNR. More generally: if signal and noise can be modelled as stochastic functions of different spectral characteristics, then there exists one or more post-processing filters that will maximize (spectrally ignorant) SNR. I believe that a "matched filter" is one such.

Downsampling is just one (indirect) method of getting a lowpass filter, and a lowpass filter is just one (indirect) method of improving SNR. Neither method is particulary clever or "right" for the task, nevertheless they _do_ affect SNR.

-h
 
boggis the cat wrote:

What I am really thinking of is how I want to know how much DR of an actual scene a camera can capture, and thus whether it is worth upgrading because, for example, DxO give a camera a larger number.
You may be interested in this thread on DR. The upper boundary of DR is usually easy to identify. The lower boundary of DR is typically a statistic, not a fixed number - and criteria for its choice depend on the application.

For evaluating photosite performance, the engineering definition is often used (eDR, as in DxO's case). The lower boundary for photographers and their clients is usually quite a bit more stringent (see for instance Bill Claff's well reasoned PDR choice )
If 'DR' is always a calculated 'engineering' value then that doesn't seem to necessarily help a photographer.
In the end as long as the parameter used is consistent any choice of a lower boundary (i.e. engineering vs photographic DR) will do: more is more and less is less.

If you want to compare apples to apples from different systems, though, you will have to assume that images are viewed at the same size from the same distance. And that mostly presumes some form of re-sampling before final display. Resampling in theory affects DR by the same amount independently of the lower boundary condition chosen (as long as it stays the same):



Theoretical effect on DR in stops of re-sampling an image from No to N pixels.  From this page at DxO

Theoretical effect on DR in stops of re-sampling an image from No to N pixels. From this page at DxO

So if eDR for a camera is 13 stops and PDR is 11, if you dowsize both images as displayed to 1/2 the height (or 1/4 the number of pixels) both eDR and PDR will theoretically be increased by 1 stop.

Jack
 
First of all dynamic range is the ratio of the maximum input signal to the no signal noise floor. Now the noise floor is *not* the mean black level, it is the standard deviation of the noise floor. Think about it this way, if the standard deviation was zero, then once you subtracted out the black level you would have zero noise for a black pixel. Now the standard deviation is affected by filtering- like averaging or low pass filtering. If we average 4 identical independent black pixels then the total standard deviation is halved. So it looks like down-sampling by averaging by a factor of two in each dimension increases DR by 1 stop.

But wait:

What has actually happened is that we have reduced the bandwidth of the signal and the noise. Consider white (therefore independent) noise, if the 2-D noise bandwidth is reduced by a total factor of 4, then the noise power (and therefore variance) is reduced to 1/4 by the 4 to 1 averaging. So the standard deviation, which is the square root of the variance, is halved. Similarly, if we had just low pass filtered by a factor of two in each dimension, then the total noise standard deviation would be halved- whether we down-sampled or not.

Now this has calculated the ratio of the maximum signal to total noise at a pixel including all frequencies. But, when we view an image we process for image details: so we can distinguish between low and high frequency content. If we consider the signal to noise ratio frequency by frequency the filtering doesn't change the ratio for any frequencies at all. It just selectively removes both signal and noise of some of the frequencies. So perceptually, with low pass filtering we just see both the fine textured noise and fine details disappear. So, for perception, filtering doesn't so much change the signal to noise ratio as change the overall quality of how fine-grained the total image looks. We could just as well have moved further away from a print until we couldn't see the fine details anymore, and then the signal to noise ratio would be exactly the same with or without the low pass filtering. I would therefore suggest that a perceptual dynamic range comparison between photos of different resolution should be normalized to a viewing condition that doesn't include details that don't exist in the low resolution print. This is what the DXOmark "print" DR measurement does. On this scale, low pass filtering or down-sampling with pixel-averaging doesn't change the print DR measurement at all.

So, per pixel the DR is changed by low pass filtering or down-sampling with averaging.

But, an image's perceptual DR is unaffected by either process.

Note that if an image has been low-pass filtered but not decimated, then the noise is no longer white (the pixel noise is not independent). So, when performing a normalization to an output print size, it is best to measure the noise standard deviation after low-pass filtering to a standard low resolution. Then, as long as the spectrum that remains is white, pre-filtering will have no effect. DXOmark instead just uses a ratio from the square root of the number of pixels. If the raw data has not been filtered then DXOmark's method is fine, but if the camera low pass filters the raw, then DXOmark's method will overestimate the print DR.
 
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DSPographer wrote:

First of all dynamic range is the ratio of the maximum input signal to the no signal noise floor. Now the noise floor is *not* the mean black level, it is the standard deviation of the noise floor. Think about it this way, if the standard deviation was zero, then once you subtracted out the black level you would have zero noise for a black pixel. Now the standard deviation is affected by filtering- like averaging or low pass filtering. If we average 4 identical independent black pixels then the total standard deviation is halved. So it looks like down-sampling by averaging by a factor of two in each dimension increases DR by 1 stop.

But wait:

What has actually happened is that we have reduced the bandwidth of the signal and the noise. Consider white (therefore independent) noise, if the 2-D noise bandwidth is reduced by a total factor of 4, then the noise power (and therefore variance) is reduced to 1/4 by the 4 to 1 averaging. So the standard deviation, which is the square root of the variance, is halved. Similarly, if we had just low pass filtered by a factor of two in each dimension, then the total noise standard deviation would be halved- whether we down-sampled or not.

Now this has calculated the ratio of the maximum signal to total noise at a pixel including all frequencies. But, when we view an image we process for image details: so we can distinguish between low and high frequency content. If we consider the signal to noise ratio frequency by frequency the filtering doesn't change the ratio for any frequencies at all. It just selectively removes both signal and noise of some of the frequencies. So perceptually, with low pass filtering we just see both the fine textured noise and fine details disappear. So, for perception, filtering doesn't so much change the signal to noise ratio as change the overall quality of how fine-grained the total image looks. We could just as well have moved further away from a print until we couldn't see the fine details anymore, and then the signal to noise ratio would be exactly the same with or without the low pass filtering. I would therefore suggest that a perceptual dynamic range comparison between photos of different resolution should be normalized to a viewing condition that doesn't include details that don't exist in the low resolution print. This is what the DXOmark "print" DR measurement does. On this scale, low pass filtering or down-sampling with pixel-averaging doesn't change the print DR measurement at all.

So, per pixel the DR is changed by low pass filtering or down-sampling with averaging.

But, an image's perceptual DR is unaffected by either process.
Hi DSPographer,

I would argue, per Bill Claff, that when viewing an image at the same size there is re-sampling being performed in the circle of least confusion of our visual system. If we step back, the number of pixels that fall (are binned) within it increases, with the relative loss of perceived detail - but at the same time with the relative gain in perceived SNR and DR. I believe that's why a smaller image typically looks cleaner to us than its larger counterpart.
 
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Jack Hogan wrote:
Hi DSPographer,

I would argue, per Bill Claff, that when viewing an image at the same size there is re-sampling being performed in the circle of least confusion of our visual system. If we step back, the number of pixels that fall (are binned) within it increases, with the relative loss of perceived detail - but at the same time with the relative gain in perceived SNR and DR. I believe that's why a smaller image typically looks cleaner to us than its larger counterpart.
Yes. But, I would argue that in the large print we still can see the high frequency noise as distinct from the low frequency noise. So, the perceived SNR doesn't really follow the mathematical ratio of the per pixel SNR. That is why you can see quotes about "fine grained" noise as being less objectionable than coarse noise.
 
DSPographer wrote:
Jack Hogan wrote:

Hi DSPographer,

I would argue, per Bill Claff, that when viewing an image at the same size there is re-sampling being performed in the circle of least confusion of our visual system. If we step back, the number of pixels that fall (are binned) within it increases, with the relative loss of perceived detail - but at the same time with the relative gain in perceived SNR and DR. I believe that's why a smaller image typically looks cleaner to us than its larger counterpart.
Yes. But, I would argue that in the large print we still can see the high frequency noise as distinct from the low frequency noise. So, the perceived SNR doesn't really follow the mathematical ratio of the per pixel SNR. That is why you can see quotes about "fine grained" noise as being less objectionable than coarse noise.
Interesting. Do you know of anyone who has studied the phenomenon?
 
boggis the cat wrote: If I shoot a scene and can capture a dark area (2, 3, 2, 3) through to a bright area (99, 100, 99, 100), then when I down-sample it to yield 2.5 through 99.5 I don't see this as having resulted in more of the scene becoming perceptible. It would be, on average, unchanged -- just less visible noise.
Momento, senor. In the full size original of our example, the darkest thing you dare print at brighter than full black "without" speckling, has a scene-brightness-value of more than 3. With the downsampling, the darkest values you can print are any values above 2.5. So you really can see in a good-looking print, deeper into the shadows with downsampling. Or analogous multi-exposure stacking of a static scene.
boggis: Yes, but then you've dropped the highlights to 99.5 at the other end.
But if dynamic range is related to the brightness ratio of the lightest part of a scene, to the darkest clearly rendered part of the scene, that reduction due to downsizing of the darkest parts renderable, from more-than-3, to 2.5, in our silly example, is very significant. The brightest-to-darkest renderable scene value ratio goes from something over 33 (100 divided by something over 3) to around 40 (99.5 divided by 2.5, speaking very roughly).

What that more-darker-detail means is that the photographer could for example, lighten that part of the final image, and more dark (albeit low-resolution) details could emerge, that would have looked as merely finely speckled noise before downsampling.

Usually, highlight detail is more noticeable (hence most important to photographers) than shadow detail. We're usually not as bothered seeing blank black areas in a photo, than we are bothered seeing blank white areas. So usually a skilled photographer starts deciding exposure by turning down the exposure just enough that the brightest parts of a scene are rendered with detail.

The dynamic range of the imaging system then determines, for that important-highlight-preserving exposure setting, how much of the darkest parts of the scene can be rendered as smooth-looking, non-speckled shadow detail. If the dynamic range of the camera system is real narrow, and the darkest parts of the scene are "way darker" than the brightest important parts, the darkest parts of the scene will simply not have any recognizable detail in them that can be brought-out in post-processing by brightening. Because brightening those darkest parts will result in noise speckles rather than emerging dark detail.

But downsampling (or any other way of reducing shadow noise which is another way of talking about increasing dynamic range) gives the photographer the luxury of brightening the shadows (merely moving a shadow slider in Lightroom for example) without seeing speckled noise blotches emerge.
Basically, you have 'smoothed out' the photo -- blurred then down-sized it, in effect.
Not the worst description of "getting rid of noise", to say you've smoothed out the photo.
(And printing is a whole different matter, in any case. I am thinking of the captured data and how you can or cannot squeeze more information from it, prior to additional processing or printing. Different strategies such as hardware pixel-binning or multiple-exposures are a different consideration, and can obviously yield benefits in capturing the DR of a scene.)
Well by "printing" I meant preparing for final display on some medium, which either your camera JPEG firmware does, and/or you the photographer are going to do in post-processing.
A big win is that you get to record and playback darker shadow values, without having to increase the exposure to dig out that greater shadow detail, thus blowing out the highlights to blank white.
That's getting a bit more complex. You're now into applying tone curves and such, when you are trying to preserve the highlights and lift the blacks.
Assuming the exposure was low enough to preserve highlight detail, dynamic range tells you how dark are the darkest parts of the scene that you'll be able to lift up in some kind of post-processing, to be made visible as dark detail in the final "print" or otherwse displayed image.
All that I wanted to establish was whether you really can get more DR from a captured photo -- the data -- by sacrificing resolution.
Yes. You give up peak resolution wherever you downsample, but the shadow noise speckling goes down nicely also. If you downsample from way 16 megapixels to 4 megapixels, ideally you will reduce the amplitude of the shadow noise by 2 (the square root of the downsampling ratio, 4).
It appears that this depends on what you mean by 'DR', but you can't 'unhide' actual DR by magically sweeping away noise
Now you're getting way over my head into sampling theory and statistics, but there's nothing magical about reducing shadow noise by downsampling. You reduce speckling as you reduce resolution. You're paying for your dynamic range increase with resolution decrease, it's not something for nothing.
downsampling doesn't exactly elevate or reduce the shadow values in the image file. What it does do it let you set the "black point" darker, i.e. with less dark-value noise you don't have to "pull down" the values of 3, 3.25 etc in post-processing (or indeed JPEG firmware) to pure black, just to bury the shadow noise speckling.
I don't see why you'd necessarily want to do that. If you were, for example, putting a 1:1 crop up on a website then yes, it may look bad unless you try to de-noise the shadow areas -- but routinely? I never bother, and haven't had any problems.
Check out this photo. If my camera had infinite dynamic range, instead of its merely reasonable DR of about 9 exposure values or so, it would have been trivial for me to move the exposure slider and/or shadow slider upwards in Lightroom, and reveal more shadow detail. But instead I am forced to present the image to you with the darkest areas consigned to featureless black, since if lightened them they would at best be featureless gray (hence more obtrusive) and at worse super noise-speckled (even more obtrusive).



My own experience is that almost every photo of every non-super-gray-scene is unable to be rendered with "all" its highlight detail, and "all" its shadow detail with my current gear. And I have to in almost every exposure just keep the exposure low enough to preserver highlights. Then in post-processing, futz with exposure, shadow and highlight sliders (in for example Lightroom) to tweak/optimize how bright in the displayed image or print to present the various dark and light parts of the original scene.

If you don't regularly have to do these things, then you either have a camera with more dynamic range capability than the dynamic range of the scenes you regularly photograph...or you are just quite lucky in that your default workflow and exposure-setting gear just always does an unassisted great job in both preserving highlights and not allowing dark parts of the scene to display as noisy speckled areas.
What I am really thinking of is how I want to know how much DR of an actual scene a camera can capture, and thus whether it is worth upgrading because, for example, DxO give a camera a larger number. If 'DR' is always a calculated 'engineering' value then that doesn't seem to necessarily help a photographer.
Well resolution is sort of a calculated value, but it's not just a mere engineering flight of fancy, it's a useful number that a whole bunch of us use to figure out what lenses to risk buying or trying.

Dynamic range really does tell you how contrasty a scene you can capture with clean shadow detail (or with great ISO-pushing-in-post-processing), in a single exposure at some certain resolution. Can't think of a scenario where more DR isn't better. The more DR, the less you have to worry about accidentally underexposing an image. I.e. the more you can err on the side of really well preserving the usually-more-important highlight detail.
 

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Actually, I know that it does, but I have a point. (I think.)
Jack Hogan wrote:
boggis the cat wrote:

What I am really thinking of is how I want to know how much DR of an actual scene a camera can capture, and thus whether it is worth upgrading because, for example, DxO give a camera a larger number.
You may be interested in this thread on DR. The upper boundary of DR is usually easy to identify. The lower boundary of DR is typically a statistic, not a fixed number - and criteria for its choice depend on the application.
Yes; and personal preferences.

What is 'unacceptably noisy' to one person may be imperceptible to another (or even preferable, if you consider the many people objecting to the typical Canon 'plastic' look).

We all have an idea of how we want the final result to look, and that will typically fall somewhere between 'grainy' and 'airbrushed to the limit of recognisability'.
For evaluating photosite performance, the engineering definition is often used (eDR, as in DxO's case). The lower boundary for photographers and their clients is usually quite a bit more stringent (see for instance Bill Claff's well reasoned PDR choice )
If 'DR' is always a calculated 'engineering' value then that doesn't seem to necessarily help a photographer.
In the end as long as the parameter used is consistent any choice of a lower boundary (i.e. engineering vs photographic DR) will do: more is more and less is less.

If you want to compare apples to apples from different systems, though, you will have to assume that images are viewed at the same size from the same distance. And that mostly presumes some form of re-sampling before final display. Resampling in theory affects DR by the same amount independently of the lower boundary condition chosen (as long as it stays the same):

Theoretical effect on DR in stops of re-sampling an image from No to N pixels. From this page at DxO

Theoretical effect on DR in stops of re-sampling an image from No to N pixels. From this page at DxO

So if eDR for a camera is 13 stops and PDR is 11, if you dowsize both images as displayed to 1/2 the height (or 1/4 the number of pixels) both eDR and PDR will theoretically be increased by 1 stop.

Jack
I am aware of the mathematics behind this.

Your basic assumption here appears to be ignoring the actual 'taking a photo' part, though. By this I mean that it is fine to talk about how the SNR is reduced by down-sampling and this produces an increase in DR and so forth -- but what has that got to do with the actual process of capturing light from a scene via a sensor that is then read and quantised into data?

As an example that you might follow, consider the difference between pixel-binning a group of four pixels on-sensor and performing an averaging function on the full resolution data post-capture. The on-sensor pixel-binning technique reduces analogue noise by reducing the read noise -- one read operation for four pixels. Applying a down-sampling method to the full resolution data post capture does not cut the read noise in the same manner (nor reduce the noise by nearly the same amount).

What we are trying to consider is: when we point our camera at a scene with high dynamic range (this having nothing to do with SNR), what can we expect to capture if we ensure that the brightest parts are not clipped? I would like to know how to convert 'engineering' DR to this 'capturable DR', because it is this 'DR' that I am interested in.
 
Jack Hogan wrote:
DSPographer wrote:
Jack Hogan wrote:

Hi DSPographer,

I would argue, per Bill Claff, that when viewing an image at the same size there is re-sampling being performed in the circle of least confusion of our visual system. If we step back, the number of pixels that fall (are binned) within it increases, with the relative loss of perceived detail - but at the same time with the relative gain in perceived SNR and DR. I believe that's why a smaller image typically looks cleaner to us than its larger counterpart.
Yes. But, I would argue that in the large print we still can see the high frequency noise as distinct from the low frequency noise. So, the perceived SNR doesn't really follow the mathematical ratio of the per pixel SNR. That is why you can see quotes about "fine grained" noise as being less objectionable than coarse noise.
Interesting. Do you know of anyone who has studied the phenomenon?
Perhaps more important than this is 'unmeasured' attributes that may affect an image.

Consider these (not very artistic, I know) test shots that I used to gauge the low light / high ISO results from my E-5 when I bought it:


Low light, high ISO -- banding / blotching 'acceptable'


(Very) low light, higher ISO -- banding / blotching 'nasty'

The banding / blotching becomes quite noticeable, but methods such as those used by DxO will not give you any hint about such easily visually perceived issues.
 

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Downsampling do not increase dynamic range in the image.

But it increases the dynamic range per pixel.
 
Roland Karlsson wrote:

Downsampling do not increase dynamic range in the image.

But it increases the dynamic range per pixel.
Right...

This is what I feared, really.

Averaging four grey pixels into one grey pixel makes that one grey pixel more dynamic and stuff... Meh...

:-P
 
boggis the cat wrote:

I am aware of the mathematics behind this.

Your basic assumption here appears to be ignoring the actual 'taking a photo' part, though. By this I mean that it is fine to talk about how the SNR is reduced by down-sampling and this produces an increase in DR and so forth -- but what has that got to do with the actual process of capturing light from a scene via a sensor that is then read and quantised into data?

As an example that you might follow, consider the difference between pixel-binning a group of four pixels on-sensor and performing an averaging function on the full resolution data post-capture. The on-sensor pixel-binning technique reduces analogue noise by reducing the read noise -- one read operation for four pixels. Applying a down-sampling method to the full resolution data post capture does not cut the read noise in the same manner (nor reduce the noise by nearly the same amount).

What we are trying to consider is: when we point our camera at a scene with high dynamic range (this having nothing to do with SNR), what can we expect to capture if we ensure that the brightest parts are not clipped? I would like to know how to convert 'engineering' DR to this 'capturable DR', because it is this 'DR' that I am interested in.
And this is where information theory comes in. Let's take a look at what limits the DR of a typical camera, DR being the ratio between the largest signal and the smallest signal of acceptable quality that can be recorded.

You capture light (photons) from the scene through a physical device that has limitations. In fact you sample it spatially through a matrix of physical devices (photosites) with roughly the same properties. Each Photosite counts the number of photoelectrons generated by photons hitting its effective area during Exposure.

The Numerator. Each photosite can store only a maximum number of photoelectrons before filling up (the Full Well Count, in photoelectrons or e-). This is the numerator of the DR ratio, a figure dependent on the physical characteristics of the photosite and related technology (area, capacitance etc.)

The Denominator. Photosites and the supporting analog electronics needed to count photoelectrons and store them in memory add a minimum of random noise to the signal, what is normally referred to as Read Noise (in e-) which degrades image quality. Can one estimate Read Noise from one photosite and one capture alone?

No, because read noise is random, so if we just have one reading of, say, 56 e- we cannot tell whether that's signal or noise (in a 5DIII for example). To determine what is signal and what is noise we need a sample, whether that's many captures with one photosite in the same conditions or it's one capture of a uniform subject by a multitude* of contiguous photosites (what we typically do). The mean of the sampled data set will be our signal, the standard deviation an indication of noise strength (our eyes work similarly). Their ratio is what is called Signal to Noise ratio (SNR) in imaging, an indication of image quality.

Psychovisual studies have shown that an SNR > 10 is considered to be a mimimum acceptable level to most people watching TV. Engineers find that an SNR of 1 is often an acceptable lower limit for their purposes. Photographers have other standards again. So the denominator in our DR ratio is subjective and depends on the application - and is simply the signal in e- at which that minimum SNR is achieved.

But what's more important is simply choosing one acceptable limit and sticking with it, because the ratio between two DR definitions (say 10:1) stays the same in stops aotbe, and so they move in unison with that gap. You will simply know that outstanding eDR for a photographic sensor today is represented by 14 stops and in PDR 11 for example - and if a new sensor comes out with a measured eDR of 15 stops you know that it will be measured at roughly 12 stops by PDR.

Back to your example. Let's assume that for the same exposure (that is the same number of photons arriving per micron^2) you have two choices of sensor: one with photosites x times the area of the other. Are the DRs different if their technology is similar? The answer is, surprisingly, not much because the larger photosite will have a larger FWC, but it typically also has a correspondingly larger read noise. Not exactly in proportion, but close - there are good technical reasons why this is so. So it turns out that today read noise scales roughly with photosite size and it makes little difference in terms of DR on a final image viewed at the same size whether you capture it with 36 or 24MP on a FF sensor of the same technology. See for instance DxO's eDR measurement for the D800/e vs the D600 .

As long as you know and understand your captured DR's frame of reference it is easy to relate it to the DR of the incoming light from the scene, as shown in the post I linked earlier.

Jack

* How many do you need? Good question, suffice it to say that you need something of the order of 10,000 for about 1% accuracy (Janesick). So next question: how few is good enough?
 

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