Resolution, sharpness and colordepth.

That article is flawed in the basic fact I repeated for about 4 or 5 times:) The figures are insanely high in order to support some nonsense on how 4K produces some super tonality.

I explained how the shades are created, ADDITION of photons. There is nothing peculiar about it.

My example proves that it raises tonality (by higher light gathering) by a theoretical two bits if everything else is the same. Like increasing the sensor area 4 times with the 4x increase in resolution (keeping the pixel size). This is irrelevant though. Designs are for specific sensor sizes, and doing that on a given sensor size produces 4x smaller pixels, which has the problems I explained. It will not get higher tonality with 4x smaller pixels. There are also additional problems in sensor design which compromise the high resolution sensor further. If it's CCD there is higher bandwidth which leads to higher noise, the higher noise problem of the small pixels etc.

My "manual" summing method was written to explain a simple fact you could not understand or accept. The equation is very easy to use. Not that anyone needs equations like these in practice.

2+2=2x2 also, but that doesn't mean you can replace addition with multiplication. Have you tried his formula for 4 pixels having 256 combinations? :) It has 259! in it:) No, my formula does not agree with that. It only contains reasonable numbers. The only reason it agrees is the one bit bit depth which calms down that insane equation due to the (2-1) part.

If you try to apply that equation to digital processing, the equation is flawed because filter kernels simply sum pixel values for red, green, blue. Addition. You only get 2 bits max from that as I explained.

If you try to apply that equation to a display system and to our vision, the equation is flawed again. Our color receptors which capture a part of the spectrum each will sum the energy of the photons coming from the 4 pixels to a single value at that spectrum part. The receptor does not care where the energy came from. If you go really close to the image, you will see the individual pixels, but that's extra resolution, not color depth.

Another related subject is dithering. But anyone that experimented with dithering knows what with rectangular blocks of 2x2 you will not get far. In order to represent different energy levels beyond the limits of your quantisation, you need error diffusion which requires far more resolution for a relatively small gain in tonality.

Assume that the 4 theoretical RGB pixels are different. Now we are talking! Make the mono pixels different in sensitivity and you have higher dynamic range and tonality. Make the 4 color pixels for each color different in sensitivity and you get the same advantages. Make them 4 different color shades and you get higher tonality with a difference in dynamic range (not as impressive as the previous methods).

To sum this up (pun intended) I will say that imaging systems, display systems and human vision all use trichromatic elements. Calculating "unique combinations" is not enough, you also have to rule out all combinations that produce equal energy on the colored sensor pixel, lcd pixel color element, or human vision color receptor. The combined energy that will hit each of these elements is calculated by summing. If you are close enough, you are within the color resolution of our vision, so you don't even get the small advantage from energy summing. You see the 4 original pixels with their original tonality.
 
No one has suggested increasing resolution to gain color depth. I was merely stating the often neglected fact that higher resolution boosts color depth.

The rise in color depth that accompanies an increase in viewing distance was demonstrated earlier in this thread. The banding in the sky of the enlarged section of the photo turns into a smooth gradation (blends) as one moves away from the screen.

Increasing the viewing distance heightens the angular resolution of the image being viewed (the pixels get smaller). Hence, adjacent RGB cells eventually start to interblend, and the color depth increases.

I don't disagree that pixels are electronically and optically summed. I derived an equation for that and I explained why it happens. I just disagree with that article. It's 2bit and only in theory, not 20 bits or whatever the equation in that article outputs.
 
That article is flawed in the basic fact I repeated for about 4 or 5 times The figures are insanely high in order to support some nonsense on how 4K produces some super tonality.
The figures are accurate for digital systems that have pixels with non-uniform shading increments.

Who said anything about "4k producing super tonality?" I even stated that 1920x1080 is enough for 98% of cinematography. In the John Galt article (linked in my original post), he also downplays hyper-resolution, and he even goes into how erroneous and questionable it is to use the term "4K" and "2K to describe camera resolution. Furthermore, in the color depth article, it suggests that one should quit cinematography if one can't create compelling images with a 10-bit, 1920x1080 sensor.


I explained how the shades are created, ADDITION of photons. There is nothing peculiar about it.
It makes perfect sense, when the all shading increments of a pixel are identical.

Designs are for specific sensor sizes, and doing that on a given sensor size produces 4x smaller pixels, which has the problems I explained. It will not get higher tonality with 4x smaller pixels. There are also additional problems in sensor design which compromise the high resolution sensor further. If it's CCD there is higher bandwidth which leads to higher noise, the higher noise problem of the small pixels etc.
None of these parameters are really relevant because we are discussing basic photographic principles, not the current practical limits in digital imaging.

Furthermore, there is no given pixel size nor sensor dimensions. As I said, we could start with square, 40-micron pixels, and, if we then increased the resolution 4x, we would end up with square, 20-micron pixels -- still very huge with a lot of dynamic range and high bit depth potential. Such a sensor is possible in the real world today, and we wouldn't be getting even close to limits posed by the parameters that you mention.

Now, one could also claim that such big-pixeled sensors don't exist (even though such sensors could be made if someone "plopped-down" the money). In that case, we could merely use angular resolution as our measure, and just use off-the-shelf sensors of different sizes. For instance, we could compare the lowest-res, 10-bit capable DV censor with the highest-res, 10-bit capable, hyper-HD sensor. In such a instance, we would easily have a 4x increase in resolution with real-world, 10-bit sensors.

Heck, if we consider digital still photography, we could start with a 10-bit SD-res sensor and expand our resolution using the 8984x6732 Dalsa sensor that is employed in the Phase One P65+ digital back. I think that Dalsa sensor actually has 16-bit capability.

So, instead of specifying all of these processing parameters and particular sensors, let us just assume that the examples are given in such a way that we never reach current practical limits. Okay?

However, even if we did reach practical limits, the basic resolution/color depth relationship still transcends any problems we encounter trying to create sensors with our specs. Higher resolution always gives greater color depth, even if we currently could not create cameras that fit our examples.


2+2=2x2 also, but that doesn't mean you can replace addition with multiplication. Have you tried his formula for 4 pixels having 256 combinations? It has 259! in it No, my formula does not agree with that. It only contains reasonable numbers. The only reason it agrees is the one bit bit depth which calms down that insane equation due to the (2-1) part.
I don't understand your example. Please give more details on the scenario.


If you try to apply that equation to digital processing, the equation is flawed because filter kernels simply sum pixel values for red, green, blue. Addition. You only get 2 bits max from that as I explained.
As I explained above, all of the parameter arguments are meaningless, as we can use existing technology in our examples that is fully capable to meet basic requirements in the examples. And again, we are going to assume that all of the "givens" do not approach current practical limits.

Once more, none of these photographic concepts have anything to do with filter kernels summing/binning pixel values, because the interblending occurs in the viewer's eye. We assume that every image matches "pixel-per-pixel" perfectly, from capture to display.


If you try to apply that equation to a display system and to our vision, the equation is flawed again. Our color receptors which capture a part of the spectrum each will sum the energy of the photons coming from the 4 pixels to a single value at that spectrum part. The receptor does not care where the energy came from.
You are absolutely correct with respect to digital imaging systems in which the increments of pixel shading are perfectly linear. Furthermore, the color depth article should at least have a qualification acknowledging this fact for such systems.

The color depth formula applies to any imaging system in which all the potential colors from a single resolution "cell" are unique. So, the formula works with all analog imaging systems and with digital systems in which the increments of pixel shading are not linear/uniform.

Of course, the quantum efficiency of video sensors is not perfect, nor is the linearity of shading in monitors. For instance, consider two adjacent, interblending RGB cells. Their respective RGB values (R:G:B) might be 30:0:0 and 50:0:0, but the two blended together might not equal exactly 80:0:0, because the shading system isn't perfectly uniform. These minute discrepancies in the shading increments of each pixel might be enough to yield the color depth numbers listed in the article. However, I don't think that this reality should be relevant to this discussion, as we are talking about principles which transcend practical limitations.

So, I agree, a formula that "adds" the values from each color channel should apply to most digital systems, if we want to find the color depth of a group of cells. Yet, such a color depth equation doesn't really contain any addition, unless you do it manually in the fashion that you demonstrated.

The formula would be something simple, like this: R x N = C

R" is resolution -- the number of RGB cells (or non-unique pixels) in a given group; "N" is the number of available colors/shades of each RGB cell (or non-unique pixel); and "C" is the resulting color depth.

With the group of four, 10-bit RGB cells, the color depth with this new equation is figured in this way:
4 x 1,073,741,824
= 4,294,967,296

Now we have a color depth of 4,294,967,296 colors in a group of four, 10-bit RGB cells. No addition necessary.

So, results from this formula are the low extreme of potential color depth, while the results from the formula in the color depth article is the high extreme of potential color depth. Most real-world imaging systems fall somewhere in between these two extremes.


If you go really close to the image, you will see the individual pixels, but that's extra resolution, not color depth.
Actually, the angular resolution of an image decreases as the viewer moves closer -- the pixels get bigger/coarser for the viewer.


Another related subject is dithering.
Dithering is strongly related to this discussion. The resolution within the "dither" cell largely determines the color depth, and dithering is an effective way to apply threshold/sensitivity mapping.


But anyone that experimented with dithering knows what with rectangular blocks of 2x2 you will not get far. In order to represent different energy levels beyond the limits of your quantisation, you need error diffusion which requires far more resolution for a relatively small gain in tonality.
Once again you have unwittingly demonstrated that a boost in resolution begets greater color depth. The higher the resolution of the dither cell, the greater the tonality.

You are correct that it is not practical to use dithering in cinematography imaging. Utilizing bit depth (over resolution and dithering) is much easier and is compatible with all current digital cinematography systems. However, high resolution dithering is constantly utilized in halftone printing.


Assume that the 4 theoretical RGB pixels are different. Now we are talking! Make the mono pixels different in sensitivity and you have higher dynamic range and tonality. Make the 4 color pixels for each color different in sensitivity and you get the same advantages. Make them 4 different color shades and you get higher tonality with a difference in dynamic range (not as impressive as the previous methods).
Yes. With cameras, threshold/sensitivity mapping can "kick-in" the extra color depth possible from higher resolution, in the large, smooth areas of the image. However, the higher color depth will appear automatically in the more intricately patterned areas of the image.

By the way, the upcoming Panavision Dynamax sensors will incorporate sensitivity mapping of the RGB cells. They supposedly are fitting six RGB cells into the area equal to a single cell on a 1920x1080 sensor. As I understand, the relative sensitivity of the six cells can be dynamically.
 
By the way, the upcoming Panavision Dynamax sensors will incorporate sensitivity mapping of the RGB cells. They supposedly are fitting six RGB cells into the area equal to a single cell on a 1920x1080 sensor. As I understand, the relative sensitivity of the six cells can be dynamically.

This would be interesting to see the details. The first thought I would have would be some sort of 'lut' where each pixel would have a 'gain' value associated with it for each x,y array location... perhaps 'gain' is not quite the correct term... but something that would control the charge that is stored in the cell depending on the amount of 'light' that the cell receives.

I think it would have to be on the 'cell' level, as a 'gain' at the digitizer would still have the problem of the cells 'saturating' based on the light differences between highlights and shadows.
 
h-munster,

I presented a method that might actually improve dynamic range, different pixels, and you are using it as an argument? The equations at that article are still wrong, they wouldn't even apply in that case. But the claim was double resolution, not double resolution AND introduction of new technology with different pixel types. If the low res sensor has the same technology it would still be only 2 stops for 4x resolution.

I agree with John Galt, I'm even working on a 1080p bayer camera.

You might get 2 extra stops if you use a sensor 4x larger for the 4x larger resolution. The article is still wrong, right?

The 2+2=2x2 part was an explanation about why the wrong formula gave correct results for 2bit pixels.

Human vision is analogous to digital imaging. The eye sums energy in its sensors. Everything is analogous up to the AD converter actually. Think of the eye as a very advanced sensor with monochromatic pixels for low light and thrichromatic for good light. The AD and DSP is very advanced but it's not very different from a sensor.

The "color depth" formula is nonsense. There is no "color depth" formula that includes resolution. Everybody knows how bits combine in RGB. 8bit per color is 24bit RGB, I doubt the writer wrote that article to explain that:) IMHO it was written by someone who does not understand imaging or mathematics.

Why do you provide an example of 10bit pixel into 30bit color? That doesn't contain addition because it's three pixels of different color. The eye can tell one from the other because they are in different parts of the spectrum. We should have established that by now.

The angular resolution increases and you believe that contradicts the fact that you will see individual pixels when you get close?!

The resolution in dither must be massively larger in order to provide a real benefit, because the dots are SUMMED. Photons from these dots are SUMMED.

You are constantly trying to find excuses for that nonsensical article:)
 
The resolution in dither must be massively larger in order to provide a real benefit, because the dots are SUMMED. Photons from these dots are SUMMED.

You are constantly trying to find excuses for that nonsensical article:)

Once I realized the fellow was talking about 'human perception', it was clear this was at best a subjective evaluation of 'color', the effect of which is highly dependent on viewing distance, just as a 'color' TV (or any other 'screen/pixel' based method) looks like a series of dots up close, and only at a distance does the human perceive the variety of colors that are produced from just stimulating R, G, B. (or which ever color system is used...) Same is true for printed materials... etc...

The discussion did remind me of 'getting color from your black and white TV'... which I've never seen demonstrated, but recall the process involved twirling a black and white target and at specific rotation rates, 'color' was supposed to be perceived by the human viewer...

I suppose I could experiment these days, and capture some footage, render it in a monochrome and see what happens for various rotation rates...
 
I presented a method that might actually improve dynamic range, different pixels, and you are using it as an argument?
I am not arguing that the methods that you mentioned will not improve dynamic range. Those methods are great to know. Thanks for explaining them.

However, we seem to be having some semantic confusion, especially concerning dynamic range, contrast range and color/luminance depth.

I assert that dynamic range and color depth are two different properties. Color depth is the number of colors possible from a system (with a given contrast range and dynamic range). One can have infinite color/luminance depth within a 1-stop range. There won't be a lot of contrast (nor dynamic range), but, nevertheless, the number of possible colors/shades within that 1-stop range is practically infinite.


The equations at that article are still wrong, they wouldn't even apply in that case.
That formula is correct for analog systems and for digital systems in which the shading increments non-uniform/non-linear.

I agree that the color depth formula does not apply to dynamic range.


But the claim was double resolution, not double resolution AND introduction of new technology with different pixel types. If the low res sensor has the same technology it would still be only 2 stops for 4x resolution.
I don't recall ever seeing a "double resolution" example. There was a quadruple resolution example (4x).

Are we still talking about dynamic range? "Stops" does not refer to color depth.


I agree with John Galt, I'm even working on a 1080p bayer camera.
I agree with John. Galt, too, and I am glad that you are developing your camera.

By the way, I think that Mr. Galt is partial to RGB sensors.


You might get 2 extra stops if you use a sensor 4x larger for the 4x larger resolution. The article is still wrong, right?
Again with the "stops" (and dynamic range).

The article is correct, except that the formula does not apply to digital imaging systems in which the pixel shading increments are uniform.


The 2+2=2x2 part was an explanation about why the wrong formula gave correct results for 2bit pixels.
Not to be pedantic, but the examples that you gave were 1-bit pixels -- each had two shades.

I understand what you are trying to suggest with that simple equation, but it does not explain why the color depth formula worked for those examples. It worked in both cases because the bit depth in both examples was limited to one bit.

In other words, if we combined three one-bit pixels in both examples, the color depth formula would still have worked. However, 2+2+2 != 2x2x2.


Human vision is analogous to digital imaging. The eye sums energy in its sensors. Everything is analogous up to the AD converter actually. Think of the eye as a very advanced sensor with monochromatic pixels for low light and thrichromatic for good light. The AD and DSP is very advanced but it's not very different from a sensor.
In a general sense, yes the eye is analogous to digital imaging and to analog imaging. The eye probably doesn't have anything quite like digital pixel shading increments. At any rate, I don't see how any of this relates to resolution and color depth.


The "color depth" formula is nonsense. There is no "color depth" formula that includes resolution.
As I mentioned earlier in this post, the formula in the article is accurate for analog imaging systems and for imaging systems with non-uniform pixel shading increments. That formula includes a factor for resolution.

The straightforward formula that I gave (R x N = C) covers all digital imaging systems with uniform pixel shading increments. That formula also includes a factor for resolution.

You have demonstrated by your own examples (and by your own manual math) that an increase in resolution yields greater color depth. So, resolution must somehow "figure-in" to the equation.

The relationship between resolution and color depth is mostly described in the two formulas -- the one in the article and the one that I gave.

In addition, in the printing industry, there are plenty of charts and calculators that determine the range of tones relative to resolution. The fact that resolution affects color depth is not a new concept.


Everybody knows how bits combine in RGB. 8bit per color is 24bit RGB,...
Most are not aware of how resolution affects color depth.


... I doubt the writer wrote that article to explain that IMHO it was written by someone who does not understand imaging or mathematics.
Everyone has a right to their opinion.


Why do you provide an example of 10bit pixel into 30bit color? That doesn't contain addition because it's three pixels of different color. The eye can tell one from the other because they are in different parts of the spectrum. We should have established that by now.
The example in question from the color depth article involves 10-bit RGB cells (10 bits per color channel). Both of us have been referring to that example.

Not sure what you are trying to say by pointing out that each pixel is a unique color (relative to the other two pixels).


The angular resolution increases and you believe that contradicts the fact that you will see individual pixels when you get close?!
The angular resolution of the viewer's eye remains constant, regardless of the viewing distance.

The angular resolution of the image decreases as the viewer moves closer to the image. Hence, the viewer begins to see individual pixels.


The resolution in dither must be massively larger in order to provide a real benefit, because the dots are SUMMED. Photons from these dots are SUMMED.
Yes. Photons can be "summed." However, we are not combining shades in quantum increments. We are using much coarser, pixel shading increments. If the scale of pixel shading increments is non-linear, then we cannot just sum the pixels in terms of shading increments, because each shading interval along the scale adds a different number of photons. In such a scenario, each shading increment is unique.

Therefore, if the increment shading scale is non-linear, a 10-increment pixel combined with a 30-increment pixel will not yield the same shade as a 40-increment pixel.

The inaccuracy of "summing" in such systems holds true, whether or not the imaging system is dithered. However, most dithered images are 1-bit (otherwise, we would just utilize the greater bit-depth and resolution).


You are constantly trying to find excuses for that nonsensical article
The essence of that article is the assertion that higher resolution begets greater color depth. You keep belittling it, and calling it "nonsensical," yet you have inadvertently proved this fundamental photographic principle on two occasions, with your own examples.

Furthermore, the article's formula worked perfectly for the two math examples that you put forth.

Perhaps there is something actually valid in the article and in all of the printing articles that relate resolution to color/luminance depth.
 
Once I realized the fellow was talking about 'human perception', it was clear this was at best a subjective evaluation of 'color', the effect of which is highly dependent on viewing distance, just as a 'color' TV (or any other 'screen/pixel' based method) looks like a series of dots up close, and only at a distance does the human perceive the variety of colors that are produced from just stimulating R, G, B. (or which ever color system is used...) Same is true for printed materials... etc...
Yes. What you are saying about viewing distance and resolution and color depth are exactly true. The viewing distance affects the angular resolution of the image, which affects the color depth.

However, the "evaluation" is not subjective. Indeed, given the resolution and the number of possible colors in each "resolution unit," the resulting color depth can be calculated with precision.

The same formula and result would apply if the "viewer" were a camera, that possessed a higher bit depth and lower resolution than that of the image. So, it is not tied to "human perception."


The discussion did remind me of 'getting color from your black and white TV'... which I've never seen demonstrated, but recall the process involved twirling a black and white target and at specific rotation rates, 'color' was supposed to be perceived by the human viewer....
I think you are referring to "Benham's Disk."

That optical illusion has nothing to do with the basic photographic principle that higher resolution begets greater color depth.
 
This would be interesting to see the details. The first thought I would have would be some sort of 'lut' where each pixel would have a 'gain' value associated with it for each x,y array location... perhaps 'gain' is not quite the correct term... but something that would control the charge that is stored in the cell depending on the amount of 'light' that the cell receives.

I think it would have to be on the 'cell' level, as a 'gain' at the digitizer would still have the problem of the cells 'saturating' based on the light differences between highlights and shadows.
John Galt hints in his article that the "exposure time" of each Dynamax photosite can be controlled individually.
 
By any definition of science, if your result is 2,000,000,000,000,000 instead of 2, you should get your head cut off:)
 
By any definition of science, if your result is 2,000,000,000,000,000 instead of 2, you should get your head cut off
Thanks for the pleasant sentiment.

Nevertheless, the color depth increase can be astronomical for analog systems and for digital systems in which the pixel shades are scaled non-linearly or logarithmically.

Furthermore, I am now adding to this thread, because I just realized that I made a mistake with my formula. It turns out that we gain 64-times more color depth in our 4x resolution example with the linear pixel-shading scale -- instead of just a 4-times color depth increase, as we previously thought.

This greater result is the absolute minimum increase in color depth, because the formula applies only to the systems with a linear pixel-shading scale. The color depth increase is greater in all other pixel shading scenarios (which are scaled non-linearly).

My mistake was that the pixel "summing" has to be done separately for each color channel, which I did not do in my earlier formula.

Here is how the formula should actually read: (B x R)^N

"B" is the bit depth of a single pixel within an RGB cell. "R" is the resolution increase (the number of cells within the given group). "N" is the number of pixels within a single cell (which is always "3" for an RGB cell).

Thus, to find out how many colors are possible from the group of four, 10-bit RGB cells (with a linear pixel shading scale), the figures would be:

(2^10 x 4)^3
= (1024 x 4)^3
= 4096^3
= 68,719,476,736

The total number of colors possible from a single 10-bit, RGB cell is 1,073,741,824, which happens to be 1/64th of 68,719,476,736.

So, we have a 64-times increase in color depth, from a mere 4-times increase in resolution. Again, the color depth increase would be much greater in systems that use non-uniform pixel shading increments.
 
Every 4 color pixels are using identical filters, so you sum energy, 4x as many photons, and gain 2 bits per color which is 6 bits in total for three filters. 64x. 4x is correct for mono and 64x is correct for color and I have been explaining that in the previous posts. You would gain the same by having a single large pixel that gets 4x as much energy (what the 4x smaller pixels get). By using four 10bit pixels instead of one 12bit pixel you just gain resolution. If you can see individual pixels, you get inferior precision (in return for higher resolution), if you downsample or if you are far enough from the screen, you are only matching the precision of the large pixel (but you just lost the resolution advantage).
 
Every 4 color pixels are using identical filters, so you sum energy, 4x as many photons,...
No. You get 4x as many unique "summed" shades -- not 4x as many photons.

You probably meant to say "shades" instead of "photons." However, this distinction is crucial to understanding the difference between dynamic range and color depth in digital systems. It is the number of unique shades per color channel along with resolution that determine color/luminance depth. The number of photons is irrelevant to color/luminance depth (as long as we always have more photons than unique shades).

Of course, if we divide a single pixel into four smaller pixels, the quantum sensitivity/output of each smaller pixel should be 1/4 of the original pixel (given that all variables remain equal and perfect). This principle has nothing to do with color/luminance depth nor with bit depth.


4x is correct for mono and 64x is correct for color and I have been explaining that in the previous posts.
Okay, but a 64x color depth boost from a mere 4x resolution increase is still a lot of gain for a small increase, and it cannot exactly be described as "summing the energy."

Also, keep in mind that the color depth increase becomes astronomical, if the pixel shading scale has non-uniform increments between shades.


You would gain the same by having a single large pixel that gets 4x as much energy (what the 4x smaller pixels get).
No. 4x the energy means nothing in reference to bit-depth nor to luminance/color depth.

A 1-bit pixel might sense/display 1000x the energy of a 10-bit pixel. Nevertheless, the 10-bit pixel will have a much greater bit depth/luminance depth.


By using four 10bit pixels instead of one 12bit pixel you just gain resolution.
Yes -- in addition to the gain in color depth.


If you can see individual pixels, you get inferior precision (in return for higher resolution),
Huh? If the pixels are large enough for you to see, you are getting lower pixel resolution than if the pixels were too small to see (from the same viewing distance).


if you downsample or if you are far enough from the screen, you are only matching the precision of the large pixel (but you just lost the resolution advantage).
The farther you move from the screen, the greater the color depth.

Also, color depth doesn't necessarily increase when you "downsample" -- one could downsample four 10-bit pixels into a single 1-bit pixel.
 
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