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Okay, so I've read questions such as this one explaining the difference between the two which was illuminating, but I still have a few questions I didn't really quite gather from this.

What I took away from this, presuming I understand, is that the color gamut for a display essentially defines the border of what's possible theoretically and the bit-depth in determines the number of shades / tints available in a respective color as described there.

Wuld it be correct in saying that I could have a color gamut and divide that color gamuts representational possibilities, in an arbitrary display, according to bit depth?

Taking a step back.... more abstractly... some screens are paletted and some are not paletted. Meaning, I could divide some digital displays according to whether they are monochrome screens or paletted wherein these monochrome screens could be grayscale or not grayscaled (determined by a bit depth of 1 to 8 forming a black / white to full grayscale palette of potential colors).

Similarly, we have dichrome as a step up from this using permuted pairs of RGB.

Beyond this... in paletted screens using RGB color models we have 3-bit, 6-bit, 8-bit, 9-bit, 12-bit, 15-bit, and 16-bit (theoretically 32-bit) color depths that are possible.

Now, this is where I personally get fuzzy interconnecting these display possibilities with color gamuts and more abstractly color models.

In short, what is the hierarchical structure between these - if any? Is it even possible to say, for example, AdobeRGB on display X with bit-depth Y or is that just fundamentally incorrect?

If that's possible.... great that's just for the RGB color model using additive / subtractive representations. What about other color models and the above bit-depth considerations?

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    I’m voting to close this question because I don't see it has any bearing on photography.
    – Tetsujin
    Jan 30 at 19:04
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    Ehhh, what? I understand colour spaces, and I understand bit depth. I don't understand your question.
    – osullic
    Jan 30 at 19:52
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    Also, I do think it's worth re-mentioning that Stack Exchange is for practical, answerable questions based on actual problems that you face.
    – osullic
    Jan 30 at 22:12
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    I see the relevance to photography, it's good to understand colour spaces. But after reading your text 3 times, I still don't get the actual question. Sorry, but you should clarify. When you say: "what is the hierarchical structure between these - if any?" - what is "these" refering to? What hierarchical structure? I don't know any such structure regarding colour spaces. And when you say: "Is it even possible to say, for example, AdobeRGB on display X with bit-depth Y" - there is a verb missing. Sure a display can show colours of a given space with a given bit depth. Is that it?
    – Matt
    Jan 30 at 23:32
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    @Pythonista The comments are not clarifying the question. Without clarification the question won’t better fit the format of this StackExchange site. Jan 31 at 0:13
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A color-space is a basically all possible colors within a certain bounded bounded volume. There are numerous color-spaces and they are usually defined by a set of variables. sRGB for example is all colors possible by linear combinations of its 3 color-primaries.

A color-gamut normally refers to all possible color that a monitor can display. These are very similar to a color-space except that a color-space is conceptual but color-gamut is practical. It is the limit of what was achieved when constructing a display. More times there is a huge overlap but there could be areas of a color-space not covered by gamut and vice-versa. The ratio of color-space to gamut is known as coverage. You often see a good monitor state 98% coverage but you can also see some that say 108% of sRGB (for example), meaning their gamut is larger than the color-space.

Color-Depth is the granularity of colors with the color-gamut that defines the limits of what a screen can display. All screens have a certain gamut, whether specified by the manufacturer or not. Digital displays also have their own bit-depth which is sometimes different than the color-depth rendered by the operating system.

Color-depth is essentially precision. It is like measuring the distance between two points and stating it as 102km while it could also be measured in meters which would result in a more precise distance, it could be 102,207m. Color-depth is necessary because computers produce images digitally. Even on analog displays where the display had no color-depth, the operating system or at least application had to output its signal at a certain color-depth. The graphics cards back then had DAC (Digital-to-Analog Converters) that turn a signal of a certain bit-depth into an analog wave. Analog monitors themselves though could be driven at any precision and although desktop computers usually output 6-8bps, there were more powerful computers that used 12-bpp on the same displays.

Paletted colors as you call them are another variant of this. The common term is Indexed Color which will make sense in a moment but let's break it down first:

  • Most computer displays are made of a backlight and a liquid crystal panel where each sub-pixel can vary the amount of light that passed through it. The interface to the panel is digital and sets the maximum bit-depth of the screen. Most modern screens use 8-bits per sub-pixel but there exists 6-bit ones which were common in laptops plus 10, 12 and 14 bit ones at least.

  • When you set the bit-depth of the operating system, you are defining how colors are specified in software but the operating system translates it to the color-depth of your display. Displays can do that internally too and high-end monitors often do that to improve accuracy. So while 24-bit color (8-bits per channel) may be selected in the operating system, a monitor can translate this into 14-bits using a Look-Up-Table set by a calibration device. Many panels with only 6-bit depth allow the OS to address them as 8-bit but they drop the lower two bits.

  • A Look-Up-Table (LUT) translates input colors received by the operating system into colors that are sent to the display panel. This translation can happen inside the monitor or in the graphics card. Implementations differ but generally these LUTs are interpolated and do not actually specify a mapping from every possible input color.

  • Indexed Color is a simplification of this designed to reduce memory usage. The depth-of-the-palette defines how many entries it has. So a 4-bit color palette can address 16 colors. Usually a program starts by setting the palette which defines a color to output for each possible 4-bit number. Then when a color is specified, it is the index in the palette that is used and the displayed color is the value stored in the palette.

Possibly the most common indexed color are GIF images. Each pixel in an image can be one of 256 colors but every image can use a different set of 256 colors from 16 million. So, while you can evenly distribute colors of a palette across a color-gamut, that is rarely the case.

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Would it be correct in saying that I could have a color gamut and divide that color gamuts representational possibilities, in an arbitrary display, according to bit depth?

Yes a person could do that.

It is probably not worth doing from a photographic point of view because human perception is not linear from a mathematical point of view. Human perception is usually the problem a photograph needs to solve to be successful.

The science of human visual perception is photometry. Color spaces already include photometric considerations in order to be useful.

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  • Photometry is the science of measurement of light, weighted by the Human Visual System (HVS) in opposition to radiometry which ignores it. Colour science would be more appropriately the science of the HVS, and it encompasses/accounts for photometry .
    – Kel Solaar
    Jan 31 at 3:32

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