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clange wrote:This means that any combination of base colors can be used and only three parameters is enough to model the colors that we can see.
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It is of course only true with respect to the human visual system

Another problem with this model (other than what Solar has already picked up) is that the three parameters you mention are generally three discrete values. On the other hand, the photoreceptors in the human eye are actually sensitive to a range of colours with non-symetrical distributions around a given peak.

Even if you pick your "RGB" with colours selected to match these peaks, you still won't be able to map the entire visible spectrum.

Cheers,
Adam

AJ wrote:Even if you pick your "RGB" with colours selected to match these peaks, you still won't be able to map the entire visible spectrum.

I want a colour system that can map the entire visible spectrum (moving away from RGB). Even if each channel can peak at different heights.

Yup - sorry, got a bit OT there!

I've mentioned the CIE diagram quite a bit, and that makes for some quite good thought experiments. Basically, if you pick any three coordinates as primaries, you can represent any colour within that triangle. The key, then, is to make that triangle as large as possible. Depending on whether or not you want to represent things psychophysically, this representation may be a red herring, though. The CIE diagram is adjusted so that certain "steps" in change of hue appear even to a human observer. That doesn't help you with how things are represented in the physical world.

I also had a link hidden away to this site. Bad news:

Above link wrote:Color gamut: subspace of visible colors

No system of mixing colors from fixed number of primaries can represent all visible colors.

As far as I can tell (and I'm no mathematical genius), this means looking at calculus (specifically, Fourier domain calculus), because you can do maths which takes in to account that colour-space is continuous.

For some basic groundwork, have a look here.

Cheers,
Adam

Solar wrote:

clange wrote:(*) And three samples is of course not enough to describe colors when doing calculations. Imagine a fluorescent light source illuminating a lemon. 3 samples will never be enough to represent both the relative smooth "reflection" of the lemon compared to the very narrow spike of the light source.

Erm...

I think you are confusing color (which could be a single pixel on the screen) and stuff like texture, reflection etc...

No, you are confusing colour with light.

S: (n) color, colour, coloring, colouring (a visual attribute of things that results from the light they emit or transmit or reflect)
S: (n) color, colour (the appearance of objects (or light sources) described in terms of a person's perception of their hue and lightness (or brightness) and saturation)

As long as it looks like a uniform colour, it is a colour (even if it's made up by several "pixels").

Solar wrote:
Erm...

I think you are confusing color (which could be a single pixel on the screen) and stuff like texture, reflection etc...

Nope, but I may not be very clear with my terminology.

My main point was that colors (as perceived by humans) can be expressed using only 3 (arbitrary) coefficients. But calculations involving colors (light emission, reflection, transmission, etc.) will require "more precision" to give physical correct results. In reality it is of course rarely needed to provide a physically accurate result.

clange

Hi,

clange wrote:

Solar wrote:I think you are confusing color (which could be a single pixel on the screen) and stuff like texture, reflection etc...

Nope, but I may not be very clear with my terminology.

My main point was that colors (as perceived by humans) can be expressed using only 3 (arbitrary) coefficients. But calculations involving colors (light emission, reflection, transmission, etc.) will require "more precision" to give physical correct results. In reality it is of course rarely needed to provide a physically accurate result.

You could have a realistic model based on physics, where "objects" (textures, points, etc) can emit, reflect, refract, absorb and/or mutate rays of light, where each ray of light consist of the an entire spectrum (e.g. the intensity of light at each possible frequency) and a direction (and a polarization?). You could do ray casting, and you'd end up with a picture calculated from this realistic model based on physics; but the resulting picture will be an array of pixels where each pixel has a color (based on the intensity of light at each possible frequency that reaches the viewer), and where each color could be converted to RGB without distortion (excluding distortion resulting from "lack of precision" - e.g. for 15 bpp the colors will be distorted more than they would be for 32-bpp, but only because of limited range).

Basically, your "calculations involving colors" would actually be "calculations involving the intensity of light at each possible frequency".


Cheers,

Brendan

clange wrote:My main point was that colors (as perceived by humans) can be expressed using only 3 (arbitrary) coefficients.

Which is wrong. Because several different "colour spots" may actually form what is percieved as a perfectly uniform, non-textured, non-specular colour that may not be formed with just a single type of "colour spot".

Brendan wrote:Basically, your "calculations involving colors" would actually be "calculations involving the intensity of light at each possible frequency".

Exactly. I should have explained that myself - I'll try to be less lazy in the future and choose my words more carefully . But I must say that you write very well and your explanations on all your topics are very clear. And thanks for all the posts you have made - they a really helpfull.

It is also worth noting that this will be very expensive to calculate but very useful as a reference rendering. And using just a few more samples (going from 3 to 9 for example) gives significant more realistic results [Hall & Greenberg, "A Testbed for Realistic Image Synthesis, 1983]. It is also possible to choose higher order basic functions but to my knowledge you mainly substitute one set of problems with another. I haven't tried it myself and only read briefly about it.

Regarding polarization I just checked my books: they basically says: "it is not too difficult to include, but would add little practical value" I can easily ask around and find out more if you are interested (it peaked my interest and I have a good friend that does research in realistic image synthesis).

Craze Frog wrote:

clange wrote:My main point was that colors (as perceived by humans) can be expressed using only 3 (arbitrary) coefficients.

Which is wrong. Because several different "colour spots" may actually form what is percieved as a perfectly uniform, non-textured, non-specular colour that may not be formed with just a single type of "colour spot".

Could you please explain in more detail. I would like to fill the gaps in my knowledge.

clange

clange wrote:

Craze Frog wrote:

clange wrote:My main point was that colors (as perceived by humans) can be expressed using only 3 (arbitrary) coefficients.

Which is wrong. Because several different "colour spots" may actually form what is percieved as a perfectly uniform, non-textured, non-specular colour that may not be formed with just a single type of "colour spot".

Could you please explain in more detail. I would like to fill the gaps in my knowledge.

clange

It's difficult to show it properly on a computer screen because the resolution is too low, but I'll show you an example, and you can imagine the result with a much higher resolution (like in the real world).

Here is an image (click it):

To compensate for the low resolution, move away from the screen until the left part of the image suddenly looks like one uniform, non-textured colour. This "uniform colour" on the left can't be reproduced by filling all the pixels on the right side with an equal colour. Just try it, it's impossible. No matter how long you fiddle with your RGB values, the colour will be either too bright, too colourful, too dark, too grey, and so on. This is our brain at work.

On my LCD monitor it looks like there is a lot more colour and less black and white in the right one, when I look at the big version. For some reason the colours look perfectly equal on the thumbnail, though. This is because the same amount of red, green and blue was used in each half, and the downscaling destroyed the effect.

Craze Frog wrote:I learned that from experience after getting education in arts. There is a very significant part of RGB that can't be represented properly with CMYK, for example. I'm not talking about minor visual differences here, I'm talking about huge ones.

You can represent any RGB colour in CMYK when the full black and full white levels are equal and the precision is sufficient. The problem with this, of course, is that most uses of CMYK involve print, where your white level is constrianed by the reflectivity of the surface your printing on.

One important question to raise when designing a new system to handle the full human gamut: Do you also include information for tetrachromats?

By looking at the male or female poll that was a round sometime ago I have a feeling that not to many people on this forum are tetrachromats

Jules

We may have some bichromats though, on the other hand

(Partial colour blindness is more almost twice as common in males since it's most often caused by recessive genes on the X chromosone - and females have the backup of a second. This also means that in males it almost always comes from the mother, since by virtue of being male your father gave you a Y chromosome )