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### AuthorTopic: Color Gamut RGB Cube  (Read 65854 times)

#### JeremyLangford

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##### Color Gamut RGB Cube
« on: September 15, 2009, 06:46:21 pm »

Is a 2d diagram of a color gamut such as this one.....

basically an overhead view of an RGB cube with the white corner in the center?

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#### madmanchan

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##### Color Gamut RGB Cube
« Reply #1 on: September 16, 2009, 08:17:08 am »

No, it is not. A 2D projection of a cube would not give you the smooth shape of your first diagram.

The term given to the object depicted in the first diagram is the spectral locus.

See http://en.wikipedia.org/wiki/CIE_1931_color_space
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Eric Chan

#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #2 on: September 16, 2009, 01:14:59 pm »

Quote from: madmanchan
No, it is not. A 2D projection of a cube would not give you the smooth shape of your first diagram.

The term given to the object depicted in the first diagram is the spectral locus.

See http://en.wikipedia.org/wiki/CIE_1931_color_space

Wikipedia also says this about Color Gamut Diagrams here

"A typical CRT gamut:
The grayed-out horseshoe shape is the entire range of possible chromaticities. The colored triangle is the gamut available to a typical computer monitor; it does not cover the entire space. The corners of the triangle are the primary colors for this gamut; in the case of a CRT, they depend on the colors of the phosphors of the monitor. At each point, the brightest possible RGB color of that chromaticity is displayed, resulting in the bright Mach band stripes corresponding to the edges of the RGB color cube."
« Last Edit: September 16, 2009, 01:16:55 pm by JeremyLangford »
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#### madmanchan

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##### Color Gamut RGB Cube
« Reply #3 on: September 16, 2009, 02:34:48 pm »

Correct, the spectral locus is the shape and range of perceivable colors for an average viewer.

This is not the same thing as a RGB cube, which is a mathematical abstraction of an additive color space with three primaries.

As indicated above in the diagram you posted, if the primaries are visible (i.e., the vertices of the triangles lie within the horseshoe shape), then there will be physical colors that cannot be reproduced in that RGB space. This is clear, because no matter where you place the three vertices of the triangle within the horseshoe, there will be colors that lie outside the triangle.

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Eric Chan

#### Pat Herold

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##### Color Gamut RGB Cube
« Reply #4 on: September 16, 2009, 02:43:04 pm »

Jeremy,
If you want to see a visual description of how 2D color space relates to 3D color space,  download ColorThink Pro.  Even the free demo version allows you to choose between Lab space, Yxy, and Luv spaces.  Then, clicking on the 2D graph or 3D graph buttons will automatically animate the change between the two.  It's a great way to get your head around these concepts.

https://www.chromix.com/colorthink/download

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-Patrick Herold
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#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #5 on: September 16, 2009, 05:01:02 pm »

Both of these pictures seem to be showing the same thing: A 2d representation of a 3d RGB color space. The edges of the RGB cube even seem to show up in the color gamut diagram. Are they not doing the same thing: Mixing Red, Green, And blue together to show every possible color?

« Last Edit: September 16, 2009, 05:07:46 pm by JeremyLangford »
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#### Jeremy Payne

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##### Color Gamut RGB Cube
« Reply #6 on: September 16, 2009, 05:33:04 pm »

.
« Last Edit: October 22, 2009, 09:54:15 pm by Jeremy Payne »
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#### madmanchan

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##### Color Gamut RGB Cube
« Reply #7 on: September 16, 2009, 05:33:21 pm »

They are related, but definitely not the same. The spectral locus shows, approximately, the range of colors visible to humans. The cube shows the set of colors that can be generated by three primaries. These are not the same. Pick any set of real primaries. There are colors that are visible to us, that cannot be produced by those primaries, no matter how you add them up.

Furthermore, these shapes are quite different, which should be a straightforward giveaway. It's like comparing a square and a circle. They have different shapes, represent different things, and have different properties.
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Eric Chan

#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #8 on: September 16, 2009, 08:37:12 pm »

Quote from: madmanchan
These are not the same. Pick any set of real primaries. There are colors that are visible to us, that cannot be produced by those primaries, no matter how you add them up.

I didn't know that. Wouldn't that make the spectral locus pretty incomplete when viewed on an RGB monitor or printed with a printer that only uses CMYK?
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#### MPatek

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##### Color Gamut RGB Cube
« Reply #9 on: September 17, 2009, 01:50:03 am »

Quote from: JeremyLangford
I didn't know that. Wouldn't that make the spectral locus pretty incomplete when viewed on an RGB monitor or printed with a printer that only uses CMYK?

That is correct. There is no display nor printer that can reproduce such saturated red, green and blue colors as depicted in the CIE (x,y)-chromaticity diagram (AKA spectral locus).

For the RGB cube and 2D x,y-chromaticity diagram, there is a way to transform the cube into spectral locus representation, but the opposite is not true. RGB values can be transformed into CIE-XYZ values using a linear transformation. XYZ values then can be further transformed into x,y coordinates which are the basis of the spectral locus diagram. However, along the way, the Y (luminance) component is lost and only 2D graph projected. Not knowing the luminance values, one cannot get back to XYZ, thus precluding calculation of RGB values. As Eric Chan pointed out, the RGB gamut (and cube) shown in your previous post would not match the x,y-diagram. However if you had a hypothetical RGB color space (gamut) that has primaries of the spectral locus, then there would be a mathematical translation going in direction RGB->XYZ>x,y. Prolem is that while RGB space is linear, x,y-chromaticity diagram is not. That means that same changes in the RGB cube would not correspond to perceived changes in the x,y diagram.

Some more details and pictures are at this webpage. For transformation of sRGB space to XYZ (->y,y), see equation VII-inv.
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#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #10 on: September 17, 2009, 09:07:51 pm »

So the XYZ is a color space made in 1931 by CIE that encloses the visible gamut with three primaries that are actually outside the human spectral locus gamut, meaning that it will never be outdated and there will never be a color outside of it. And this makes it the standard reference space for viewing other color spaces.

Is that right?
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#### joofa

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##### Color Gamut RGB Cube
« Reply #11 on: September 18, 2009, 03:17:18 pm »

Quote from: JeremyLangford
So the XYZ is a color space made in 1931 by CIE that encloses the visible gamut with three primaries that are actually outside the human spectral locus gamut, meaning that it will never be outdated and there will never be a color outside of it. And this makes it the standard reference space for viewing other color spaces.

Is that right?

The digital cinema initiative has incorporated that thinking into canonizing XYZ space. Otherwise, actually that "out of gamut" concept is more applicable when you are ready to display, and at that time you need to consider the gamut of colors that the display can accommodate. Any color, including out of gamut, and those outside of spectral locus may be expressed in any standard RGB model where the primaries are inside the spectral locus -- only that some of the values for the intensities of these primaries will be negative, and/or in normalized values greater than +1. And, when it comes to display, or for whatever reason, these negative or greater than +1 values may be dropped or mapped into the target gamut under consideration. Even in the XYZ space, since the primaries are physically non-realizable, when it comes to display then some sort of gamut conversion stage has to be employed to map the colors outside the gamut of the display device into colors that it can display, therefore some reduction happens even during XYZ->display gamut.

Think about it: the spectral locus is outside the CIE RGB primaries, i.e., the triangle formed by the location of these RGB primaries. So that means negative numbers for at least one of the CIE RGB intensities. But, CIE still measured those RGB numbers and then converted them to XYZ, since XYZ is always positive for the spectral locus. (CIE did that by adding some of the RGB primaries to the test color to make the overall system positive.)
« Last Edit: September 18, 2009, 03:56:43 pm by joofa »
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#### MPatek

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##### Color Gamut RGB Cube
« Reply #12 on: September 18, 2009, 04:20:45 pm »

Quote from: JeremyLangford
So the XYZ is a color space made in 1931 by CIE that encloses the visible gamut with three primaries that are actually outside the human spectral locus gamut, meaning that it will never be outdated and there will never be a color outside of it. And this makes it the standard reference space for viewing other color spaces.

Is that right?

I agree with your summary. XYZ system is quite nonintuitive, so other color systems were created based on it (Lab, xyY, RGB). Think of the XYZ color space as of computational rather than visual system. And yes, it is the underlying system of color science, digital photography, imaging ,..
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Marcel

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#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #13 on: September 22, 2009, 05:44:59 pm »

How is this

converted into this?

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#### MPatek

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« Reply #14 on: September 22, 2009, 11:49:24 pm »

Quote from: JeremyLangford
How is this

converted into this?

The following tools offer even more transformations and mappings: Couleur.org (free download, install).
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#### joofa

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##### Color Gamut RGB Cube
« Reply #15 on: September 22, 2009, 11:50:17 pm »

Quote from: JeremyLangford
How is this

converted into this?

Your second graph (the wiggly one) is actually the monochromatic stimuli of constant radiance for all wavelengths shown in the first graph. When this wiggly curve is projected on the plane x+y+z=1, you get that "standard" spectral locus diagram shown in the figure in the first message (post # 1) of this thread, that I copy below (the figure below is a further projection on the z-axis to show just x-y diagram, instead of an x-y-z diagram):

I.e., from the origin draw a straight line connecting any point on the wiggly curve and extend it to the plane x+y+z=1. Where this line meets the plane draw a dot; do that for all points on the wiggly curve and you have now a bunch of dots on the plane. Connect the dots on the plane and you get your standard spectral locus diagram shown in post #1.
« Last Edit: September 23, 2009, 12:00:07 am by joofa »
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#### JeremyLangford

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« Reply #16 on: September 23, 2009, 04:02:29 pm »

I'm sorry but this stuff is really getting to be over my head.

Do you think someone here can give me an easy to understand, very basic idea on how these three diagrams are converted into each other?

This

Becomes This

Which Becomes This

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#### joofa

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« Reply #17 on: September 23, 2009, 04:21:25 pm »

Quote from: JeremyLangford
Do you think someone here can give me an easy to understand, very basic idea on how these three diagrams are converted into each other?

Trying again. Pick any single color (monochromatic) from your first diagram and note its radiant power (used later). Then measure the amount of X, Y, and Z primaries, which are calibrated using a certain process, that you need to match that color, and this gives you 3 numbers. Plot the 3 numbers and you get a point on the wiggly curve in your second diagram. Now divide each of the X,Y,Z by their sum (X+Y+Z), and you get another set of 3 numbers. Plot them again and that gives you a point on spectral locus on the third diagram. Now go back to the first diagram and pick another color at the same radiant power as the first color picked and repeat the process. Keep on doing until you have done for all/enough colors in the first diagram. Now you have a whole bunch of points on the second and third diagrams and you just join them together to get the curves shown.
« Last Edit: September 23, 2009, 04:23:02 pm by joofa »
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#### JeremyLangford

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##### Color Gamut RGB Cube
« Reply #18 on: September 23, 2009, 04:29:13 pm »

Quote from: joofa
Trying again. Pick any single color (monochromatic) from your first diagram and note its radiant power (used later). Then measure the amount of X, Y, and Z primaries, which are calibrated using a certain process, that you need to match that color, and this gives you 3 numbers. Plot the 3 numbers and you get a point on the wiggly curve in your second diagram. Now divide each of the X,Y,Z by their sum (X+Y+Z), and you get another set of 3 numbers. Plot them again and that gives you a point on spectral locus on the third diagram. Now go back to the first diagram and pick another color at the same radiant power as the first color picked and repeat the process. Keep on doing until you have done for all/enough colors in the first diagram. Now you have a whole bunch of points on the second and third diagrams and you just join them together to get the curves shown.

How do I find a color's radiant power?

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#### joofa

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« Reply #19 on: September 23, 2009, 04:46:40 pm »

Quote from: JeremyLangford
How do I find a color's radiant power?

Firstly, your second curve doesn't seem fully okay to me. I have a slight problem trying to reconcile it with one of the primaries. But that is fine, as the process I outlined will result in a wiggly nature of the curve and after that "beauty pass" of dividing by X+Y+Z your third diagram will emerge.

As far as measuring the radiant power you will need certain specialized hardware for that and even for setting up an experiment for matching the colors.
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