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Essay on Color, Para. 3, obtaining colors by mixing (continued)

3.3 Gamuts of Reproducible Color Space
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What is a gamut in our context? - It is the total range of colors that can be produced by mixing from a given set of primary colors.

If we want to get the best possible access to all the colors that our eyes can see, then the devices (e.g. scanner, monitor, printer) in our image handling chain should be able to reproduce everything that lies within the "horseshoe" of the CIE 1931 chromaticity diagram (fig 1.3.2-b in para. 1.3.2).
Now how close to this ideal can we get?

The chromaticity diagram itself is the most comfortable tool for this judgment:
Just enter the three loci of the primary colors into the diagram; everything within the area of this triangle is reproducible; everything without is not.

I found a beautiful figure with these triangles:


    fig.3.3-a: gamuts within chromaticity diagram (54 kByte)

It is nearly too nice and simple because of two reasons:

- Remember that all the colors that are shown within the horseshoe are reproduced by your monitor or printer. So no truly monochromatic colors are shown ... though required at the perimeter of the horseshoe.
Worse yet: outside the triangle of your monitor or printer there is nothing but (color-)guesswork.

- Remember that the 1931 chromaticity diagram is not based on sensational equal distances (see fig 1.3.2-c in para. 1.3.2). So, the size of the area between triangle and horseshoe does not necessarily show the importance of this area.


But anyway: as shown in fig. 3.3-a, there is a remarkable portion of the colored world beyond the scope of image sensing and image rendering devices.

What if an image sensing device (e.g. camera, scanner) is encountered with such a "beyond"-color?
Quite simple: in the device's output signal, the color locus will appear as the nearest possible spot on the triangle perimeter. That means: all color qualities beyond the triangle area are cut away or "clipped". All color differences between color loci on the triangle perimeter   and color loci beyond   will be lost.

And what if an image rendering device (e.g. monitor, printer) receives a signal "beyond" its scope? -- It depends.
Either device and associated software are simple and straightforward. Then the color quality will also be clipped.
Or you got a system striving for high fidelity. Then it will interpolate and transform all color loci in such a way that they fit into the triangle area.
One possible algorithm for "interpolation and transformation" is:
* in the chromaticity diagram, draw a straight line from point   E(x=0.33|y=0.33)   to the horseshoe perimeter at   (lambda) = 380 nm .
* Measure the distance from   E   to triangle perimeter and call it   a .
* Measure the distance from   E   to horseshoe perimeter and call it   b .
* Now shift all points on the line   b   towards point   E   by the factor   a/b .
* Repeat all preceding steps for   (lambda) = 381 nm .
* Repeat all through the visible spectrum.
We can call this "compressing the signal into the available gamut".
But remember: algorithms of this kind can only achieve that colors between triangle perimeter and horseshoe perimeter stay distinguishable. They can never make the colors be reproduced correctly.


Especially pitiable is the very small area within the CMY triangle. It shows that four-color printing will always suffer from flat color contrast. And nearly more pitiable: These subtractively-working primary colors (para. 3.2 mixing subtractively) always are complementary to the additively-working primary colors RGB; so, the CMY triangle is always positioned wrong for best fit into the CIE horseshoe (as you see above in fig. 3.3-a).

People in graphic arts have learnt this long time ago. They found a remedy very similar to the introduction of "black" into colour printing. They introduced several additional colored printing inks for the use in art printing. This way, the original CMY triangle has been extended to a much bigger polygon which makes art reproduction worth seeing (and expensive).

For the following figure (Gustav Klimt's famous "The Kiss") I scanned a postcard-sized reproduction at 72 dpi and, for the enlarged detail, at 1200 dpi. The enlarged detail shows the use of screening dots in several different colors.


    fig.3.3-b: art printing example (250 kByte)

And I found another related example of people striving for better color rendition by expanding the gamut polygon ... this one in the semiconductor industry: In the conventional Bayer color mosaic filter, Sony suggests to replace every second green pixel by an emerald one. They call it "RGBE filter" and claim that "... colour reproduction errors have been halved ..." (1). See next figure.


    fig.3.3-c: RGBE filter (45 kByte)

Carrying this principle to the extremes, we can think of image acquisition and/or image rendering processes that use a complete spectrum of, say, 20 monochromatic colors. It would need expensive devices and inks; but the advantages would include:
* maximum gamuts (whatever can be seen can be reproduced -- no clipping and no compression);
* color profiling would be rendered obsolete (or replaced by one simple spectral characteristics per device);
* meaningful and safe archives of precious old colored originals could be installed;
* metamerism (para. 3.4, metamerism) would no more be an issue.
* Using this principle only in image acquisition devices (e.g.scanners) would at least enable the use of "compression" instead of "clipping".




Link List and Literature
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Subject used in source
chromaticity diagram with gamuts fig. 3.3-a Adobe
"The Kiss" by Gustav Klimt fig. 3.3-b Postcard Book by Benedikt Taschen Verlag GmbH, Koeln, 1992
RGBE filter text reference (1) "Opto & Laser Europe" (optics.org), September 2003, p.17
RGBE filter arrangement fig. 3.3-c optics.org: emeraldpixels


  Continued: 3.4 Metamerism     Contents of entire essay     Contents of entire web site

Last modified Sept. 12th, 2003; 23:37