The Gamut
Aug 5th, 2007 by Leo A. Geis
Roses are orange,
Violets are pink.
My monitor’s crazy,
And my prints stink!
This post is dedicated to my friends Josh and Marc, who are considering conversion to a color-managed workflow at their office. An understanding of Color Theory is indispensable, and a properly functioning Color Management System (CMS) is a gift from God.
The fundamental organization of a CMS is a “Gamut,” also called a “color space.” A Gamut is a three-dimensional volume of colors that represent the entire set of colors that either:
- We use as a reference volume, or
- A device, such as a monitor or printer, can produce.
A reference volume is called a “Working Space” or “Device-Independent Space” and functions strictly as a 3D playing field. The Gamut produced by a monitor or printer is called a “profile,” or “Device-Dependent Space” and simply describes the colorimetric capacity of a device.
To describe the three dimensions of color we generally use a 3-axis system and simply label the axes differently.
The following graphic (click the icon to view the full-sized image) is a screen capture of Norman Koren’s invaluable GamutVision program, and shows a representative L*a*b* Color Space positioned upon the classic X, Y, and Z axes:
The L*a*b* Gamut uses the letter “L*” to identify what we might normally refer to as the “Z” axis, which protrudes orthogonally from the origin (0, 0) in a Cartesian Coordinate System, but in this case it represents Luminosity. The “a*” axis describes Hue from green to magenta, and the “b*” axis describes Hue from yellow to blue. The asterisk is used simply to distinguish the CIE (an international color committee) L*a*b* from a previous Lab system, but you may see CIE L*a*b* system also referred to as “CIELAB.”
This color wheel may help visualize why one L*a*b* axis would be blue-yellow, and other green-magenta. Those two axes will form right angles if graphed upon the color wheel plane.
CIELAB is formulated to describe human vision. Since you have already familiarized yourself with my Gamma post, you know that this will somehow involve a linear nature and is therefore distinguished from our Gamma-manipulated colors during image processing. That’s not particularly important to know, I suppose. CIELAB is predicated on a color temperature of 5000K (though it doesn’t act exactly like light at 5000K), which isn’t really important to know right now either. Sorry.
Another type of Gamut is based not upon L*, a*, or b*, but upon the Primary Colors: R, G, and B. These are usually referred to as “tristimulus models” because “tristimulus” is such an impressive word, what with multisyllabic architecture and balletic meter and all. R, G, and B are plotted on an x, y Cartesian Coordinate system, and the z axis is used as a Luminance axis…however, it is given the letter “Y” as an identifier as well, which must be converted to the letter “Z” if you are trying to not appear impaired:
Arresting Officer: Can you walk a straight line for me?
Subject: Certainly.
Arresting Officer: Can you touch your nose with your index fingers, eyes closed, quickly?
Subject: That’s easy.
Arresting Officer: Can you explain the difference between Absolute and Relative Colorimetric conversions of a 16-bit working space and the factory canned profile of an HP2500CP LFP using UV inks and C8316A media, ambient 1750 lux D55, no allowance for metamerism, using your body to spell out the words like those guys that sang “YMCA?”
Subject: Shoot me now.
At this point, it is necessary to understand why I would add the word “normalized” to my description of human vision. The fact is that human visual acuity is wildly variable, and is dependent upon everything from various pathologies (such as diabetes, dyschromatopsia/color blindness, et. al.) to cognitive fatigue. The same wild variability is true of monitors and printers: Manufacturing tolerances, differences in ink formulations and media, and even the light under which you view your monitor or print have a drastic influence on what you perceive. These very issues mandate digital color management.
Incidentally, constructing a variety of separate luminance specifications for colors has certain advantages in perceptual calculations because of the way humans see. You know, it really is all about us!
A perfect monitor would transduce linearly, meaning that there would be no variance of output values from input values. If a pixel was instructed to radiate 116/0/0 (pure red at a luminance of 116), it would do so-not 114/8/3 or 121/0/16. Unfortunately, guns in CRT’s and crystals in LCD’s are imperfect-a bit recalictrant, in fact, and do not do exactly what they are told. Nor do printer inks, since the ink dyes, pigments, and vehicles vary, nozzles vary, and even the algorithms that convert your RGB file into a CMYK (or CPCMPMYRGB if you’ve got a more sophisticated inking system) don’t all work the same.
In short, the digital realm is an orchestra, and it needs a conductor to get everyone in key and on tempo. This will mean something to Josh, who is a pianist. I don’t know what Marc does for fun…and I couldn’t think of a good analogy for a mad scientist anyway…perhaps something to do with FrankenGerbil?
A CMS is that conductor.
Let’s take a look at two device-independent working Gamuts (click on the thumbnail for a larger image):
Note that the aRGB Gamut (in wireframe) exceeds the sRGB Gamut (solid). The numbers to the lower right of the display graphic are their relative volumes. The sRGB Gamut was produced jointly by Microsoft and HP as sort of a “lowest common denominator” Gamut early in the digital imaging timeline, but it is not without merit today.
The most saturated colors available in each luminosity level lie on the outside skin of the Gamut. Thus, we can determine that aRGB offers significantly more saturation potential than sRGB. However, the matter is compounded by perceptual realities and the linear nature of the color spaces. You know, life just can’t be easy, can it? The functional manifestation of the differences between these two working spaces is significant and can be observed by preparing a nicely saturated image in aRGB then displaying it in sRGB (say, within an e-mail or web page, inside of .html). You’ll witness a marked desaturation of the aRGB image when it is so displayed. If you prepare the same image and save it as sRGB, you’ll probably not see much if any difference on your monitor during image preparation, and it won’t desaturate at all when you display it within .html. This is why images prepared for monitor display should be prepared in sRGB.
Finally, let’s take a look at a device-dependent profile-that of a large format printer (Epson 9800) using branded inks and a high grade photographic media-Crane Museo (click on the thumbnail for a larger image):
The first difference you’ll notice is that the Gamut of the printer-ink-media combination (the solid shape) is, as is typical, much smaller than the aRGB Color Space. Prints rely upon media brightness, ink performance and ambient light, so they don’t have the gamut capacity in low or high luminance levels that working spaces might allow us to work in-thus, the Gamuts are constricted toward the luminance margins. If you’re extremely critical, you’ll notice too that the white point of a printer profile doesn’t perfectly coincide with working space white-because your media isn’t perfectly white. The same is true with the black point-your black ink isn’t perfectly black, so the effective luminance axis of the printer gamut is actually offset and meanders up through the gamut…a bit like a worm. Pretty cool, eh?
I’ll threaten right now that we’re going to have to develop an understanding of saturation and how one Gamut might be mapped to another. At that point, you’ll have a fairly comprehensive understanding of color management other than how various software actually applies CMS elements. We’ll also have to discover why black ink is necessary in the printing process if all the other inks are subtractive, and then you’ll never speak with me again.
For the time being, we need to reinforce and supplement what has been outlined above. To do that, I’d respectfully recommend that you visit Cambridge in Colour’s ColorSpaces and sRGB vs. AdobeRGB tutorials. There’s no sense in my replicating much of this material, particularly when Sean does a better job with it.
Norman Koren offers Gamutvision for under $100. It’s the Gamut and remapping visualization application I’ve used to produce the preceding graphics. It is more advanced than Colorthink but does not provide tristimulus mapping. We’ll explore it in subsequent posts on more advanced color topics. It is a superb learning and process control tool.
X-Rite used to have a superb Flash-based tutorial series on their website. I love their gear.
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