# Gamut mapping

Applet: Nora Willett
Text: Marc Levoy

The Chromaticity diagram is a two-variable system for specifying the hue and saturation of colors (together called chroma) producible using a particular set of primaries. It is derived from the 3D colorspace defined by those primaries [link to Katie's threedgamut applet] by factoring out brightness as a variable. The XYZ chromaticity diagram is one such chromaticity diagram, defined by the CIE in 1931. While its primaries are physically unrealizable, they are standardized. This allows colorists in different industries to talk precisely to each other about colors.

One of the things colorists talk about is - what is the range of colors displayable on a particular computer screen or reproducible on paper by a particular printer? This range is called the gamut of that display or printer. Another question they ask is - if the colors I want to reproduce lie outside the gamut of my display or printer, how should I modify them to make them displayable, without excessively distorting the overall design of my image. The modification process is called gamut mapping, and the alternative strategies for avoiding color distortion (there are several of them) during gamut mapping are called rendering intents. In this applet we explore these concepts.

#### The XYZ chromaticity diagram

As explained in the preceeding applet, in the XYZ chromaticity diagram the locus of spectral colors sits in the all-positive octant. In the brightness-removed (i.e. projected) 2D version of this diagram, the axes are x and y, and the locus sits in the all-positive quadrant. In other words, the familiar horseshoe shape of the locus (plus the line of extra-spectral purples that connects its red and blue endpoints) lies entirely to the right of the y-axis and entirely above the x-axis. As already explained, the neutral point (doubly outlined white dot) lies at (x,y) = (1/3,1/3).

#### Gamuts of reproducible colors

Inside the locus of spectral colors is a triangle, labeled sRGB. sRGB is a standardized colorspace, based on three standardized primaries. The chromaticities of these primaries are given by the apices of the triangle (red, green, and blue dots), and the interior of the triangle represents all colors that can be reproduced using mixtures of the primaries. Note that the spectral power distribution of these primaries is not specified, only their chromaticities.

One could undoubtedly build a physical display device whose primaries exactly matched those of the sRGB colorspace, but most devices don't. To represent the gamut for a hypothetical display device, we've drawn a second triangle (purple dots) inside the sRGB triangle. The primaries of this hypothetic device are reddish, greenish, and blueish, like those of sRGB, but they are clearly less saturated, because they lie closer to the neutral point. If you click on one of the purple dots, you can move these primaries around, although we limit you to the interior of the sRGB gamut. We'll see shortly what this is good for.

On the left side of the applet is a radio button labeled NTSC Display. In 1953 the NTSC (National Television Standards Committee) defined a particular set of three primaries, hence a 3D colorspace, by which the R,G,B values of a color television signal could be interpreted. (These RGB values are actually converted to another system, YIQ, for transmission, then converted back to RGB for display.) The sRGB standard was developed after NTSC, and as you can see it has a slightly smaller gamut, especially in the greens. To the extent that manufacturers could build physical television sets whose primaries were as saturated as the apices of the NTSC triangle, these sets could display all colors in the NTSC gamut at full fidelity.

Below this is another radio button labeled Typical Printer. Its gamut has six apices, hence six primaries. As we discussed in the introductory applet, adding more primaries doesn't create a higher-dimensional colorspace, but it does allow you to create more saturated colors within the 3D colorspace humans can perceive. Modern offset printing consists of laying down dots of cyan (C), magenta (M), and yellow (Y) ink. Where the cyan and yellow dots coincide, their inks sit atop one another, hence their spectra mix subtractively, yielding green. Similarly, superpositions of cyan and magenta dots yield blue, and superpositions of magenta and yellow dots yield red. Thus, the printed page contains dots of cyan, magenta, yellow, red, green, and blue, which mix additively in your eye if you stand back far enough. This constitutes a six-primary system, denoted in the chromaticity diagram by a six-pointed figure. The mathematics that describe how CMY dots mix subtractively to produce CMYRGB dots, and how these mix additively in your eye, are called the Neugebauer equations.

Finally, we invite you to create your own hypothetical 3-primary, 4-primary, or 5-primary gamut, by clicking on the corresponding radio buttons, then dragging around the purple dots. By the way, if you're confused about how additive versus subtractive mixing works, then you're a candidate for our final applet on color.

#### Gamut mapping and rendering intents

In the top-left corner of the applet is a picture of a parrot. Actually, parrots don't look this bright; we've fiddled with his hairdo a bit to make his colors more saturated and to span more parts of the gamut. Superimposed on the picture is a grid of small white dots. The colors in the picture at each dot are denoted in the chromaticity diagram at right by the small white dots. If you click on a dot on the picture, the corresponding dot in the chromaticity diagram is highlighted, and vice versa - a visualization technique called brushing.

Click on the 3-primary gamut. Suppose this represented the gamut of your display device. Note that many of the parrot's colors lie outsite this gamut. To display the parrot on this device, you must modify these colors to like inside the device's gamut. This process is called gamut mapping. There are several reasonable strategies for performing this modification; these are called rendering intents. Four particular strategies were defined by the International Color Consortium (ICC), with the four names shown on the applet. Interestingly, these strategies were defined in prose only; see this web site to read these definitions, or this one. The actual implementation of each strategy was left to the software writer. Indeed, different vendors compete fiercely on the alleged quality of their gamut mapping techniques.

To see how these gamut mapping strategies compare, click on Absolute Colormetric and watch the animation. The intent of this gamut mapping strategy is to bring out-of-gamut colors back into gamut with the minimum possible change to them, and to leave in-gamut colors alone. We've interpreted this as projecting each out-of-gamut color perpendicularly onto the nearest edge of the gamut. Compare the Before and After pictures of the parrot. Only his face changed dramatically (those pesky out-of-gamut blues!). Note that his face both desaturates and turns slightly purple.

Now click on No Gamut Mapping, then Relative Colorimetric. The intent of this strategy is to bring out-of-gamut colors back into gamut by desaturating them, but trying hard not to change their hues. We've interpreted this as projecting each each-of-gamut color towards the neutral point until it falls within gamut. This makes a bigger change in the parrot's face than under Absolute Colorimetric, but at least it stays blue, rather than turning purple.

Now try Perceptual. The intent here is to bring out-of-gamut colors back into gamut, while minimizing changes in the relationships between different colors. We've interpreted this as projecting all colors proportionately towards the neutral point until every color lies within gamut. This dramatically desaturates everything, but the relationships between colors stay plausible. It's as if the parrot were being viewed through white fog (technically, fog whose color is equal to the device's white point).

Finally, try Saturation. It's like Perceptual, but the projection is not proportional. Instead, out-of-gamut colors are moved more than in-gamut colors. The effect is to keep highly saturated colors as saturated as possible. This strategy is commonly employed for corporate logos and similar graphics, but not for photographs. The most common strategy for photographs is Perceptual. In Photoshop, this is the default.

#### Some implementation details

The astute reader will notice that our locus of spectral colors is filled with color, even though most parts of the locus must certainly lie outside the gamut of the physical display they are looking at. Indeed, we should be displaying any colors there. However, we wanted to give you an intuition for which colors lie where in the locus, and we don't know the gamut of your display anyway, so we decided to fill the entire locus with color, even if they are less saturated than real near-spectral colors would be. In fact, we have desaturated these colors more than strictly necessary, to make sure the various triangles and dots we draw within the locus are clearly visible. As a result, the colors under the dots in the picture of the parrot don't exactly match the colors under the corresponding dots in the chromaticity diagram. In other words, it's a visualization, not an accurate depiction.

One more point. We've described gamut mapping as a projection in flatland, operating in the 2D xy chromaticity diagram. In reality it should be a projection in 3-space, operating in the 3D XYZ chromaticity diagram depicted in the preceeding applet. As discussed on this web page, it is possible for a dark color to lie within the gamut of a particular device, while a brighter color of the same chromaticity lies outside the gamut. However, this effect is relatively minor, and limiting ourselves to a two-dimensional view makes the story easier to tell.

### References

• Picture by: MrClean1982. <http://www.flickr.com/photos/23084352@N00/393367066>.