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July 11th, 2011, 07:08 PM
 Doug Kerr Senior Member Join Date: May 2006 Location: Alamogordo, New Mexico, USA Posts: 8,506
The two meanings of "color space"

The term "color space" has two meanings, one that is rooted in basic mathematical terminology, from "way back", and one more recent. We mostly only see it used in the "more recent" way.

But often in my technical discussions I have to use the term with its original meaning, so I thought I would clear the air on that.

The term color space in its original meaning is a particularization of the concept of a number space. A number space refers to the entire range, or collection, of numbers that can be represented by a particular number "format" or a particular phenomenon with a numerical implication .

For example, the number space of a 6-digit decimal number (without any factions) comprises all the integers from 0 through 99999. The number space of a 5-digit binary numbers comprises all the numbers from 00000 through 11111.

We don't have to be limited to discrete numbers. The number space of the reading of a 1" micrometer is (in inches) the number line 0-1.

We can get into more than one dimension. For example, the number space of the expression x, y, which represents the coordinates of a point on an 8.5" x 11.0" page, is (in inches) the two-dimensional space from 0,0 to 8.5,11.0; that means any combination where x is in the range 0 to 8.5 and y is in the range 0 to 11.0..

A related concept is a code space. That refers to all the coded values that are allowed in some coding system. For example in ASCII, its code space runs from 0000000 through 1111111.

But the code space of a bank account number system, with a check digit, is not all the possible numeric values - just the ones with a valid check digit (just about 1/10 of all the possible values). This is in fact described as a "sparse number space".

Now, let's consider color description systems (to use a cagey name). One type of color description system is what we call "RGB". Its color space is defined as the range of all permissible color descriptions. Thus, this is the three-dimensional space (in the mathematical sense) bounded by the planes R=0 and R=255, the planes G=0 and G=255, and the planes B=0 and B=255.

Said in a less geometrical way, the color space of this system is all the combinations of values of R, G, and B for which R is in the range 0 to 255, G is in the range 0 to 255, and B is in the range 0 to 255.

Now, in fairly recent times, a quite different meaning of color space has come into use - the one that we commonly see. Color space in that sense means "a specific color description system following a particular color model (coordinate scheme) with the basis for determining the coordinate values completely specified". Thus, sRGB (to be precise, sRGB per a particular specification) is a color space, as is the CIE XYZ color coordinate system.

Now that we know that, we can be not confused by a silly-sounding conversation like this:

"Say, what is the color space of the sRGB color space?"

"Well, the color space of the sRGB color space is R=1 to 255, G=0 to 255, B=0 to 255."

A matter related to color space in the first meaning is the matter of gamut. Gamut refers to the range of colors that can be represented over the color space (in the first sense) of some particular color space (in the second sense). And of course we have to use some particular color space (in the second sense) to describe that.

One choice is to use the color space itself, but that doesn't tell us much.

For example, we can legitimately say that the gamut of the sRGB color space, described in terms of the sRBG color space, is R=1 to 255, B=0 to 255, B =0 to 255. No kidding.

Best regards,

Doug

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