What is Color Space and the Tristimulus Values XYZ?

Color Space

If a color model is a language, then think of color spaces as variations in a language, like British English versus American English.

Fun fact: The word ‘color’ is spelled ‘colour’ in British English.

Maybe we need a simpler analogy. How about ice cream?

Think of the color model as the ice cream. Ice cream is only ice cream if it has certain essential ingredients – milk, cream, sugar, etc., – and if it’s served a certain way at a certain temperature. It’s the rules you lay down in the beginning. Once you decide you’re going to eat ice cream, you don’t want pasta.

Once you’ve decided to eat ice cream you head to your local ice cream parlor. Let’s say they have 31 flavors. That entire range of flavors is the color space. If you go to the same brand in another part of town they should also theoretically have the exact same 31 flavors.

So, technically, Rec. 709 (a color space) from one camera should be the same as Rec. 709 from another camera. It helps keep things consistent so displays and TVs can show a uniform image to everyone.

That’s approximately how color spaces work.

A Color Space is a mathematical model that maps the colors that can be reproduced by a device to a standard color model, usually the RGB model.

It’s a complex thing that goes underneath the hood.

Another way to think about color spaces is its all the possible colors possible in a given system. One good system to go by is our own eyes.

CIE XYZ 1931

The eye is as good as any reference when building a color space. Why? Even though we have displays that claim to show a billion colors, the eye can never see all of those colors.

One of the first mathematically determined color spaces is the CIE XYZ 1931 color space, created by CIE (International Commission on Illumination) in 1931.

It utilizes three main concepts –

• It is based on and derived from the CIE RGB model, which was formed from actual experiments
• It assumes Y to represent luminosity, and Cb and Cr to shoulder the burden of representing all colors. It is sometimes referred to as the CIE xyY color space
• XYZ is not RGB. XYZ are extrapolations of RGB created mathematically to avoid negative numbers (In 1931 there weren’t any computers) and are called Tristimulus values.

It is not critical to understand how the values of the CIE XYZ color space are derived, but the following information is good to know:

• A color space is actually a 3D image. Think of it as a bag containing color goodies.
• The two-dimensional image seen here is only a cross-section of the entire color space.

• It is called a Chromacity diagram.
• The diagram represents all of the chromaticities visible to the average person. The color region is called the Gamut of human vision.
• The curved edge is called the spectral locus and corresponds to monochromatic light, with wavelengths listed in nanometers.
• The straight edge is called the line of purples. These colors have no counterpart in monochromatic light.
• White is at the center (E).
• There are no three points within the gamut that form a triangle that includes the entire gamut of human vision; or more simply, the gamut of human vision is not a triangle.

Other color spaces are also represented with similar chromacity diagrams that make it slightly easier to visualize them in comparison with each other.

There are color spaces ‘smaller’ and ‘larger‘ in volume than CIE XYZ. Therefore, a two-dimensional diagram shouldn’t be used exclusively to compare various color spaces. It is possible for one color space to have lesser colors than another but still have colors that the “larger” color space doesn’t have.

Common color spaces are:

• PAL – SD PAL TV and NTSC – SD NTSC TV
• sRGB – computer monitors
• Rec. 709 (Officially ITU-R Recommendation BT.709) – HDTV and online video
• Rec. 2020
• DCI P3 – cinema projectors and DCI XYZ – cinema DCP
• Display P3 – a variant of DCI P3 developed by Apple for their devices

Your takeaway from this should be the understanding that a color space is a theoretical space. It is the limit you are imposing on a particular device.

For beginner filmmakers, understanding color spaces helps in:

• Shooting: Knowing the color space of your camera (like Rec. 709 or DCI-P3) tells you what colors it can record.
• Editing and color grading: When you edit or grade your footage, working in the right color space ensures that the colors you see on your screen match what was recorded.
• Distribution: Different platforms (TV, streaming, cinema) may require different color spaces, so it’s important to know how your film will be viewed.

If the color you want isn’t in the color space, you’re not going to get it. Theoretically at least.

I hope this simple explanation has been helpful.