## CIE RGB Color Space

CIE RGB color space is one of many RGB color spaces. It is based on the series of experiments conducted on human eye, to determine the colors in human vision. Eye reacts to the three primaries i.e. Red, Green and Blue separately. Colors we see are sensations these wavelengths in the eye. Primaries standardized by the CIE in 1931

- Red (R): 700 nm
- Green (G): 546.1 nm
- Blue (B): 435.8 nm

In the above Chromaticity diagram, white is at the **center**. Edges are color at the maximum saturation. The triangle is known as CIE RGB. Chromaticity diagram are three dimensional. Above diagram is the cross section of the below diagram

## CIE XYZ Color Space

This color space is based on the results of the CIE RGB version of the human eye. Colored area in above chromaticity diagram is the CIE XYZ 1931 color space. This area is the mathematical limit of human eye with respect to color. XYZ primaries are hypothetical because they do not correspond to any real light wavelengths. It is additive scheme color spaces, since it define the amounts of three stimuli provided to the eye (the three primaries).

XYZ system is based on the color matching experiments. X, Y and Z are extrapolations of RGB created mathematically to avoid negative numbers and are called Tristimulus values. X-value in this model represents approximately the red/green part of a color. Y-value represents approximately the lightness and the Z-value corresponds roughly to the blue/yellow part.

X, Y and Z, also color value can also be specified in proportions. These are written in lowercase and called **x**, **y** and **z** and they are calculated as follows:

x = X/(X+Y+Z) y = Y/(X+Y+Z) z = Z/(X+Y+Z)

Derived color space specified by x, y, and Y is known as the **CIE xyY** color space and is widely used to specify colors in practice. The X and Z tristimulus values can be calculated back from the chromaticity values x and y and the Y tristimulus value:

X = (Y/y)x Z = (Y/y)*(1−x−y)

Below figure shows approximate colors assigned to areas on the chromaticity diagram.

## Color Space Conversion

CIE XYZ is used for transforming coordinate values in one color space (one set of primaries) to corresponding values in another color space (another set of primaries). If the primaries of the first color space are called R, G, and B, and the corresponding coordinate values are called R, G, and B. Assume the primaries of the second color space are X, Y, and Z with the corresponding coordinate values called X, Y, and Z. Then the equation to convert the color space is given by

**m** define the transformation, its values depend on the chromaticities of the primaries of the **RGB** and **XYZ** color spaces. X,Y,Z,R,G and B color primaries are linear.