Color matching

 Consider a bipartite field subtending an angle (<) of 2⁰ at a viewer's eye. The entire field is viewed against a dark, neutral surround. The field contains the test color on left and an adjustable mixture of 3 suitably chosen primary colors on the right  as shown in Figure (2.7).

Figure (2.7) : 2⁰ bipartial field at view's eye

 It is found that most test colors can be matched by a proper mixture of 3 primary colors as long as the primary colors are independent. The primary colors are usually chosen as red, green & blue or red, green & violet.

The “tristimulus values” of a test color are the amount of 3 primary colors required to give a match by additive mixture.They are unique within an accuracy of the experiment.

Much of colorimetry is based on experimental results as well as rules attributed to Grassman. 

Two important rules that are valid over a large range of observing conditions are “linearity “ and “additivity”.  They state that,

1) The color match between any two color stimuli holds even if the intensities of the stimuli are increased or decreased by the same multiplying factor, as long as their relative spectral distributions remain unchanged.

 As an example, if stimuli  and  match, and stimuli  and  also match, then additive mixtures  and will also match.

         2)  Another consequence of the above rules of Grassman trichromacy is that any four colors cannot be linearly independent. This implies tristimulus value of one of the 4 colors can be expressed as linear combination of tristimulus values of remaining 3 colors.. That is, any color C is specified by its projection on 3-axes R, G, B corresponding to chosen set of primaries. This is shown in Figure 2.8

  

Figure( 2.8) R,G,B tristimulus space. A color C is specified by a vector in three-dimensional space with components R,G and B (tristimulus values.)