Diagonal color transform

Suppose that we have two different illuminants. Each illuminant defines a local coordinate system inside the three- dimensional space of receptors as shown in Figure 3.23. A diagonal transform, i.e. a simple scaling of each color channel, is not sufficient to align the coordinate systems defined by the two illuminants. A simple scaling of the color channels can only be used if the response functions of the sensor are sufficiently narrow band, i.e. they can be approximated by a delta function. 

Figure 3.23 Two different illuminants define two coordinate systems within the space of receptors. A simple diagonal transform, i.e. scaling of the color channels, is not sufficient to align the two coordinate systems.

In order to obtain an output image that is corrected for the color of the illuminant we only need to divide each channel by L,. The output image will then appear to have been taken under a white light. This can be done by applying a diagonal transform. Let S be a diagonal... 

We now have to determine a linear map that will transform the observed gamut of colors to the canonical gamut of colors. This map will simply be a diagonal 3x3 matrix of the form... 

Finlayson GD, Drew MS and Funt BV 1994a Color constancy generalized diagonal transforms suffice. Journal of the Optical Society of America A 11(11), 3011-3019. 

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