Canonical gamut

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... 

Figure 6.15 Two different views of the observed gamut of colors. If we assume that the canonical gamut is the unit cube and that the illuminant is given by [0.7, 0.5, 0.2]r, then the observed gamut will be the unit cube scaled by S(0.7, 0.5, 0.2).

Figure 6.16 Results obtained using Forsyth s gamut-constraint algorithm. The algorithm assumes a single illuminant for the entire image, so we cannot use this algorithm if multiple illuminants are present. For both images, the RGB cube was assumed to be the canonical gamut.

One can now use this set to additionally constrain the illuminant. The map we are looking for, which transforms the observed gamut to the canonical gamut, has to be a member of... 

The three-dimensional gamut-constraint method assumes that a canonical illuminant exists. The method first computes the convex hull TLC of the canonical illuminant. The points of the convex hull are then scaled using the set of image pixels. Here, the convex hull would be rescaled by the inverse of the two pixel colors cp and Cbg. The resulting hulls are then intersected and a vertex with the largest trace is selected from the hull. The following result would be obtained for the intersection of the maps Mn-... 

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