YES can also be obtained from XYZ by:
The gamut mapping is then carried out on the logarithms of these
coordinates:
The sign function returns either plus or minus depending on the
value of E or S. A, B and N are used to determine the range and domain
of E & S, whereby A results in scaling, B in offset and N prevents
determination errors by providing a non-zero cut off value. A similar transformation
can also be applied to Y, but this is considered by the author to be optional.
After the colours are divided into four quadrants, they are arranged according
to hue and lightness using the following correlation of hue:
To obtain the gamut boundary, four tables (one for each quadrant)
are set up, whereby the maximum values for |le| are stored for each combination
of H and Y and this is done for both source and destination gamuts. From
these, another set of four tables (F[H,Y]) can be determined, which contains
the factors by which the two gamuts differ:
F[H,Y]=max(0,Table[H,Y]-PrinterTable[H,Y])
Here Table[H,Y] represents the input and PrinterTable[H,Y] the output.
As all the values involved are logarithms, their difference represents
the factor by which the original values (E & S) differ. The gamut compression
can therefore be carried out as follows:
|leí|=max(0,|le|-F[H,Y])|lsí|=max(0,|ls|-F[H,Y])
Alternatively, the compression factor can be forced to be below
a chosen value (M):
|leí|=max(0,|le|-min(F[H,Y],M))|lsí|=max(0,|ls|-min(F[H,Y],M))
As can be seen, a non-uniform compression technique is used, since
the compression factors are determined depending on the hue angle and lightness.
After the compression, the |leí| & |lsí| values are converted back
to le & ls (their sign will be determined by their source quadrant)
and then to E & S. The method described above uses a cylindrical method
of compression i.e. hue and lightness are constant and compression is only
applied to chroma. The patent also discusses a spherical implementation
of the linear compression described above, which is analogous.
This is certainly one of the more useful patents as it describes a computationally
effective way of implementing linear chroma compression, or linear compression
towards the centre. However, in terms of actual gamut mapping approaches
it does not propose any new solutions.
