Two approaches of gamut mapping are presented in this paper. They both start with normalising the lightness ranges of both gamuts to be in the range between 0 and 100 range, which in effect is uniform, linear lightness compression. The first GMA then compresses colours towards the lightness axis along lines of constant lightness and hue angle (Figure 1a). Note, that the rate of compression is determined independently along each individual line, which ensures that the amount of compression used for fitting the original gamut into the reproduction gamut in a given region of colour space is as small as possible. However, this approach was abandoned by the author as it results in potentially large variations of the rate of compression between lightness levels.
The second compression method is defined in terms of spherical coordinates,
which are calculated as follows:
The formulæ shown above are the ones given in the paper, however,
they would not give the desired data, as they take L*=0 to be the centre.
To give the correct angles and distance, L* should be changed to (L*-50)
in the above equations (the result of this is shown in the above illustration).
Compression is then carried out towards the centre of the lightness
axis (L*=50), whereby the rate of compression is again determined independently
along each individual line (Figure 1b). This compression, which is carried
out only on the distance from the centre (r) uses the following formula:
Here the indices pr and or represent proof and original respectively.
Note, that the gamut of the original image is used instead of the gamut
of the original medium, which, as has already been mentioned, has the advantage
of compressing colours only where this is actually needed.
