1. CARISMA - a slightly modified version of the algorithm proposed in (CARISMA, 1992), which has the following stages:

(1) Map the white and black points of the two media onto each other and then scale lightness between them linearly.
 

(2) Determine the hue shift of the six primary and secondary colours between the two gamuts and translate the original mediumís hues half-way towards the reproduction mediumís hues (Figure 1). The purpose of this hue shift is to move colours into parts of colour space where there is more chroma available. Note, that the impact of this hue shift in terms of colour difference is chroma-dependent - colours of low chroma are affected only slightly and the effect is larger for more chromatic colours.

(3) Perform additional compression of L* and C* depending on the characteristics of the gamut boundaries of the two media at the hue angles of the primary and secondary colours of the original medium and their corresponding hue angles obtained after the hue shift on the reproduction medium:

(a) Define the cusp at each of these hue angles. After this there are three possible cases for which different mappings are used:
 

(b) Case 1: If the original gamut completely encloses the reproduction gamut and the intersection of the line going through the two cusps with the lightness axis is within the lightness range of the reproduction gamut then map towards Ea (Figure 2a). Case 2: If it is not within that range then map towards the point (Ea) on the lightness axis, which has the same lightness as the reproduction gamutís cusp (Figure 2b). In both these cases compression along a given line is determined using the following equation:
 

whereby the d values are distances from Ea.

Case 3: Otherwise, if the reproduction gamut is not enclosed by the original gamut, map towards Ea on the C* axis, which has half the chroma of the reproduction cusp.

Compression along a given line is determined using the following equation:
 

whereby the d values are distances from Ea (Figure 2c).

Then, for a given colour, calculate the gamut-mapped reproduction with the methods used for its neighbouring primary and secondary colours and interpolate between them using the angular differences between the given colour and the closest primary and secondary colour as weights. That is, if the two angular differences are *a1 and *a2 and the two corresponding gamut mapped lightnesses are L*1 and L*2 then the resulting L* is calculated using the following formula:
 

whereby a* and b* are interpolated analogously.

2. GCUSP - This new method was intended as a direct implementation of the results of (Morovic and Luo, 1997a) and consists of an initial chroma-dependent lightness compression followed by CUSP mapping. The degree of lightness compression is calculated using the following equation:
 

Full lightness compression (pC=1) is applied to the achromatic axis and its degree is smoothly decreased as chroma increases.

3. CLLIN - In a given plane of constant hue angle the chroma range of the original gamut is fist compressed onto that of the reproduction and this is followed by the mapping of the original lightness range onto the reproduction lightness range for each individual chroma level. Note that this algorithm was also implemented in LLAB (Luo and Morovic, 1996)

4. TRIA - The gamut boundary in a given plane of hue angle is reduced to a triangle whereby each point in the triangle can be represented as a linear combination of two vectors, which are determined by the vertices of the triangle. Gamut mapping is done by calculating the scalars of linear combination from the originalís vectors and applying these to the reproductionís vectors. This mapping results in the original cusp being reproduced as the reproduction cusp and the relationship between original and reproduction colours being monotonic.

These algorithms were evaluated alongside the LLIN and SLIN algorithms from Morovic and Luo (1997a) and the results suggested that the CARISMA, GCUSP and CLLIN algorithms perform significantly better than the other methods. Again the experimental setup was similar to that of the previous study and there were significant differences between the original and reproduction gamuts.