To achieve these aims, the following technique is proposed. Lightness is calculated using relative colorimetry (hence the white points of the two media are the same in terms of CIELAB) and the lightness ranges of the two gamuts are first mapped linearly onto each other so that the black of the originalís gamut is mapped slightly below the black of the reproduction gamut. Chroma is then non-linearly mapped along lines of constant hue and lightness (Figure 1).
What is later described as a soft clipping function (Hoshino and Berns, 1993) is introduced in this paper and is a non-linear compromise between a linear mapping and gamut clipping. This is done with a higher order function which is tangent to the y=x function near the grey axis and then diverges from it near the maximum reproduction chroma. The authors also point out that the soft clipping function could be made to be tangent to a function whose slope is greater than 1, so as to increase overall chroma, which can help to obtain more pleasing results in some cases.
A problem, which was identified by the authors is that the lines along
which the compression is carried out are not lines of constant hue, which
reduces the effectiveness of this approach.