Liang (1994)

The aim of this DuPont patent is to match the responses of two different printers to RGB data. To achieve this, a number of patches with known RGB values are first printed on both printers. These are then measured using a colorimeter and LUTs are generated to relate input values to measured values. Colours from the overlap of the two gamuts are mapped by finding the RGB value from the second printerís LUT, which has the CIELAB coordinates of the RGB value chosen from the first printerís LUT. The technique chosen for mapping colours from the first gamut, which are outside of the second gamut is the following:
 

• find the two (or more) colours closest to the out of gamut colour, which have a corresponding colour in the output gamut. Find a colour in the output gamut for the out-of-gamut colour by extrapolating using the two (or more) colours inside the gamut. The extrapolation is carried out in the target printerís device gamut (it is carried out for R, G and B separately) and it can be linear or of a higher order if necessary. The linear extrapolation is shown graphically in Figure 1.
• if the extrapolated value exceeds 255, it is set to 255
• if the slope of the extrapolating line is too small (the out of gamut colours are greatly compressed), a point which is further from the out-of-gamut point is selected and the colours in between are remapped

Mapping the out-of-gamut colours as proposed in this patent would probably have unpredictable effects on its perceptual attributes, as the three device dependent coordinates are altered independently.