CIE
Division 8 - TC8-03: Survey of Gamut Mapping Papers
Granger (1995)
In this paper the ATD colour appearance model (Guth, 1989). Its properties
are exploited by the gamut compression method as it makes the largest changes
in regions which would be compressed by the visual system anyway. In the
words of the author, "pixel values should be distorted in regions where
the eye compresses the response to the input stimulus". As the colour differences
are relatively much smaller away from the neutral axis, it is possible
to make heavier compression in these regions, which is implemented in the
following way:
First it is necessary to transform all colours into the ATD colour space.
To do this, "Meta RGB" is calculated from XYZ (inverse transformation is
also shown):
The RGB values are then transformed into ATD itself:
There is also a chromaticity diagram associated with the space:
Finally, saturation is defined as C = (d2 + t2)1/2.
Saturation Compression
It was suggested by Guth (1989) that the adaptation for ATD channels is
of the following nature (V is visual sensation, S is the stimulus and K1,
K2 are the modelís parameters):
Based on the same work, a Taylor series expanded to third order
was proposed as the compression function to be used (see following formula):
Here the second order term is the "compression cost factor", which
determines how much a given region of the colour space can be compressed.
Figure 1 Adaptive compression of chroma for a particular hue angle (The
indices o and r signify original and reproduction respectively).
Note, that the compression depends on the hue angle and Figure 1 shows
the type of compression obtained with the above formula.
Lightness Compression
The same strategy is adopted for lightness (A) as was used for saturation.
However, as the visual system is less sensitive to dark colours, the mapping
is carried out on darkness, which is defined as:
D = 1 - A
Even after darkness and chroma are compressed, there could be some
out-of-gamut colours, which will be mapped in the following way.
Out-of-Gamut Colour Mapping
Out-of-gamut colours are treated depending on which extreme of the lightness
scale they are at. For light colours A and hue are maintained and chroma
is clipped to the boundary of the gamut. The chroma of dark colours is
reduced to a percentage of the maximum chroma (for a given hue angle),
depending on the darkness of the colour (Figure 2).
Figure 2 Mapping of dark out-of-gamut colours.
Last updated: 17 August 1999 by Jan
Morovic