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					              Evaluation of a Colour Gamut Mapping Algorithm

                       Lindsay MacDonald, Ján Morovic and Kaida Xiao
                      Colour & Imaging Institute, University of Derby, UK

Various methods of colour gamut compression have been proposed1, from the basic clipping of
colours to the nearest point on the gamut boundary to complex transformations of colour space in
which the lightness, chroma and in some cases also hue are modified. One of the problems with
many previous algorithms, is that they attempt to map all colours in the lightness-chroma (L-C)
plane at each hue toward a single convergence point, or ‘centre of gravity’, based on the co-
ordinates of the cusps (points of maximum chroma) of the original and reproduction gamuts. An
example is the SLIN algorithm, in which colours are mapped toward the point L=50 on the
lightness axis. Different rules may be employed for different cases (e.g. the relative lightness and
chroma of the two cusp points), and the transformations may be non-linear, but usually all the
points in the plane are governed by a single mapping formula. Such methods may result in
unnecessarily large changes in the lightness of colours at the extremities of the lightness axis
(notably in light yellow and dark blue-violet hues), and hence in significant changes to the overall
image appearance.
A new topographic gamut mapping algorithm has been developed2, which transforms values from
a source colour space into a destination colour space, preserving the relationships between source
and destination reversibly in a perceptually uniform colour space. Hue angle is assumed to be
invariant, so that the transformation maps pixel values within the lightness-chroma plane. The
algorithm is executed in four steps: (1) construct the boundary of a ‘core gamut’, within which no
colours are altered; (2) define a distance metric along both source and core gamut boundaries; (3)
construct a set of mapping chords, connecting corresponding points; and (4) perform gamut
mapping along the chords, with a ‘soft-clip’ function.
The core gamut boundary in the new algorithm is defined by a white point LW of the cusp with the
highest lightness over all hue angles (normally yellow), and by a black point LB of the lowest
lightness cusp (normally blue). Its width is determined by the ratio of the chromas of the cusps of
the destination and source gamuts, as shown in Fig. 1.

                                                                        Upper region

                 Lightness L

                                    Core gamut

                                                                        Lower region
                               0                                   Chroma C

              Figure 1 Construction of core gamut boundary and mapping chords.

Mapping chords are constructed to join corresponding points at equal intervals along the source
and core gamut boundaries. Upper and lower regions are constructed above and below a
horizontal chord passing through the core gamut cusp of lightness LM, as shown in Fig. 1. Points
outside the core gamut boundary are mapped along the chord using a ‘soft clip’ mapping function.

                                       Abstract submitted to AIC’2001
Evaluation of a Colour Gamut Mapping Algorithm                                               Page 2

Two versions of the topographic gamut mapping algorithm (TOPO) were evaluated. The first
(V2.1) used real prints produced by an ink-jet printer, whereas the second (V3.3) used ‘virtual
prints’ simulated on a CRT display. Test images were converted into the CAM97s2 colour
appearance space3, and the gamut mapping performed in the perceptual dimensions of lightness
(J) and chroma (C). The source device was a Barco Calibrator V monitor, characterised by the
Berns GOG model4. The reproduction device was a Hewlett Packard 895c ink-jet printer. For
comparison of the performance of the TOPO algorithm, three other algorithms were also applied
to each test image, using the same gamut boundary data:
   MDE         Minimum ΔECMC clipping to gamut boundary, preserving hue (in J-C plane).
   LLIN        Linear compression of lightness and chroma.
   GCUSP       Chroma-dependent lightness compression and linear compression to cusp.
The algorithms were evaluated by a simultaneous pair-comparison technique. For the first phase
the source image was displayed on the CRT with simulated D65 white point and the two physical
ink-jet prints were placed in a Verivide viewing booth under a D65 light source. For the second
phase the source image was displayed together with the two ‘virtual prints’ on the CRT, and the
experimental process was facilitated by a software framework that enabled the observer to select
the preferred image through a graphic user interface and automatically calculated the z-scores at
the end of the session. Five test images were used in the first phase and nine in the second phase,
four of which were common to both phases. Twelve observers took part in the experiment in the
first phase and twenty-one in the second phase, with each observer required to make 4C2=6 pair-
                                                                  Final Result
wise comparisons per image.



      Figure 2 Overall z-scores                            1
                                                 Z Score

      for the four algorithms tested                            TOPO GCUSP   MDE   LLIN
      in Phase 2 (virtual prints).                         -1




The matrices of comparison results were averaged over all observers and transformed into z-
scores. Results for the four algorithms across all images from the second phase experiments are
shown in Figure 2. TOPO (V3.3) and MDE were ranked highest overall and GCUSP and LLIN
were ranked lowest. The high ranking of the simple MDE algorithm was apparently due to its
maximisation of chroma, which for the majority of images was preferred by observers, even
though in some cases it led to significant loss of tonal detail in high chroma regions.
This paper will compare the two evaluation techniques, i.e. using real and virtual prints, based on
the results obtained for the three algorithms and four test images in common across the two
experimental phases. Analysis will indicate the conditions under which the very convenient
‘virtual print’ technique gives valid results and how it might be further developed for other colour
image reproduction media.

1. J. Morovic and M.R. Luo, Developing Algorithms for Universal Colour Gamut Mapping,
   Colour Imaging: Vision and Technology, Ed. L.W. MacDonald and M.R. Luo, John Wiley &
   Sons, pp. 253-282 (1999)
2. L.W. MacDonald, J. Morovic and K. Xiao, A Topographic Gamut Mapping Algorithm based
   on Experimental Observer Data, Proc. IS&T/SID 8th Color Imaging Conf., pp. 311-317
3. C. Li, M.R. Luo and R.W.G. Hunt, The CAM97s2 model, Proc. IS&T/SID 7th Color Imaging
   Conf., pp. 262-263 (1999)
4. R.S. Berns, Methods for characterizing CRT displays, Displays, 16, 4, pp. 173-182 (1996)

                                    Abstract submitted to AIC’2001