Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

CIE Guidelines for Evaluation of Gamut Mapping Algorithms: Summary and Related Work (Pub. 156)

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_3

Definition

The CIE Guidelines for the Evaluation of Gamut Mapping Algorithms (referred to as Guidelines in the remainder of this entry) set out experimental conditions under which color gamut mapping algorithms are to be evaluated so that results can be compared and combined from separate experiments. The Guidelines were published [1] in 2004 by Division 8 of the CIE and cover a number of aspects of experimental evaluation, both mandatory and optional. They also include case studies for applying them to various color reproduction scenarios and a checklist that can be used to determine an experiment’s compliance with the Guidelines.

Overview

A color gamut mapping algorithm is that part of a color reproduction process, which ensures that colors from some original (source) are adapted to fit inside the color gamut available under reproduction (destination) conditions. A typical example is a color image viewed on an electronic display that is to be reproduced in print. Here, there are colors that a display can generate (e.g., bright greens), which cannot be matched in print, and a substitution of the out-of-gamut color by an in-gamut color needs to be made. Note that the converse – representing printed colors on a display – also requires gamut mapping, since some printable colors (e.g., cyans) are beyond the capabilities of displays, and that this is the case for the great majority of original–reproduction combinations.

Since gamut mapping can have different aims (e.g., resulting in most similar reproduction to the original or resulting in a most pleasing reproduction), since its performance cannot be measured, and since optimal performance cannot be known in absolute terms, determining how well a gamut mapping algorithm works or whether one algorithm outperforms another is a challenge. Reviewing the literature on this subject [2] prior to the Guidelines’ publication reveals a great variety of experimental methods and conditions used for comparing alternative gamut mapping algorithms that yielded incomparable but seemingly contradictory conclusions.

The Guidelines therefore set out recommendations about the following aspects of a gamut mapping algorithm’s evaluation: test images (and their exchange), original and reproduction media, viewing conditions, color measurement, gamut boundary description, a pair of reference gamut mapping algorithms, the color spaces in which they are to be applied, and the psychovisual experimental method to be used. In each of these sections, there are both obligatory aspects and recommended ones, and attention is also paid to how experimental details are to be reported. Finally, the Guidelines also show how they are to be applied for specific, typical workflows (Reference Output Medium Metric (ROMM) RGB to print, Cathode-Ray Tube (CRT) to print, and transparency to print), an appendix elaborates on some of the Guidelines’ sections, and a checklist is provided to determine an experiment’s compliance with the Guidelines.

Before proceeding to the specifics of experimental evaluation, the Guidelines specify the obligatory use of the “subjective accuracy” color reproduction intent, which is defined as aiming at “reproducing a given colour image in a way where the reproduction is as close to the original as possible, this similarity is determined psychophysically and the process has no image enhancing aims.” Evaluation of other reproduction intents is not discouraged, but subjective accuracy is mandatory.

Test images are specified first, with the one mandatory image, “Ski” (Fig. 1), made available as a physical transparency, in ROMM RGB and sRGB (i.e., two colorimetrically defined RGB color spaces) rendered color encodings, and as CIELAB version of these three cases. The Guidelines further specify the need to share with the CIE any other test images used in compliant experiments and detail how such sharing is to be done.
CIE Guidelines for Evaluation of Gamut Mapping Algorithms: Summary and Related Work (Pub. 156), Fig. 1

The obligatory “Ski” test image

Reproductions of the obligatory and other test images then need to be made on a combination of color reproduction media from among the following four types: reflective print, transparency, monitor, and virtual (i.e., wide gamut color spaces such as scRGB [3] or ROMM RGB [4]). Constraints are imposed on acceptable uniformity, repeatability, and viewing geometry-dependent characteristics of these media, and the Guidelines also specify which of the media’s aspects to report (including measured characterization data).

Given a set of chosen test images, rendered on one medium as originals and to be gamut mapped to another medium, the viewing conditions under which the media are to be viewed are specified next. Here, it is mandatory to report “chromaticity and luminance level of the white point, level and correlated colour temperature of the ambient illumination, light source colour rendering index and nature of field of view (proximal field, background, surround).” A recommendation is made about the original and reproduction images being the same size, the illumination having a color rendering index of at least 90, and the uniformity of illumination dropping off to no less than 75 % of central peak illumination. Control over the viewing environment needs to be exercised to exclude extraneous light sources as well as light reflected from objects in it, and specific border and surround characteristics are mandated. Specific luminance levels for different types of media, following ISO 3664 [5], also need to be ensured, and particular care is taken to define aspects of monitor to print matching, where three alternatives are offered for how the two media’s white points are to relate: an absolute colorimetric match at D65 chromaticity, an adherence to the per media specifications (i.e., D65 for monitor and D50 for print), or a D65 chromaticity match but at luminance levels as mandated per media.

In terms of color measurement, the requirement is to carry it out as closely to experimental viewing conditions as possible and to report specific aspects of measurement procedures according to details provided in Appendix B of the Guidelines. Gamut boundary computation and description is left up to the individual experimenter, with the only obligation being to report gamut boundaries in CIELAB.

A key aspect of the Guidelines, beyond providing a tractable basis for defining and reporting psychovisual experiments, is to make the inclusion of two gamut mapping algorithms mandatory in compliant experiments. The role of these algorithms is “to make it possible to reconcile the different interval scales used in different experiments.” In other words, they act as anchors based on which of the results of multiple experiments can be compared and combined.

The first algorithm is hue-angle preserving minimum ΔEab clipping (HPMINDE) in CIELAB. Here, colors from the intersection of the original and reproduction gamuts are kept unchanged, and original colors outside the reproduction gamut are mapped onto that point on the reproduction gamut which has the same hab as the original color and which, in that hab plane, has shortest Euclidean distance from the original color [6].

The second algorithm is chroma-dependent sigmoidal lightness mapping followed by knee scaling toward the cusp (SGCK), performed in CIELAB. Note that the use of CIELAB here is purely for experimental cross-referencing purposes and that other, more suitable color spaces for gamut mapping are recommended for use with algorithms whose performance is evaluated based on the Guidelines. The SGCK gamut compression algorithm combines the GCUSP [7] approach with sigmoidal lightness mapping and cusp knee scaling [8]. It keeps hab constant and uses an image-independent sigmoidal lightness scaling that is applied in a chroma-dependent way and a 90 % knee function chroma scaling toward the cusp.

Specifically, SGCK involves the following transformation for each original color:
  1. 1.

    Keep hab unchanged.

     
  2. 2.
    Map lightness as follows:
    $$ {L}_{\mathrm{r}}^{\ast }=\left(1-{p}_{\mathrm{C}}\right)\;{L}_{\mathrm{o}}^{\ast }+{p}_{\mathrm{C}}{L}_{\mathrm{s}}^{\ast } $$
    (1)
    where o refers to the original, r refers to the reproduction, and pC is a chroma-dependent weight computed from the original color’s C:
    $$ {p}_{\mathrm{C}}=1-{\left(\left({C}^{\ast 3}\right)/\left({C}^{\ast 3} + 5 \times {10}^5\right)\right)}^{1/2} $$
    (2)
    and where LS is the result of the original’s L o being mapped using the following sigmoidal function (Fig. 2), having x0 and ∑ parameters empirically derived for different levels of reproduction medium minimum L (e.g., for a minimum reproduction L of 15, x0 = 58.2 and ∑ = 35):
    $$ {S}_{\mathrm{i}} = {\displaystyle \sum_{n=0}^{n=i}\frac{1}{\sqrt{2\pi}\Sigma}{\mathrm{e}}^{-\frac{{\left(\frac{100n}{m}-{x}_0\right)}^2}{2{\Sigma}^2}}} $$
    (3)
    S i values generate using Function 3 for i∈[0, m] and then form a look-up table that is further scaled using the L ranges of the original and reproduction:
    $$ {S}_{\mathrm{LUT}}=\frac{\left({S}_{\mathrm{i}}- \min\ (S)\right)}{\left( \max (S)- \min (S)\right)}\left({L}_{\max\;\mathrm{r}}^{\ast }-{L}_{\min\;\mathrm{r}}^{\ast}\right)+{L}_{\min\;\mathrm{r}}^{\ast } $$
    (4)
    Finally, the L S value needed for Eq. 1 can be obtained by interpolating in the SLUT look-up table with an L o modified as follows:
    $$ L{*}_{{\mathrm{o}}^{\prime }}=100\;\left({L}_{\mathrm{o}}^{\ast }-{L}_{\min\;\mathrm{o}}^{\ast}\right)/\left({L}_{\max\;\mathrm{o}}^{*}-{L}_{\min\;\mathrm{o}}^{\ast}\right) $$
    (5)
     
  3. 3.
    The original’s C and Lr obtained from Eq. 1 are next mapped in a plane of constant hab toward the L of the cusp (the color with maximum C in the reproduction gamut at this hab) as follows:
    $$ {d}_{\mathrm{r}}=\left\{\begin{array}{c}\hfill {d}_{\mathrm{o}}; {d}_{\mathrm{o}}\le 0,9{d}_{\mathrm{gr}}\hfill \\ {}\hfill 0,9{d}_{\mathrm{gr}}+\left({d}_{\mathrm{o}}-0,9{d}_{\mathrm{gr}}\right)0.1{d}_{\mathrm{gr}}/\left({d}_{\mathrm{go}}-0,9{d}_{\mathrm{gr}}\right); {d}_{\mathrm{o}}>0,9 \times {d}_{\mathrm{gr}}\hfill \end{array}\right. $$
    (6)
    where g refers to gamut boundary, o and r to original and reproduction, and d to distance from the cusp’s L on the L axis (Fig. 3).
    CIE Guidelines for Evaluation of Gamut Mapping Algorithms: Summary and Related Work (Pub. 156), Fig. 2

    Sigmoidal function used for L mapping (for x0 = 58.2 and ∑ = 35)

    CIE Guidelines for Evaluation of Gamut Mapping Algorithms: Summary and Related Work (Pub. 156), Fig. 3

    L and C mapping toward the L of the cusp

     

Gamut mapping algorithms that are compared among themselves and versus HPMINDE and SGCK need to be described with sufficient detail for repeatability.

In terms of color spaces in which gamut mapping is to be performed, the Guidelines again only require the reporting of whichever space was used. A recommendation is made for isotropic color spaces that have greater hue uniformity than CIELAB (e.g., IPT [9],  CIECAM02).

Finally, the pair comparison, category judgment, and ranking methods are proposed as alternatives for how reproductions made using different gamut mapping algorithms are to be compared visually. Apart from the obligation to use at least 15 observers, there is an extensive list of experimental aspects that need to be reported, and Appendix C provides background on them.

To aid the application of the Guidelines, three common scenarios are described in more detail, and recommendations are made for what choices to make in terms of the Guidelines’ parts. The scenarios are ROMM to print, CRT to print, and transparency to print, and Appendix D includes a checklist that can be completed to test compliance with the Guidelines.

Future Directions

The Guidelines have been used extensively since their publication in 2004 to inform the design and execution of the experimental evaluation of gamut mapping algorithms. A notable aspect of these experiments is the use of greater numbers of test images, such as 15 [10], 20 [11], and even 250 [12], as compared to the previous trend of using around five, which has contributed to a general unreliability of results. The Guidelines have also been used by a large-scale evaluation of nine printer manufacturers’ products reported by Fukasawa et al. [13]. Since they were formulated close to 10 years ago, there are aspects of the Guidelines, e.g., their reference to CRTs and film transparencies and lack of reference to wide gamut displays, which would benefit from future revision. The Guidelines also prepared the ground for interrelating the results of multiple, compliant experiments, which too is yet to be implemented.

References

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Hewlett-Packard CompanySant Cugat del Valles/BarcelonaSpain