A REVIEW OF CHROMATIC ADAPTATION TRANSFORMS

CIE 16x:2004

UDC: 535.65 Descriptor: Colorimetry 612.843.31 Colour vision

ISBN 3 901 906 xx y

Deadline for BA and D1 votes: 23.05.2004

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CIE 2004 – All rights reserved

A REVIEW OF CHROMATIC ADAPTATION TRANSFORMS

CIE 16x:2004

UDC: 535.65 Descriptor: Colorimetry 612.843.31 Colour vision

ISBN 3 901 906 xx y

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II

This Technical Report has been prepared by CIE Technical Committee 1-52 of Division 1 "Vision and Colour" and has been approved by the Board of Administration of the Commission Internationale de l'Eclairage for study and application. The document reports on current knowledge and experience within the specific field of light and lighting described, and is intended to be used by the CIE membership and other interested parties. It should be noted, however, that the status of this document is advisory and not mandatory. The latest CIE proceedings or CIE NEWS should be consulted regarding possible subsequent amendments.

Ce rapport technique a été élaboré par le Comité Technique CIE 1-52 de la Division 1 "Vision et Couleur" et a été approuvé par le Bureau de la Commission Internationale de l'Eclairage, pour étude et emploi. Le document expose les connaissances et l'expérience courantes dans le domaine particulier de la lumière et de l'éclairage décrit ici. Il est destiné à être utilisé par les membres de la CIE et par tout les intéressés. Il faut cependant noter que ce document est indicatif et non obligatoire. Il faut consulter les plus récents comptes rendus de la CIE, ou le CIE NEWS, en ce qui concerne des amendements nouveaux éventuels.

Dieser Technische Bericht ist vom CIE Technischen Komitee 1-52 der Division 1 "Sehen und Farbe" ausgearbeitet und vom Vorstand der Commission Internationale de l'Eclairage gebilligt worden. Das Dokument berichtet über den derzeitigen Stand des Wissens und Erfahrung in dem behandelten Gebiet von Licht und Beleuchtung; es ist zur Verwendung durch CIE-Mitglieder und durch andere Interessierte bestimmt. Es sollte jedoch beachtet werden, daß das Dokument eine Empfehlung und keine Vorschrift ist. Die neuesten CIE-Tagungsberichte oder das CIE NEWS sollten im Hinblick auf mögliche spätere Änderungen zu Rate gezogen werden.

Any mention of organisations or products does not imply endorsement by the CIE. Whilst every care has been taken in the compilation of any lists, up to the time of going to press, these may not be comprehensive.

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Die Erwähnung von Organisationen oder Erzeugnissen bedeutet keine Billigung durch die CIE. Obgleich große Sorgfalt bei der Erstellung von Verzeichnissen bis zum Zeitpunkt der Drucklegung angewendet wurde, ist es möglich, daß diese nicht vollständig sind.

CIE 2004 – All rights reserved

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The following members of TC 1-52 "Chromatic Adaptation Transforms", took part in the preparation of this report. The committee comes under Division 1 "Colour and Vision".

Members:

M. Ronnier Luo (Chair) United Kingdom

O. Da Pos Italy

M. Fairchild USA

K. Hashimoto Japan

R. W. G. Hunt United Kingdom

Y. Nayatani Japan

M. Pointer United Kingdom

K. Richter Germany

B. Rigg United Kingdom

H. Sobagaki Japan

M. Stokes USA

TABLE OF CONTENTS

SUMMARY V

RESUME V

ZUSAMMENFASSUNG V

1. INTRODUCTION 1

2. EXPERIMENTAL TECHNIQUES FOR OBTAINING CORRESPONDING COLOURS 2 2.1 Haploscopic matching 3 2.2 Local-adaptation matching 4 2.3 Memory matching 4 2.4 Magnitude estimation 5

3. EXPERIMENTAL DATA SETS STUDIED 5 3.1 Colour Science Association of Japan (CSAJ) 5 3.2 McCann et al. data 6 3.3 Breneman data 6 3.4 Helson et al. data 6 3.5 Lam and Rigg data 6 3.6 Braun and Fairchild data 6 3.7 Luo et al. data 7 3.8 Kuo and Luo data 7

4. CHROMATIC ADAPTATION TRANSFORMS 7 4.1 von Kries chromatic adaptation transform 8 4.2 Wassef chromatic adaptation transform 9 4.3 Sobagaki et al. chromatic adaptation transform 9 4.4 Burnham et al. chromatic adaptation transform 10 4.5 MacAdam chromatic adaptation transform 10 4.6 Bartleson chromatic adaptation transform 11 4.7 CIECAT94 transform 11 4.8 RLAB chromatic adaptation transform 13 4.9 CIELAB 14 4.10 CMCCAT97 transformation 14

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4.11 CMCCAT2000 transformation 15 4.12 CAT02 transform 16 4.13 Sharp adaptation transform 17

6. CONCLUSION 24

REFERENCES 24

APPENDIX 28

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A REVIEW OF CHROMATIC ADAPTATION TRANSFORMS

SUMMARY

This report reviews a number of studies on chromatic adaptation. Four different experimental techniques are first described and their pros and cons are analysed. Eight experimental data sets commonly used to evaluate chromatic adaptation transforms are detailed. Thirteen chromatic adaptation transforms are also described and their equations are given in full. Finally, various studies for testing different transformations are reviewed. The results show that there are four possible candidates for future CIE recommendation, CMCCAT2000, CMCCAT97, CAT02 and CIECAT94. The first three give a better performance than the last one for the data sets employing reflection samples observed with natural viewing conditions. However, the TC members have not found it possible to agree on which if any of the four should be recommended.

REVUE DES FORMULES DE CONVERSION POUR L'ADAPTATION CHROMATIQUE

RESUME

Ce rapport fait le point sur plusieurs études relatives à l'adaptation chromatique. On décrit d'abord quatre méthodes expérimentales différentes, dont on analyse les avantages et inconvénients. L'évaluation des formules de conversion pour l'adaptation chromatique repose sur huit bases de données expérimentales d'usage courant. On décrit aussi treize formules de conversion pour l'adaptation chromatique, en donnant les équations en détail. Enfin, on passe en revue différentes études relatives au test de plusieurs formules de conversion. Les résultats montrent qu'il se dégage quatre formules susceptibles de faire l'objet d'une recommandation CIE à venir: CMCCAT2000, CMCCAT97, CAT02 et CIECAT94. Les trois premières donnent un meilleur résultat que la dernière avec des échantillons réflectifs observés en vision naturelle. Cependant, les membres du TC n'ont pas pu parvenir à un accord pour recommander l'une de ces quatre formules.

ÜBERSICHT ÜBER FARBUMSTIMMUNGSTRANSFORMATIONEN

ZUSAMMENFASSUNG

Dieser Bericht beschreibt eine Anzahl von Untersuchungen über Farbumstimmung. Vier verschiedene experimentelle Techniken werden zuerst beschrieben und ihre Vorteile und Nachteile analysiert. Acht experimentelle Datensätze werden benutzt, um die Farbumstimmungstransformationen zu bewerten. Dreizehn Farbumstimmungs-transformationen werden ebenso beschrieben und ihre Gleichungen werden vollständig angegeben. Schließlich werden verschiedene Untersuchungen vorgestellt, die unterschiedliche Transformationen testen. Die Ergebnisse zeigen, daß es vier mögliche Kandidaten für eine zukünftige CIE-Empfehlung gibt: CMCCAT2000, CMCCAT97, CAT02 und CIECAT94. Die ersten drei geben eine bessere Übereinstimmung als die letzte für die Datensätze, die reflektierende Muster unter natürlichen Beobachtungsbedingungen benutzen. Jedoch war es den TC-Mitglieder nicht möglich, sich auf eine zu einigen, falls eine der vier empfohlen werden sollte.

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1. INTRODUCTION

Chromatic adaptation transforms (CAT) are important for many industrial applications including a colour inconstancy index, colour appearance models, the prediction of corresponding colours, and the prediction of the colour rendering of sources. A colour inconstancy index has long been desired by industry for estimating the change in colour appearance with change in illuminant for a coloured product. The key component of this index is a chromatic adaptation transform. In 1999, the Colour Measurement Committee (CMC) of the Society of Dyers and Colourists (SDC) recommended the CMC 1997 Colour Inconstancy Index, CMCCON97 (Luo et al., 1999), which includes the CMC 1997 Chromatic Adaptation Transform, CMCCAT97 (Luo & Hunt, 1998a). A colour appearance model is also essential for cross-media colour image reproduction. It is capable of predicting the change in colour appearance under different viewing conditions such as different illuminants, levels of luminance, background colours and different media (e.g. reflection, transmissive and CRT). The CIE (Luo & Hunt, 1998b; Luo & Hunt, 1998c) has standardised a model, CIE 1997 Colour Appearance Model (CIECAM97s), for image applications. The CMCCAT97 is also included in the CIECAM97s for predicting corresponding colours. For illumination engineering, a CAT is also required for predicting the colour rendering properties between a test and a reference illuminant.

Chromatic adaptation has been intensively studied by many colour scientists over several decades. The typical study includes psychophysical experiments for accumulating visual data, derivation of transforms based on colour vision theory, and testing the performance of various CATs using different experimental data sets. This report reviews a number of studies and summarises the recent efforts that have been made by the CIE TC 1-52. The terms of reference of this TC were to review the chromatic adaptation transform with a view to make a recommendation. The TC, while agreeing that a standard chromatic adaptation transform would be very useful, was unable to agree on which of the various chromatic adaptation transforms, which have been suggested should be recommended. Basically the members were split as to the purpose of the committee. One group held that to be acceptable as an international standard, a suitable chromatic adaptation transform (CAT) must be theoretically based, while another group held that while such an objective is desirable, it is more important at the present time that a suitable CAT should work as well as possible, even if only applicable to a limited range of conditions. The reasons for the failure to reach agreement are described in more detail in the Appendix to this report. However the committee all agree that the main body of this technical report provides a useful review of the available literature, models currently available and experimental data used to test the models.

Chromatic adaptation is the visual mechanism for adapting to changes in the spectral composition from a light source entering the eyes. The typical example is the appearance of a piece of paper, which is seen in daylight, tungsten or fluorescent light. Although these sources are completely different, the appearance of the paper remains the same: white. The reflectance values for a non-fluorescent sample are always independent of the source, but the tristimulus values are usually very different. A simple chromatic adaptation transform takes the tristimulus values for a test specimen under a test illuminant (e.g. CIE standard illuminant A) and calculates the tristimulus values for the corresponding colour under a reference illuminant (e.g. CIE illuminant C or CIE standard illuminant D65). (The corresponding colour, when seen by an observer fully adapted to the reference illuminant, should look the same as the test specimen when seen by an observer adapted to the test illuminant.) Some transforms are based on colour appearance models, and may require extra information to be input, typically the tristimulus values (Xw, Yw, Zw) for a reference white under the test illuminant and the tristimulus values (Xrw, Yrw, Zrw) for the reference white under the reference illuminant. Sometimes the luminance of the test adapting field (La) in cd/m2 is also required (see Fig.1).

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X Y Z Xw Yw Zw Xrw Yrw Zrw La

Input Data

CAT Output data

Xc Yc Zc

Figure 1. The input and output parameters for a chromatic adaptation transform.

Several types of adaptation affect the colour appearance of object colours. This report is only focused on chromatic adaptation. For more information, readers can refer to some excellent review articles by Bartleson (1978), Wright (1981), Fairchild (1997) and Terstiege (1972).

2. EXPERIMENTAL TECHNIQUES FOR OBTAINING CORRESPONDING COLOURS

Many experimental techniques have been used to obtain corresponding colours for pairs of illuminants. These can be divided into four categories: haploscopic matching, local-adaptation matching, memory matching, and magnitude estimation. Several experimental parameters also have significant impact on the experimental results. These are the contents in the viewing field (simple and complex), and modes of colour (aperture and non-aperture). In usual situations, we look at objects in a complex viewing field using both eyes. However, a simple field has been widely used, particularly in the earlier experiments, because it simplifies experimental conditions. Even a simple field can have different appearance modes. The aperture mode of colour is defined as a mixture of colour lights perceived as a filled colour hole against a uniform surround. This state of adaptation is vastly different from that using a non-aperture stimulus (typically presented using reflection, transmissive and self-luminous modes such as CRT).

Table 1 lists some of the classical experiments conducted using each of the 4 techniques. For each experiment, the viewing field, mode of colour and reference number are also given. The experiments marked by an asterisk in Table 1 were chosen to be extensively studied by CIE TC 1-34 on Testing Colour Appearance Models and CIE TC 1-52 on Chromatic Adaptation Transforms.

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Table 1. List of classical experiments for each technique.

Viewing Field Experiment Mode Reference

HAPLOSCOPIC MATCHING Simple Wright Aperture Wright, 1934 Hunt Aperture Hunt, 1952 Brewer Aperture Brewer, 1954 Burnham et al. Aperture Burnham et al., 1957 Wassef Non-aperture Wassef, 1959 Bartleson & Breneman Aperture Bartleson & Breneman 1967 Nayatani et al. Non-aperture Nayatani et al., 1988 *Mori et al. Non-aperture Mori et al., 1991 Complex *McCann et al. Non-aperture McCann et al., 1976 *Breneman Non-aperture Breneman, 1987 Fairchild et al. Non-aperture Fairchild et al., 1994

LOCAL-ADAPTATION MATCHING MacAdam Aperture MacAdam, 1956

MEMORY MATCHING

Simple *Helson et al. Non-aperture Helson et al., 1952 Complex *Lam & Rigg Non-aperture Lam, 1985 *Braun & Fairchild Non-aperture Braun & Fairchild, 1996

MAGNITUDE ESTIMATION Simple Sobagaki et al. Non-aperture Sobagaki et al., 1974 Pointer et al. Non-aperture Pointer et al., 1977 Bartleson Aperture Bartleson, 1979a *Kuo et al. Non-aperture Kuo et al., 1995 Xu et al. Non-aperture Xu et al., 1997 Complex *Luo et al. Non-aperture Luo et al., 1991a;

Luo et al., 1991b *Luo et al. Non-aperture Luo et al., 1993a;

Luo et al., 1993b

Note: The experiments marked by an asterisk were chosen to be studied by CIE TCs.

2.1 Haploscopic matching

As shown in Table 1, haploscopic matching [also called differential ocular conditioning and comparison (Bartleson, 1978)] is the most widely used experimental technique. Most of the earlier experiments were conducted using aperture stimuli with a simple viewing field. This technique requires a specially designed viewing apparatus that presents a different adapting stimulus to each of the observer's two eyes. An example is given in Fig. 2, in which an observer viewed from an eyepiece and saw the left field by one eye and the right field by the other eye. After allowing time to adapt, one eye is adapted to CIE standard illuminant D65 and the other to CIE standard illuminant A. The observer is then asked to adjust the stimulus, C2, seen by one eye to match C1 seen by the other eye by altering amounts of red, green and blue lights. The task is relatively simple and the results, in general, have higher precision than the other techniques. However, their validity is dependent on the assumption that the adaptation of one eye does not affect the sensitivity of the other eye. Recent results from Barlow and Mollon (1982) show that when two eyes are presented with two stimuli under different adapting fields, observers tend to bias more towards one field than the other. This is known as binocular rivalry. In addition, the technique imposes unnatural viewing conditions together with constrained eye movement.

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More recent haploscopic experiments have used non-aperture stimuli with a complex viewing field. Breneman (1987) devised an apparatus with a complex adapting field and allowed observers to use normal eye movement. Fairchild et al. (1994) also developed a new technique: successive-Ganzfeld haploscopic matching. The Ganzfeld viewing device was constructed to allow one eye to view the reference adapting field including a reference image or colour patch, while the other eye saw a spatially uniform neutral colour having the same luminance and chromaticity as the test adapting condition. After a suitable adaptation time, the process was then reversed by allowing the other eye to view the test adapting field, which includes a pair of images or samples, while the other eye saw a spatially uniform neutral colour having the same luminance and chromaticities as the reference adapting condition. Observers were asked to choose one image or colour giving the closer match to the one previously seen in the reference field. The above two techniques retain some of the advantage and overcome part of the problems occurring in simple haploscopic matching.

Illuminant A Illuminant D65

Test Colour (C1) R+G+B = C2

Figure 2. A typical viewing condition used in the haploscopic matching experiment.

2.2 Local-adaptation matching

MacAdam (1956) derived a technique to obtain corresponding colours, in which differential retina conditioning was used. In this method, two different areas of the retina in the same eye were exposed in the two halves of the visual field for colour matching.

He built a 10° visual colorimeter in which two halves of the fields were filled with different adapting stimuli. Every 10 seconds, for 1 second only, a test stimulus replaced the adapting stimulus in one-half of the field and an adjustable stimulus in the other half of the field. Observers were asked to make a colour match between the test and adjustable colour in that 1-second interval. Again, similar to haploscopic matching when the two eyes may interact with each other, it is possible that the two parts of the retina affect each other.

2.3 Memory matching

Memory matching is carried out under normal viewing conditions using both eyes and without the interposition of any optical devices. All experiments (Helson et al., 1952; Lam, 1985; Braun & Fairchild, 1996) have been conducted using object-colour stimuli. This technique provides a steady state of adaptation with free eye movement. Observers are first trained using a colour order system (say Munsell) until they are very familiar with its scales (Munsell value, chroma and hue in this case). This means that they are able to describe with reasonable accuracy and precision the colour of any object in these terms under any viewing conditions. For example, the observers of Helson et al. (1952) were asked to fully adapt under CIE illuminant C, and presented with a sample in a viewing cabinet illuminated by CIE illuminant C. Each observer estimated the Munsell hue, value and chroma. The experiment was performed with many samples and repeated under CIE standard illuminant A. Suppose that for one sample, the results were 5R 4/4.5 for CIE illuminant C and 5R 4/5 for CIE standard illuminant A, i.e. the sample appeared more colourful under CIE standard illuminant A. To form a pair of

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corresponding colours, the measured values (XYZ) for CIE illuminant C needed to be adjusted slightly to correspond to an increase in chroma of 0,5 units. This adjustment can be made because the measured XYZ values for all the Munsell samples are available. The pair of corresponding colours is comprised of the measured tristimulus values for CIE standard illuminant A and the adjusted values for CIE illuminant C. In real cases, there were changes in hue and value as well as chroma, making the calculations more complicated. However, as long as the required adjustments were small, they should be reasonably accurate.

Memory matching is not a widely used technique and has several drawbacks such as a substantial training period being required, complicated procedures for data analysis, lower precision than that of haploscopic technique, limited capacity for retaining information, and memory distortion.

2.4 Magnitude estimation

Magnitude estimation has been used more recently than the other techniques. A comprehensive data set was accumulated by Kuo et al. (1995), Xu et al. (1997) and Luo et al. (1991a; 1991b; 1993a; 1993b), known as the LUTCHI colour appearance data set, which was extensively used by members of CIE TC 1-34 to derive the CIECAM97s. Observers were asked to scale the visual percepts of lightness, colourfulness, and hue under fully adapted viewing conditions. Definitions of these attributes are given as follows:

Hue is the attribute of a visual sensation according to which an area appears to be similar to one, or to proportions of two, of the perceived colours red, yellow, green and blue.

Colourfulness is the attribute of a visual sensation according to which an area appears to exhibit more or less of its own hue.

Lightness is the brightness of an area judged relative to the brightness of a similarly illuminated area that appears to be white or highly transmitting.

The results of magnitude estimation are analysed by deriving ISO-hue and ISO-colourfulness contours on a colour diagram such as CIELAB, u’,v’ or x,y for a particular illuminant. These contours form the colour appearance grid. The intersection between the ISO-hue and ISO-colourfulness contours for any two illuminants form a pair of corresponding colours. One disadvantage of this technique is to have lower precision than that of the haploscopic technique. Many advantages are associated with this technique and these are: normal viewing conditions using both eyes, steady-state of adaptation, results are described in terms of perceived attributes which can be directly compared with the predictions of colour appearance models, and a shorter training period is required than that for memory matching.

3. EXPERIMENTAL DATA SETS STUDIED

As mentioned earlier, various data sets were generated over the years and only those marked by asterisks in Table 1 are evaluated here. This is due to fact that these data sets were generated using more carefully designed experimental techniques, more observers and were already used by many studies, i.e. they were conducted under relatively natural viewing conditions. Applying a complex viewing field (related colours) is preferred to that using a simple viewing field (unrelated colours). All experiments using the aperture-mode stimuli generated using visual colorimeters were removed due to unnatural viewing characteristics. The eight data sets were selected are: Colour Science Association of Japan (CSAJ), (Mori et al., 1991), McCann et al. (1976), Breneman (1987), Helson et al. (1952), Lam and Rigg (Lam, 1985), Braun and Fairchild (1996), Kuo and Luo (Kuo et al., 1995) and Luo et al. (1991a). Although three data sets still used the haploscopic experimental technique (CSAJ, McCann and Breneman), they used non-aperture colours assessed by a large panel of observers. A brief account for each data set is given below.

3.1 Colour Science Association of Japan (CSAJ)

An extensive study was carried out by the members of the Colour Science Association of Japan (CSAJ). The work was described by Mori et al. (1991). It includes three data sets for studying the Hunt, Stevens and chromatic adaptation effects. The former two sets studied the

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change of colourfulness and brightness perception, respectively caused by change of luminance level. The latter data were accumulated for studying chromatic adaptation. The assessments were carried out in a bipartite lighting cabinet using the haploscopic matching technique. Judgements were made by 104 observers on 87 test colours (5 cm by 5 cm in size) under CIE standard illuminants D65 and A at an illuminance level of 1000 lx. Each observer was asked to select a colour chip, which gave the closest match to the test colour from the colour chips (1,8 cm by 1,4 cm in size) in the JIS Color Atlas in accordance with the Munsell renotation system. A mask was used to cover the other colour chips in the Atlas, i.e. only one chip could be seen at a time.

3.2 McCann et al. data

McCann et al. (1976) conducted 4 phases of experiments to obtain corresponding colours using a white illuminant and 4 very chromatic illuminants using a successive haploscopic matching technique. A mondrian figure consisting of 18 object colours was used. The illuminances used ranged from 14 lx to 40 lx, i.e. very dark lighting conditions. The original data were not published using standard colorimetric notations. Nayatani et al. (1995) derived a method to transform the original data into standard colorimetric form.

3.3 Breneman data

Breneman (1987) conducted an experiment using a coloured photographic transparency as a complex adapting field (31° by 24° in size) within which the test and matching adapting fields (~5°) and stimuli (~2°) were presented. Again, the haploscopic matching technique was used. However, the apparatus was designed to allow observers to have unrestrained eye movements so that a normal degree of both general and local adaptation could be maintained.

The experiment was divided into 12 phases, in which 9 phases were performed under different illuminants but the same illuminance, and the other 3 phases under same illuminant but different levels of illuminance. At least 7 observers took part in each phase.

3.4 Helson et al. data

Helson, Judd and Warren (1952) used 59 Munsell samples (1" by 1" in size) assessed by a panel of 6 observers. Each colour was described in terms of Munsell Colour coordinates (H V/C), using the memory matching technique, against three neutral backgrounds having percentage luminance factors of 3, 21 and 78, respectively. Two illuminants were used: CIE illuminant C and CIE standard illuminant A. As described in the last section, the visual results (H V/C) for the two illuminants studied were adjusted and converted to CIE 1931 XYZ values under CIE illuminant C to form three sets of corresponding colours.

3.5 Lam and Rigg data

Lam and Rigg (Lam, 1985) used 58 wool samples assessed twice by a panel of 5 observers under CIE standard illuminants D65 and A. The memory matching technique was used to establish pairs of corresponding colours. The experiment differed from that of Helson et al. by using a complex, rather than a simple, viewing field, i.e. a subgroup of colours were first arranged in terms of chroma and hue and each was then described using Munsell H V/C coordinates. The data, in terms of H V/C, were then adjusted and converted to CIE 1931 XYZ values under CIE illuminant C. Subsequently, the data under CIE illuminant C were transformed to those under CIE standard illuminant D65 via the von Kries transform. This should be reasonably accurate because the difference of chromaticity under two illuminants is very small. The data set of all such pairs was used to derive the Bradford (BFD) chromatic-adaptation transform (Lam, 1985). The transformation has a structure similar to that of the Nayatani et al. transform, which was later recommended by the CIE for field trials (CIE, 1994), hereafter referred to as the CIECAT94-old transform. The BFD transform was later modified by Luo and Hunt (1998a) to become CMCCAT97 by removing some anomalies and adding an incomplete adaptation factor, D (see later).

3.6 Braun and Fairchild data

Braun and Fairchild (1996) also accumulated corresponding colour data sets using a short-term memory matching method, i.e. observers looked at a monitor and a print image

CIE 16x:2004

7

presented in a viewing cabinet successively such that the two images could never be seen at the same time. Five observers took part and each repeated the observations. Two images were used: fruit and golfer. Each image was divided into various colour regions according to the number of objects. Observers adjusted the colours in the monitor image to match those of printed images using Adobe Photoshop software. The monitor images were surrounded by a grey colour with the chromaticity coodinates of D65 illuminant. Three illuminants were used in the cabinet having colour temperatures of 3000 K, 6500 K and 9300 K, respectively.

3.7 Luo et al. data

During 1987 to 1993, Luo (Luo et al., 1991a; 1991b; 1993a; 1993b) led a research team at Loughborough University of Technology, Computer and Human Interface (LUTCHI) Research Centre. They carried out a large-scale experiment that described the colour appearance of many colours under a wide range of viewing conditions. The parameters studied were: four illuminants [D65, D50, A and a white fluorescent source (WF)], two illuminance levels (130 lx and 750 lx), five backgrounds (white, grey, black, grey with white border, and grey with black border), and four media (reflection print, CRT, 35 mm projection and large cut-sheet transparency). A complex viewing field was used with about 20 colours surrounding the border of a viewing pattern (25 cm by 35 cm in size). Each colour (2 cm by 2 cm in size) was placed in the centre of the pattern and was assessed by a panel of 6 or 7 observers in terms of lightness, colourfulness and hue using the magnitude estimation technique. In total, about 5000 test colours were assessed. Four sets of colour appearance grids were established under illuminants D65, D50, A, and a white fluorescent source (WF). Hence, three sets of corresponding colours (Luo et al., 1991a) using reflection print samples under high illuminance level were established between D65 and the other three illuminants.

3.8 Kuo and Luo data

In 1993, Kuo et al. (1995) carried out a project, funded by the Society of Dyers and Colourists (SDC), to investigate both colour inconstancy and metamerism. 240 textile samples were prepared to cover a large colour gamut. The same magnitude estimation method as that used for the Luo et al. data (Luo et al., 1991a; 1991b; 1993a; 1993b) was used except that a simple field with grey background was used rather than a complex field. Each colour was assessed under D65, TL84, and A illuminants (at an illuminance of about 800 lx). The results were then used to derive two sets of corresponding colours, namely between illuminants D65 and A, and between illuminants D65 and TL84.

4. CHROMATIC ADAPTATION TRANSFORMS

Various chromatic adaptation transforms have been derived to fit a particular data set. The majority of the transforms include 3 stages of calculation as shown in Fig. 3.

Stage 1 To accurately model the physiological mechanisms of chromatic adaptation, one must express stimuli in terms of cone responses, denoted R, G, B, suggestive of long-wave (red), middle-wave (green) and short-wave (blue) sensitivities. This is achieved by using a linear transform via a 3 by 3 matrix. Various transform functions are available based upon different fundamental primaries.

Stage 2 This stage transforms cone responses of the test sample, (R, G, B), under the test illuminant, defined by (Rw, Gw, Bw), into the adapted cone responses (Rc, Gc, Bc) under the reference illuminant, defined by (Rrw, Grw, Brw). The transforms are different between different CATs.

Stage 3 This uses the reverse transform (an inverse matrix) of Stage 1 to transform the corresponding cone responses, (Rc, Gc, Bc), back to tristimulus values under the reference illuminant.

Ten CATs are introduced below. The notations used in the CATs are different from those used in their original versions, but agree with those given in Fig. 3.

CIE 16x:2004

8

Stage 1

Xw Yw Zw Xrw Yrw Zrw X Y Z

Rc Gc Bc

Stage 2

Rw Gw Bw Rrw Grw Brw R G B

Xc Yc Zc

Stage 3

Figure 3. Three stages included in a chromatic adaptation transform.

4.1 von Kries chromatic adaptation transform

In 1902, von Kries (1902) studied chromatic adaptation following the Young-Helmholtz theory, which assumes that, although the responses of the three cone types (R, G, B) are affected differently by chromatic adaptation, the relative spectral sensitivities of each of the three cone mechanisms remain unchanged. Hence, chromatic adaptation can be considered as a change of sensitivity by a constant factor for each of the three cone mechanisms. The magnitude of each factor depends upon the colour of the stimulus to which the observer is adapted. The relationship, given in Equ. 1, is known as the von Kries coefficient law.

BB

GG

RR

γβα

===

c

c

c

(1)

where Rc, Gc, Bc and R, G, B are the cone responses of the same observer, but viewed under test and reference illuminants respectively. α, β and γ are the von Kries coefficients corresponding to the change in sensitivity of the three cone mechanisms due to chromatic adaptation. These are calculated using Equ. 2.

���

����

�=��

�

����

�=��

�

����

�=

w

rw

w

rw

w

rw ;;BB

GG

RR γβα (2)

CIE 16x:2004

9

where

rw

c

wrw

c

wrw

c

w

;;BB

BB

GG

GG

RR

RR ===

and Rrw, Grw, Brw, and Rw, Gw, Bw are the cone responses for the reference white under the reference and test illuminants, respectively.

In 1974, the CIE technical committee on colour rendering [updated in 1995 (CIE, 1995)] adopted a version of the von Kries model derived by Helson et al. (1952). It is still in use for making small adjustments to account for differences in illuminants to be compared for colour rendering properties. This procedure is given below.

Step 1. Calculate the R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Judd’s cone transformation (Judd, 1945) in Equ. 3.

���

�

�

���

�

�

���

�

�

���

�

�

−=���

�

�

���

�

�

Z

Y

X

B

G

R

000,1000,0000,0

100,0360,1460,0

000,0000,1000,0 (3)

Step 2. Calculate the α, β and γ von Kries coefficients and the Rc, Gc, Bc values using Equ. 2. Step 3. Calculate the Xc, Yc, Zc using Equ. 4.

���

�

�

���

�

�

���

�

�

���

�

� −=

���

�

�

���

�

�

c

c

c

c

c

c

000,1000,0000,0

000,0000,0000,1

220,0174,2954,2

B

G

R

Z

Y

X (4)

For a given pair of illuminants, such as A and C, this transform can be simplified as follows:

���

�

�

���

�

�

���

�

�

���

�

� −=

���

�

�

���

�

�

Z

Y

X

Z

Y

X

327,3000,0000,0

000,0000,1000,0

473,0458,0154,1

c

c

c

where X Y Z and Xc, Yc, Zc are tristimulus values for corresponding colours in illuminants A and C, respectively.

Although many sets of experimental data (Bartleson, 1978) do not agree with the von Kries law due to its simplicity, it does provide an approximation to fit the general trends. For example, Breneman (1987) optimised the 9 coefficients in cone transformation to fit experimental data and obtained reasonable predictions.

4.2 Wassef chromatic adaptation transform

Wassef (1959) derived a simple chromatic adaptation transform by assuming linearity. She optimised the 3 by 3 matrix coefficients to fit her experimental data (corresponding data from illuminants A to C). The transform is given in Equ. 5.

���

�

�

���

�

�

���

�

�

���

�

�

−−−=

���

�

�

���

�

�

Z

Y

X

Z

Y

X

269,3923,0553,0

303,0341,2619,0

141,0441,0926,0

c

c

c

(5)

where X Y Z and Xc, Yc, Zc are tristimulus values for corresponding colours in illuminants A and C, respectively. Note that the coefficients are quite different from those for the von Kries transformation.

4.3 Sobagaki et al. chromatic adaptation transform

Sobagaki et al. (1974) applied Wassef’s method to derive a new chromatic adaptation transform. The transform is given in Equ. 6.

CIE 16x:2004

10

���

�

�

���

�

�

���

�

�

���

�

�

−

−=

���

�

�

���

�

�

Z

Y

X

Z

Y

X

4976,23132,01467,0

1752,09028,00401,0

5293,01389,08354,0

c

c

c

(6)

where X Y Z and Xc, Yc, Zc are tristimulus values for corresponding colours in CIE standard illuminants A and D65, respectively.

4.4 Burnham et al. chromatic adaptation transform

Burnham et al. (1957) also derived a transform similar to that of Wassef but using a 3 by 4 matrix. The transform is given in Equ. 7.

����

�

�

����

�

�

���

�

�

���

�

�

−−−−−

=���

�

�

���

�

�

10036,01114,23666,00776,0

0016,02144,09994,00296,0

0005,03725,04054,00972,1

c

c

c

Z

Y

X

Z

Y

X (7)

where X Y Z and Xc, Yc, Zc are tristimulus values for corresponding colours in illuminants A and C, respectively.

It is obvious all the above simple transformations are different from each other. (The difference between illuminants D65 and C is far too small to account for the differences.)

4.5 MacAdam chromatic adaptation transform

As mentioned earlier, MacAdam (1956) also accumulated a set of experimental data based on his classical local-adaptation matching technique. The data were used to derive a chromatic adaptation transform (MacAdam, 1963) from tungsten light to daylight as described below.

8048,0/18048,0

c

9496,0/19496,0

c

3341,0/13341,0

c

2612,01676,1290,5252,2

4554,23723,1774,10195,1

4554,25983,1233,9004,1

��

�

�

��

�

� −+=

��

�

�

��

�

� −+=

��

�

�

��

�

� ++=

RB

RG

RR

(8)

and

���

�

�

���

�

�

=���

�

�

���

�

�

B

G

R

Z

Y

X

A

c

c

c

where

���

�

�

���

�

� −=

000,1000,0000,0

000,0410,0590,0

216,0950,0750,1

A

For calculating the R, G, B in Equ. 8, the following equation is used:

���

�

�

���

�

�

=���

�

�

���

�

�−

Z

Y

X

B

G

R1A

CIE 16x:2004

11

4.6 Bartleson chromatic adaptation transform

Bartleson (1979a) also produced 5 independent data sets based on aperture mode colours using the magnitude estimation technique. He then derived a transformation (Bartleson, 1979b) to fit the experimental data. It includes a single set of Konig-type cone response functions, and the R and G cone responses were altered by changes in adaptation according to the von Kries coefficient law while, in addition, the B cone response was modified through a power transform. The Bartleson transform procedure is given below.

Step 1. Calculate R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Konig-type cone transformation in Equ. 9.

���

�

�

���

�

�

=���

�

�

���

�

�

YZ

YY

YX

B

G

R

/

/

/

A (9)

where

���

�

�

���

�

�

−−

=5610,0000,0000,0

0815,01668,13952,0

0147,09625,00713,0

A

Step 2. Calculate Rc, Gc, Bc using Equ. 10.

pBakBandGaGRaR )(, bcgcrc === (10)

where

wrwbwrwgwrwr /an/,/ BBadGGaRRa ===

and

45,0b

91,3g

45,27r 340,0325,0326,0 −− ++= aaap

pBaBak )(/ wbwb=

Step 3. Calculate Xc, Yc, Zc using Equ. 11.

���

�

�

���

�

�

=���

�

�

���

�

�−

YB

YG

YR

Z

Y

X

c

c

c1

c

c

c

A (11)

4.7 CIECAT94 transform

The CIE (1994) recommended a transformation for field trials in 1994. This non-linear chromatic-adaptation transformation was derived by Nayatani et al. (1981). It is a two stage transformation. The first step is a modified von Kries transformation, and the second is a non-linear transformation corresponding to a compression in the response of each mechanism. This transformation takes into account the luminance level used. More recently, Nayatani et al. (1999) proposed a colour appearance model, called CIECAT94LAB, including a modified version of their original chromatic adaptation transform. This latest version of chromatic adaptation transform is named CIECAT94 as given below. The earlier version is named CIECAT94-old hereafter.

Step 1. Calculate R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Equ. 12. The reference illuminant is D65.

���

�

�

���

�

�

=���

�

�

���

�

�

Z

Y

X

B

G

R

A (12)

where

CIE 16x:2004

12

���

�

�

���

�

�

−−

=91822,0000,0000,0

04570,016532,122630,0

08081,070760,040024,0

A

Step 2. Calculate Rc Gc and Bc using Equ. 13.

nnY

nBKnYR

nnY

nGKnYG

nnY

nRKnYR

BBB

GG

o

G

RRR

−��

���

�

+++=

−��

���

�

+++=

−��

���

�

+++=

)(/)(

o

)(/1rwoc

)(/)()(/1

rwoc

)(/)(

o

)(/1rwoc

rw2w2

rw2

rw1w1

rw1

rw1w1

rw1

')(

')(

')(

βββ

βββ

βββ

ζζ

ηη

ξξ

(13)

where each symbol will be described later (see Note).

Step 3. Calculate the Xc, Yc, Zc using Equ. 14

���

�

�

���

�

�

=���

�

�

���

�

�−

c

c

c1

c

c

c

B

G

R

Z

Y

X

A (14)

Notes:

1) ξw , ηw , ζw and ξrw , ηrw, ζrw correspond to test and reference illuminants, respectively. (The chromaticities (xo yo) of test and reference illuminants are entered into the following equation.)

ooo

ooo

ooo

/)1(91822,0

/)04570,011962,127200,0(

/)080811,078841,048105,0(

yyx

yyx

yyx

−−=++−=

−+=

ζηξ

2) ξ’, η’,,ζ’, are the adapting ξ, η, ζ, values and are calculated below.

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�

�

���

�

�

−+���

�

�

���

�

�

=���

�

�

���

�

�

rw

rw

rw

w

w

w

)1(

'

'

'

ζηξ

αζηξ

αζηξ

and

)510,022,0()50*(0025,0log1151,0 a10 ++−+= DLLα

where La is the adapting luminance (cd/m2) in test field, and L* the CIELAB lightness of the sample in question. For object colours D=1, and for luminous colours (typically CRT) D=0. The α value must be less than one.

3) Rw Gw Bw and Rrw Grw Brw are calculated as follows.

���

�

�

���

�

�

=���

�

�

���

�

�

���

�

�

���

�

�

=���

�

�

���

�

�

rw

rw

rw

ra

rw

rw

rw

w

w

w

a

w

w

w

,

ζηξ

ζηξ

L

B

G

R

L

B

G

R

where Lra is set to 63,66 cd/m2.

4) β1 and β2 functions are given below.

���

����

�

++=

++=

5128,0

5128,0

2

4495,0

4495,0

1

414,8091,8414,8

7844,0)(

469,6362,6469,6

)(

II

I

II

I

β

β

CIE 16x:2004

13

5) Calculate K factor.

)()3/1(rwrwo

)()3/1(o

)()3/2(rwwo

)()3/2(o

rw1

r1

rw1

r1

)]20/()[(

)]'20/()'[(

)]20/()[(

)]'20/()'[(G

G

Rr

R

nnY

nnY

nnY

nnYK β

β

β

β

ηηηη

ξξξξ

++++

++++=

For Yo=20, K equals one.

6) The noise factor of all the above equations is 0,1.

The differences between the CIECAT94 (above) and CIECAT94-old include: the introduction of the incomplete adaptation factor, α, described in Note 2) and the change of the noise factor from 1,0 to 0,1.

4.8 RLAB chromatic adaptation transform

Fairchild (Fairchild & Berns, 1993; Fairchild, 1996b) at the Munsell Color Science Laboratory, Rochester Institute of Technology, also developed a colour appearance model, RLAB, including a chromatic adaptation transform. The model is focused for imaging applications. Various experiments were conducted to test the model using complex images. Its transform is described below.

Step 1. Calculate R, G, B and Rw, Gw, Bw from X Y Z and Xw, Yw, Zw for test sample and reference white respectively using Equ. 15.

���

�

�

���

�

�

=���

�

�

���

�

�

Z

Y

X

B

G

R

M (15)

where

���

�

�

���

�

�

−−

=0000,1000,0000,0

0464,01834,12298,0

0787,06890,03897,0

M

Step 2. Calculate PR, PG and PB and rE, gE and bE.

)/0,10,1(

)0,1(

)/0,10,1(

)0,1(

)/0,10,1(

)0,1(

E3/1

a

E3/1

aB

E3/1

a

E3/1

aG

E3/1

a

E3/1

aR

bL

bLP

gL

gLP

rL

rLP

++++=

++++=

++++=

where La is the adapting luminance in cd/m2, which is calculated by multiplying the luminance of the reference white by the reflectance of the background. The rE, gE and bE values are calculated below.

www

wE

www

wE

www

wE

0,3

0,3

0,3

BGRB

b

BGRG

g

BGRR

r

++=

++=

++=

Step 3. Calculate the coefficients in the A matrix.

���

�

�

���

�

�

=

B

G

R

00

00

00

a

a

a

A (16)

CIE 16x:2004

14

where

w

BB

wG

w

RRR

)0,1(

)0,1(

)0,1(

B

GG

B

pDpa

G

pDpa

RpDp

a

−+=

−+=

−+=

where D is the partial chromatic adaptation factor and should set to 1,0 for hard-copy images (complete discounting illuminant, or full adaptation), 0,0 for CRT images, and an intermediate value for viewing conditions such as projected transparencies in completed darkened room.

Step 4. Calculate the Xc, Zc, Zc using Equ. 17.

���

�

�

���

�

�

=���

�

�

���

�

�

Z

Y

X

Z

Y

X

c

c

c

RAM (17)

where

���

�

�

���

�

� −=

0000,1000,0000,0

0000,06388,03612,0

2313,01882,19569,1

R

where Xc, Yc and Zc are always under CIE standard illuminant D65 with a luminance of 318 cd/m2 for the reference white.

4.9 CIELAB

Although the CIELAB colour space (CIE, 1986) was recommended by CIE in 1976 solely for quantifying colour differences in colours of near-daylight colour, if it is used with other illuminants, it can then be considered as a chromatic-adaptation transformation. The assumption made is that L*, a* and b* are the same for a pair of corresponding colours.

4.10 CMCCAT97 transformation

Lam and Rigg (Lam, 1985) at Bradford University studied the degree of colour constancy for object colours with change of illuminants. As mentioned earlier, they conducted a memory matching experiment using 58 textile samples under CIE standard illuminants D65 and A. A transformation was derived to fit the experimental data. The transform was named the BFD transform, which is similar to the structure of Bartleson's. At a later stage, this transform was further enhanced by Luo and Hunt (1998a) to become CMCCAT97. It is included in the CIE 1997 colour appearance model, CIECAM97s, which was recommended by the CIE for colour image applications.

The CMCCAT97 is given below.

A parameter, La (adapting luminance), is required for calculating a parameter, D, which allows for the degree of chromatic adaptation taking place. La is calculated as LwYb /100 where Lw is the luminance in cd/m2 of the reference white under the test illuminant and Yb is the luminance factor of the background. The whites are normally the perfect reflecting diffuser, in which case Yw=Yrw = 100. Other whites may be used but, to avoid ambiguity, their details should be recorded.

Step 1. Calculation of R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Equ. 18.

���

�

�

���

�

�

=���

�

�

���

�

�

YZ

YY

YX

B

G

R

/

/

/

M (18)

CIE 16x:2004

15

where

���

�

�

���

�

�

−−

−=

0296,10685,00389,0

0367,07135,17502,0

1614,02664,08951,0

M

Step 2. Calculation of degree of adaptation (D) using Equ. 19.

300/21 2a

4/1a LL

FFD

++−= (19)

where F = 1 for surface samples seen under typical viewing conditions.

D is set to one if the colour of the illuminant is usually discounted during visual colour-inconstancy assessments for object colours. This is proposed by CMCCON97 (Luo et al., 1999).

Step 3. Calculation of the corresponding RGB cone responses using Equ. 20.

( )[ ]( )[ ]( )[ ] pp BDBBDB

GDGGDG

RDRRDR

−+=

−+=−+=

1/

1/

1/

wWRc

wwc

wwc

(20)

(when B is negative, Bc must be made negative)

where

( ) 0834,0wrw / BBp =

Step 4. Calculation of the corresponding tristimulus values using Equ. 21.

���

�

�

���

�

�

=���

�

�

���

�

�−

YB

YG

YR

Z

Y

X

c

c

c1

c

c

c

M (21)

CMCCAT97 is a modification of the BFD transform. The differences are in Steps 2 and 3, in which, in the BFD transform, D is set to unity, thereby assuming complete adaptation or discounting illuminant colour, and there is no modulus (absolute value) of B in the calculation of Bc. The latter would cause a computation problem if B were less than zero.

4.11 CMCCAT2000 transformation

As mentioned earlier, CMCCAT97 is included in CIECAM97s for image applications. At a later stage, it was found that there is a major drawback in the transform - it cannot be exactly reversed, i.e. an iterative process is required because of the inclusion of the p factor in Equ. 20. Hence, p was set to one to avoid this problem. The D function in Equ. 19 was also revised to improve the fit to the available data sets. In addition, a new 3 by 3 transform matrix was developed to replace matrix A in Equ. 18, i.e. the matrix in CMCCAT97, which was derived to fit only one data set (Lam and Rigg data), using all available data sets. This will give the most accurate prediction to all data sets. All input parameters have the same symbols as those used in CMCCAT97. The full CMCCAT2000 is given below:

Step 1. Calculation of R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Equ. 22.

���

�

�

���

�

�

=���

�

�

���

�

�

YZ

YY

YX

B

G

R

/

/

/

M (22)

where

CIE 16x:2004

16

���

�

�

���

�

�

−−

=9753,00239,00008,0

0406,05512,15918,0

1371,03389,07982,0

M

Step 2. Calculation of degree of adaptation (D) using Equ. 23.

)/()(45,076,0)(log08,0 2aa1a2a1a2a110 LLLLLLD +−−++= (23)

where F = 1 for "average" viewing condition, and F equals to 0,8 for "dim" and "dark" conditions, and where La1 and La2 are the luminances of the test and referenced adapting fields, respectively. If D is greater than one or less than zero, set it to one or zero, respectively.

Step 3. Calculation of Rc, Gc, Bc from R, G, B (similarly Rwc, Gwc, Bwc from Rw, Gw, Bw)

BDBBDB

GDGGDG

RDRRDR

]1)/([

]1)/([

]1)/([

wwrc

wwrc

wwrc

−+=−+=−+=

(24)

Step 4. Calculation of the corresponding tristimulus values using Equ. 25.

���

�

�

���

�

�

=���

�

�

���

�

�−

YB

YG

YR

Z

Y

X

c

c

c1

c

c

c

M (25)

The CMCCAT2000 is a lot simpler than CMCCAT97. It also gives more accurate prediction than CMCCAT97 for the majority of the data sets (see later).

4.12 CAT02 transform

Since the recommendation of CIECAM97s (which includes CMCCAT97), many trials have been conducted (Li et al., 2000; Fairchild, 1996a; Hunt et al., 2002; Hunt et al., 2003). The results showed that the model has some major shortcomings; one of them is the complication of CMCCAT97. CIE TC 8-01 Color Appearance Models for Color Management Applications was formed to overcome these shortcomings, to improve the model performance and in some degree to simplify the model. This resulted in CIECAM02 (Moroney et al., 2002; CIE, 2004) which includes yet again a different transform, called CAT02, or modified CMCCAT2000, as modified by Li et al. The model is given below:

Step 1. Calculation of R, G, B, Rrw, Grw, Brw, and Rw, Gw, Bw using Equ. 26.

���

�

�

���

�

�

=���

�

�

���

�

�

Z

Y

X

B

G

R

CAT02M (26)

where

���

�

�

���

�

�

−−

=9834,00136,00030,0

0061,06975,17036,0

1624,04296,07328,0

CAT02M

Step 2. Calculation of degree of adaptation (D) using Equ. 27.

��

�

�

��

�

�

��

�

�−=��

���

� −−92

42a

6,31

1L

eFD (27)

where La is the luminance of the adapting field. In theory D should range from 0 for no adaptation to the adopted white point to 1 for complete adaptation to the adopted white point. In practice the minimum D value will not be less than 0,65 for a "dark" surround and will exponentially converge to 1 for "average" surrounds greater than 1.

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Step 3. Calculation of Rc, Gc, Bc from R, G, B (similarly Rwc, Gwc, Bwc from Rw, Gw, Bw)

BDBBDB

GDGGDG

RDRRDR

]1)/([

]1)/([

]1)/([

wwrc

wwrc

wwrc

−+=−+=−+=

(28)

Step 4. Calculation of the corresponding tristimulus values using Equ. 26.

���

�

�

���

�

�

=���

�

�

���

�

�−

c

c

c1

CAT02

c

c

c

B

G

R

Z

Y

X

M (29)

It can be seen that there are some major differences between CMCCAT97, CMCCAT2000 and CAT02. First, the model is simplified by replacing X/Y, Y/Y, Z/Y in Equ’s. 18 and 22 by X, Y, Z in Equ. 26, and replacing RcY, GcY, BcY in Equ. 25 by Rc, Gc, Bc in Equ. 29. These changes were made possible due to the multiplication by Yw in Equ. 28. Second, the matrix coefficients in all three transforms are all different. The CAT02’s coefficients were obtained by the optimisation of all data sets except for the McCann data set (the reason will be given later). There have been strong debates between TC 8-01 members on whether this data set should be excluded. The majority of members agreed to reject this data set due to the highly chromatic colours, and low illuminances, of the illuminations used in the experiment. These conditions are less relevant for typical applications, especially for imaging use. However, this view is not shared by some of the members in this TC. They believe that this set of conditions can provide a particularly severe test of chromatic adaptation transforms. As shown by Sobagaki et al. (1999), the CMCCAT97 gives large errors for predicting corresponding colours under the very dim saturated yellow illumination used in one of the McCann experimental phases.

If a CAT is only to be used under "normal" conditions of illuminations such as daylight, tungsten and fluorescent tubes then McCann’s experiments are irrelevant. However, if conditions such as sodium street lighting are to be included, then the McCann data becomes important.

4.13 Sharp adaptation transform

The better transforms described above such as CMCCAT97, CMCCAT2000 and CAT02, have a common feature in that the spectral sensitivities are narrower than the human cone responses. Other studies also show that the spectrally sharpened sensors do appear to be psychophysically relevant (Poirson & Wandell, 1990; Thornton, 1973; Brill et al., 1998). Finlayson and Süsstrunk (2000) proposed a sharpened sensor transform by fitting sharp sensors to the Lam and Rigg data.

The basic structure of the sharp adaptation transform is given below:

Step 1. Calculation of cone responses

���

�

�

���

�

�

=���

�

�

���

�

�

���

�

�

���

�

�

=���

�

�

���

�

�

���

�

�

���

�

�

=���

�

�

���

�

�

rw

rw

rw

rw

rw

rw

w

w

w

w

w

w

,,

Z

Y

X

B

G

R

Z

Y

X

B

G

R

Z

Y

X

B

G

R

TTT (30)

where

���

�

�

���

�

�

−−

−−=

0018,10315,00297,0

0357,08006,18364,0

1706,00988,02694,1

T

where the matrix coefficients obtained by fitting the Lam and Rigg data set were used. These were optimised using sensor-based technique (Finlayson et al., 1994).

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Step 2. Calculation of corresponding cone responses

���

�

�

���

�

�

=���

�

�

���

�

�

B

G

R

B

G

R

Diagonal

c

c

c

D (31)

where

�����

�

�

�����

�

�

=

w

rw

w

rw

w

rw

Diagonal

00

00

00

BB

GG

RR

D

Step 3. Calculation of corresponding tristimulus values

���

�

�

���

�

�

=���

�

�

���

�

�−

Z

Y

X

Z

Y

X1

c

c

c

T (32)

5. METHODS FOR COMPARING CHROMATIC ADAPTATION TRANSFORMATIONS

The performance of various CATs has been evaluated using experimental data sets. As mentioned earlier, each transform was derived to fit a particular set of experimental data. Hence, each transform directly reflects the characteristics of its corresponding-colour data set. Bartleson (1978) initially developed a qualitative method including 120 suitably chosen Munsell samples. Their chromaticity coordinates were transformed using eight CATs from CIE illuminant C to CIE standard illuminant A. The transformed results were plotted in the CIE u’v’ chromaticity diagram as constant Munsell hue and chroma contours for adaptation to CIE standard illuminant A. The patterns predicted by different CATs can be divided into two categories, i.e. those derived from aperture-mode and non-aperture-mode experimental data. These were called Types I and II data, respectively. The mean Munsell coordinates from different CATs for these two types are plotted in Fig. 4. This shows that the Type I pattern has a more oblique, or less horizontal orientation compared to Type II pattern. The Type II pattern is more compressed in the yellow to purple direction than the Type I pattern. The figure shows that for Type I data, some saturated colours in the range of the Munsell YR and GY hues can not be matched under CIE standard illuminant A. Takahama, Sobagaki and Nayatani (1978) considered that the Type II results show a higher degree of colour constancy than the Type I results. The non-aperture colours are normally presented by reflecting surfaces such as textile or paint samples. The colour seen depends on the light source used as well as the reflectance values for the surface. Furthermore, these textured surfaces reflect more or less specular reflectances, which provide clues to the colour of illuminant and thereby allowing for more effective "discounting of the illuminant". This is the main reason that the experiments obtained using aperture colours were discarded in the studies carried out by the CIE. Also, since a colour inconstancy index such as CMCCON97, is intended to be used only for surface colours, only results obtained from surface colours should be considered when deriving the index metric.

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v'

0,6

0,5

0,40,1 0,2 0,3 0,4 u'

G

BG

B

PB P

10

6 2

GY Y YR

R

RP

Type I

Type II

YR Y GY

G

BG

0,6

R

0,5

v' B

PB P 10

6 2

RP

0,40,1 0,2 0,3 0,4 u'

Figure 4. Contours of constant Munsell hue and chroma, at value 5, as predicted for adaptation to CIE standard illuminant A by Type I and Type II chromatic adaptation transforms.

Quantitative analysis has also been used to compare the performance between different CATs in fitting different experimental data sets. The method of testing the performance of each transform or model is illustrated in Figure 5. The points E and F represent raw (i.e. not transformed) data for a pair of corresponding colours plotted in any suitable colour space, e.g. CIELAB, or CIE u’v’. These two specimens are perceived the same colour when one is viewed under the reference illuminant and the other under the test illuminant. The point F under the test illuminant is then transformed by a particular transform to point G under the reference illuminant. The points E and G are coincident if there is perfect agreement between the visual and predicted results. The vector EG therefore represents the direction and magnitude of the error in prediction of the transform or model for this pair of colours. The mean or root mean square (RMS) of the distances of vectors EG from a number of corresponding-colour pairs has been used to measure the overall performance of each transform. These are expressed in terms of colour difference (∆E) calculated by a suitable colour difference formula such as CIELAB, or CMC(1:1) (Clarke et al., 1984). For a perfect agreement between the predicted and visual results, these measures should be zero. A larger value means a poorer performance.

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E

F

G

Figure 5. Method for estimating the error of prediction (vector EG) by a chromatic-adaptation transform or colour-appearance model. Points E and F represent a pair of corresponding colours, and point G is the prediction from F.

Bartleson (1979b) derived his transform based upon his own experimental data (Bartleson, 1979a). He also tested his transformation with other experimental data and concluded that his transformation agreed reasonably well with all the sets of data studied and, in many cases, even better than the transformations suggested by the original papers from which the data was drawn.

Lam and Rigg (Lam, 1985) compared 7 CATs using 7 sets of data: Bartleson, Burnham, Wassef, Helson et al. and Lam and Rigg data. The mean CMC(1:1) colour differences are given in Table 2.

The findings are summarised below.

1. The errors of predictions for each CAT are quite large. For example, the least error in Table 2 is predicted by Wassef’s CAT to fit her own data, i.e. 3,3. This suggests that there are large experiment errors included in the experiments for studying chromatic adaptation.

2. The CAT derived from a particular data set normally fits that data set relatively well, i.e. see the figures in bracket in Table 2.

3. The mean measures for Types I and II data for each CAT show a large difference in performance. This confirms Bartleson’s finding that there are two types of data.

4. BFD CAT performs the best for Type II data, followed by von Kries (Helson), CIELAB and Sobagaki et al. the worst.

5. Bartleson’s CAT performs better than Burnham’s CAT for Type I data.

Table 2. Comparison of the RMS errors of prediction of five CATs for seven data sets.

Type I Type II Mean Transform\ Data Bar. Bur. Was. Hel

(W) Hel (G) Hel (B) L&R Type I Type II

Bartleson (5,3) 6,3 11,7 9,6 7,6 9,3 7,6 5,8 9,2 Burnham 8,8 (7,7) 11,0 12,4 10,1 11,7 9,8 8,3 11,0 Wassef 14,0 15,6 (3,3) 14,6 12,3 14,1 12,3 14,8 11,3 Von Kries (Helson) 11,1 13,4 11,2 (7,9) (5,6) (7,9) 5,4 12,3 7,6

BFD 7,1 11,2 10,4 7,9 4,4 6,9 (3,5) 9,2 6,6 Sobagaki et al. 10,8 11,5 11,9 8,6 6,7 8,5 6,4 11,2 8,4

CIELAB 9,2 10,6 11,2 9,3 6,8 8,4 5,4 9,9 8,2

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Note: Bar.: Bartleson, Bur.: Burham, Was.:Wassef, Hel: Helson et al., L&R: Lam and Rigg, (W) (G) (B): White, grey and black backgrounds, respectively.

At a later stage, Luo and Hunt (1998a; 1998b; 1998c) accumulated many data sets to derive CIECAM97s and CMCCAT97. Only those of Type II (without aperture-mode) experimental data were considered. These have already been introduced in the earlier section. (These data sets were described by Luo and Rhodes (1999) and are available on the World Wide Web site at http://colour.derby.ac.uk.) In total, 730 corresponding-colour pairs were gathered. As part of work for CIE TC 1-52 on chromatic adaptation transform, Luo used 11 data sets including 655 pairs of corresponding colours from 8 sources. (The other pairs were not used for studying chromatic adaptation.) These data were used to test 6 CATs, which are potential candidates to become a future CIE standard. The results are summarised in Table 3 in terms of mean CMC(1:1) E units.

Kuo et al. (1995) found that the typical observer variation for studying chromatic adaptation was about 4 CMC(1:1) units. Hence, if a CAT has an error of prediction equal to or less than 4 units, it may be considered to be satisfactory. As shown in Table 3, the most accurate transform for each data set (the value in brackets) is always less than 4 units except for the McCann et al. and Luo et al. (WF) data sets. The 11 data sets are divided into two groups: reflection and non-reflection samples. The Braun and Fairchild, and Breneman data sets are included in the latter group. (Braun and Fairchild data were obtained by comparing between CRT and reflection printed colours, and Breneman data were based on projected transmissive colours.) The weighted mean for each CAT was calculated to represent the performance for each group or overall. The weighted mean was used to take into account the number of corresponding pairs in each data set. The McCann et al. data were gathered using quite abnormal viewing conditions, i.e. a white light source against 4 highly chromatic illuminants at low illuminances. This results in poor observer consistency and all transforms give a poor fit to the experimental results, i.e. all models predicting this data set have almost twice the magnitude of error compared to other data sets. Hence, it was decided to also calculate the weighted means without the McCann data.

For Group 1, the results show that the performance of CATs can be divided into two categories. Category One includes CIECAT94, Sharp, CMCCAT97, CMCCAT2000 and CAT02, and the others are in Category Two. Category One CATs outperformed Category Two CATs by an appreciable margin. The weighted mean colour differences between Category One CATs are small (i.e. less than 1,2 and 0,6 units for the inclusion and exclusion of McCann data set, respectively). This indicates that their performances are very similar. Overall, the CMCCAT2000 performed the best with CMCCAT97 and CAT02 ranked second (only worse by 0,2 CMC(1:1) colour difference units). The table also shows that these three CATs performed the best for all data except for Luo et al. (D50) and Luo et al. (WF) data sets.

Table 3 also shows that there is a large improvement from CIECAT94-old to CIECAT94. This proves that a change of noise factor from 1,0 to 0,1 together with the introduction of the incomplete adaptation factor did improve the performance. CIECAT94 predicted the McCann et al. data more accurately than CMCCAT97, but less accurately than CMCCAT2000.

For Group 2 data, the CIECAT94 outperformed all the models for Breneman data by a large margin. Three CATs (CMCCAT2000, CMCCAT97 and CAT02) fit better than the rest to the Braun and Fairchild data.

Overall, four CATs (CMCCAT2000, CMCCAT97, CAT02 and CIECAT94) performed better than the others and they also gave very similar performance.

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Table 3. The performance of chromatic-adaptation transforms.

Data sets/ Transform

No. of Pairs CIELAB RLAB von

Kries CIECAT94-old

CIECAT94 Sharp CMCCAT

97 CMCCAT

2000 CAT02

Group 1 data: Reflection samples CSAJ-C 87 5,0 5,4 4,1 6,4 4,5 4,1 3,4 3,6 3,4 Helson et al. 59 6,2 5,2 5,1 7,5 5,4 4,0 3,8 3,8 3,8 Lam & Rigg 58 5,0 5,1 5,0 6,7 4,3 3,6 3,4 3,7 3,6 Luo et al. (A) 43 5,6 4,1 5,5 5,8 3,9 4,6 3,9 3,6 3,8

Luo et al. (D50) 44 4,8 3,5 4,1 3,9 4,0 4,0 4,2 4,2 4,2

Luo et al. (WF) 41 4,5 7,0 6,1 4,7 4,7 4,9 4,7 4,8 4,7

Kuo et al. (A) 40 5,6 6,3 5,8 6,8 4,5 4,9 3,6 3,5 3,5

Kuo et al. (TL84) 41 3,3 4,0 3,9 3,4 2,8 3,2 2,8 2,6 2,6

McCann et al. 85 14,6 8,7 14,1 12,8 8,9 13,0 9,7 8,2 9,4

Group weighted mean 6,4 5,6 6,2 6,8 5,0 5,7 4,7 4,5 4,7

Group mean without McCann 5,1 5,1 4,9 5,8 4,3 4,1 3,7 3,7 3,7

Group 2 data: Non-reflection samples Braun & Fairchild 66 5,5 5,6 5,2 6,6 5,0 5,0 3,7 3,6 3,6

Breneman 107 8,2 5,3 8,0 9,1 3,4 7,1 5,6 5,4 5,5 Group weighted mean 7,2 5,4 6,9 8,2 4,0 6,3 4,8 4,7 4,7

Overall weighted mean 6,6 5,6 6,4 7,2 4,7 5,8 4,7 4,5 4,7

Overall mean ex McCann 5,7 5,2 5,5 6,5 4,2 4,8 4,9 4,0 4,0

Note: The bold, underlined italic values indicate the best transform for each data set.

The predicted shifts for the nine CATs in Table 3 and the corresponding experimental shifts from all data were plotted in the CIE a*b* diagram. The Helson et al. data was used to illustrate the transformations to CIE illuminant C from CIE standard illuminant A as shown in Figures 6 and 7. This data set was chosen because it had not been used to derive a particular chromatic adaptation transform. The point where the two vectors cross, and the unmarked end represent experimental results viewed under illuminants A and C, respectively. The "+" symbol represents the predicted chromaticity from one particular transformation. The distance between each corresponding "+" and unmarked end indicates the error of prediction except for CIELAB. For a good agreement between experimental results and a particular transformation, the two vectors should overlap. For perfect agreement between CIELAB and the experimental results, each vector should have a zero length. In other words, the two corresponding colours ought to overlap, i.e. become one single point. As can be seen in Fig. 6 (CIELAB), such perfect agreement was not found. However, there is a clear pattern of colour shift to be found in each figure. That is, the colour shift increases as C* increases.

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CIELAB

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

RLAB

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

von kries

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

CIECAT94-old

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

CIECAT94

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

CMCCAT97

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

Figure 6. Graphical presentation of corresponding a*b* values showing direction and magnitude of the experimental visual results under CIE standard illuminant A and D65, plotted using the point where the two vectors cross and the unmarked end respectively, and predicted shifts plotted using an "+" symbol.

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Note that experimental errors would be expected be random. When a diagram shows a consistent pattern in the errors of prediction of a particular colour region, this is most likely to be due to a fault in the transform. See the example the RLAB diagram at very high and very low b* values.

Fig. 6 shows that there are large differences between the six different CATs in terms of predictive colour shifts. For the RLAB and von Kries transforms, the predictive shifts only move along the a* direction, i.e. red-green shift. Both of them gave reasonable predictions for the low chroma colours, but large predictive errors for high chroma colours. In comparison with CIECAT94-old, CIECAT94 predicted better especially for the low chroma regions. This strongly indicates that the change of the noise factor from 1,0 to 0,1 in the transform, together with the introduction of the incomplete adaptation factor, considerably improved the transform’s performance. CMCCAT97 gave a quite precise prediction for almost all colours with some exceptions in the colourful yellow and blue regions.

Fig. 7 shows the shifts for the other three CATs, CMCCAT2000, CAT02 and Sharp again for the Helson et al. data. It can be seen that in general, the magnitudes and shifts for these colours are very similar to those of CMCCAT97 (see Fig. 6). This is expected because both CMCCAT97 and Sharp were derived to fit Lam and Rigg data set, which was also included together with the other data sets to fit the CMCCAT2000 and CAT02 transforms.

SHARP

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

C M C C A T 20 0 0

-8 0

-

-4 0

-2 0

0

20

40

60

80

1 0

-9 0

-7 0

-5 0

-3 0

-1 0

10

30

50

70

90

a*

b*

CAT02

-80

-60

-40

-20

0

20

40

60

80

100

-90 -70 -50 -30 -10 10 30 50 70 90

a*

b*

(a) (b) (c)

Figure 7. Same as Figure 6 except for only three CATs: a) Sharp, b) CMCCAT2000 and c) CAT02.

6. CONCLUSION

The results reported here summarise the development of chromatic adaptation transforms over the years. Many experimental data sets were also accumulated based upon different experimental techniques. The data sets considered to be most relevant and reliable were selected here to test different CATs. The results show that four CATs gave quite similar performance: CMCCAT2000, CIECAT94, CMCCAT97 and CAT02. In view the considerable experimental error inherent in the experimental data sets, the small differences of their performances in terms of colour difference units and the disagreement as to whether the McCann data should be included, it is not possible to make a recommendation from this TC.

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BARTLESON, C.J., 1979b. Predicting corresponding colors with changes in adaptation. Color Res. Appl. 4, 143-155, 1979.

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FINLAYSON, G.D. and SÜSSTRUNK, S., 2000. Performance of a chromatic adaptation transform based on spectral sharpening. Proc. IS&T/SID 8th Color Imaging Conference, 49-55, 2000.

HELSON, H., JUDD, D.B. and WARREN, M.H., 1952. Object-color changes from daylight to incandescent filament illumination. Illum. Eng. 47, 221-233, 1952.

HUNT, R.W.G., 1952. Light and dark adaptation and the perception of colour. J. Opt. Soc. Am, 42, 190-199, 1952.

HUNT, R.W.G. LI, C.J., JUAN, L.Y. and LUO, M.R., 2002. Further improvements to CIECAM97s. Color Res. Appl. 27, 164-170, 2002.

HUNT, R.W.G., LI, C.J. and LUO, M.R., 2003. Dynamic cone response functions for models of colour appearance. Color Res. Appl. 28, 82-88, 2003.

JUDD, D.B., 1945. Standard response functions for protanopic and deuteranopic vision. J. Opt. Soc. Am. 35, 199, 1945.

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APPENDIX

This appendix is a brief account of the reasons why the TC was unable to reach agreement on which particular chromatic adaptation formula to recommend. The reasons gradually emerged during the TCs deliberations and it is difficult to give an account which fully represents the views of all the members. This appendix is intended to describe the differing points of view, and highlights the factors which must be addressed if any agreement is to be reached in future. Possibly these issues should be addressed when the terms of reference for any new TC in the field is set up.

One group held that for standardisation purposes, for example for using in a Colour Rendering Index, a CAT should be theoretically based (as in the case of CIECAT94-old and CIECAT94. These were originally developed only by considering fundamental physiological mechanisms and various chromatic adaptation effects (chromatic and brightness adaptations), such as changing from CIE standard illuminant D65 to CIE standard illuminant A adaptation, the Helson-Judd, Hunt, and Stevens-Jameson-Hurvich effects, using a single model without changes to its structure or parameters.

Another group held that while a theoretically based CAT is desirable, it is more important that a suitable CAT should work as well as possible, even if it is empirically based and only applicable to a limited range of conditions. Formulae such as CMCCAT2000, CMCCAT97, and CAT02 fall into this category. Although these formulae have a structure which is superficially similar to the Nayatani transform, they differ in theoretically important respects. Each of the cone mechanisms should have non-linear characteristics. The original BFD model was fitted empirically to the Lam and Rigg data and only included a non-linear term for the B response. Later CATs from this family made all the cone responses linear partly to make reverse transformations simpler. These formulae in effect reject the existence of the Helson-Judd effect, at least for the conditions under which they are meant to apply.

Members agreed that for practical purposes a CAT could be developed, at least in part, on an empirical basis to give good agreement between observed and predicted values for appropriate (but limited) experimental conditions. Much of this report concentrates on such work. The disagreement seemed to centre on whether it was appropriate for a CIE TC to recommend such a CAT for standardisation purposes. It should be noted that if such a CAT should ever be recommended, the conditions under which it could be used would need to be carefully specified. (Much of the experimental work described in this report is limited to the CIE standard illuminants D65 and A.)

One feature of the majority of the later models is that they include a parameter to account for incomplete adaptation. For most applications the observers are completely adapted to the conditions. This applies to the colour rendering of light sources, and considerations of the effect of changing from say daylight illumination to tungsten or fluorescent sources when viewing textiles, paints and plastic materials in a normal domestic environment. Any CAT containing an adaptation factor must therefore be considered to be empirical, unless the use of such a factor is strictly limited to appropriate conditions (such as the use of mixed sources when viewing a CRT display).

Most of the experimental data described in the report is limited to viewing conditions involving only two light sources such as D65 and A or D65 and a fluorescent light source at a fixed luminance level. Critics of formulae empirically fitted to such data point out that they are therefore limited in application to these conditions. Proponents claim that these are precisely the conditions which apply for almost all normal viewing. Hence such formulae would be extremely useful in practice. The critics claim that even so such formulae are unacceptable as international standards.

Members of the TC had some doubts as to the reliability and applicability of some of the data sets used to test the various CATs. The LUTCHI data sets are an important part of the experimental data considered by the TC. There are difficulties in extracting pairs of corresponding colours from such data. The raw experimental data consist of visual estimates of hue, lightness, and colourfulness for surface colours viewed under two different light sources. Grids of constant hue etc. were drawn and pairs of corresponding colours deduced from the points of intersection of the grids for the two sources. Critics point out that this procedure is subjective and has been carried out by only one party. They feel that an objective

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method of analysis would be better (Nayatani et al., 2002). However there are many different "objective" methods which could be used.

Many of the data sets are based on experiments using visual colorimeters, and some members had doubts as to how far the conditions in such experiments correspond to normal viewing conditions. The same applies to effects such as the Judd-Helson effect, which is the tendency, in coloured illumination, for light colours to be tinged with the hue of the illuminant, and for dark colours to be tinged with the complementary hue. Does this really apply for observers fully adapted to normal levels of illumination by sources such as daylight and tungsten light? One major application of a chromatic adaptation formula is to quantify the degree of non-colour constancy of surfaces such as paints or textiles. Most observers would accept black paint (reflecting very little light at all wavelengths) as being perfectly satisfactory. The same applies to white paint reflecting close to 100% at all wavelengths. Any change in colour on changing the light source would be considered to be due to the source rather than the paint. Hence a CAT predicting that such a paint would be perfectly colour constant would be preferable to one which predicted a considerable degree of non-colour constancy.