Standard Deviate Observer

Transcription

1 1 International Commission on Illumination R1-43 Standard Deviate Observer Report Boris Oicherman Hewlett Packard Laboratories, Haifa, Israel

2 2 Foreword The present report is based on the investigation conducted during the years in the Department of Colour Science in the Leeds University, UK. Full account of this investigation can be found in the PhD thesis of Boris Oicherman (reference 56, available for download at The thesis includes comprehensive literature surveys on number of topics related to the Standard Deviate Observer such as Observer Metamerism, the development of the CIE Standard Deviate Observer, Real World Metamers and Colorimetric Additivity Failures (Sections ). Chapter 3 of the thesis provide detailed description and analysis of the experimental work on large field quasi-symmetric colour matching. The present report is based primarily on the results of the cross-media colour matching experiment, described in details in the Chapter 4 of the thesis.

3 3 Abstract Observer metamerism was investigated in two colour matching settings. One was the classical large-field bipartite field matching with the use of narrow-band lights. The other was the cross-media setup typical for soft-proofing, with the use of reflective stimuli and two types of computer monitors. In the first experiment, five observers made repeated maximum saturation colour matches with a 6 bipartite field, and one observer made similar matches with a 2 field. Variability of colour matching functions within our group of observers was very similar to the variability within the Stiles and Burch colour matching dataset. In the second experiment, eleven observers made repeated cross-media colour matches between two computer displays and surface colour stimuli. Observer metamerism is shown to be an insignificant factor in the variability of colour matches in all colours except neutrals. The properties of distribution of individual judgements suggest that the precision of cross-media colour matches is governed by thresholds of colour discrimination, thus it can be modelled well by advanced colour difference formulae with suitably adjusted parametric coefficients. As the result of our findings, we conclude that:

4 4 1. Additional colour matching data is not required for successful modelling of observer metamerism. Stiles and Burch colour matching dataset for 2 and 10 degrees viewing field provide a reliable and repeatable data for such modelling. 2. Most importantly: Observer metamerism can not be assumed to govern the individual differences in matches in conditions different from quasisymmetric colour matching. Thus, any model based on variability of colour matching functions alone cannot account for variability of colour matching in real-world situations. Recommendation to the CIE We do not recommend investing more resources in the study of variability of quasisymmetric colour matching, and into the development of the Standard Deviate Observer in its present form. Rather, we recommend investing into gaining new knowledge of the practical effect of variations in colour vision in real life situations and, perhaps, forming a CIE Technical Committee on the subject. Introduction Metameric matches happen when two colour stimuli having different spectral power distributions give rise to identical photoreceptor signals. Due to inter-individual variations, eyes of different observers filter light differently on its way to the receptors, and respond differently within the receptors themselves: given the same light entering the

5 5 eye, cones of different observers will produce different signals. The result is that pairs of spectrally-different lights that match in colour to one observer mismatch in varying degrees to another. This exposure of the degree of metamerism is sometimes called observer metamerism. The causes of individual variations in colour matching have been extensively studied. The density of the lens of observers younger than 30 years old varies approximately 25% about the average. 1 In addition the density within the same observer increases with age by approximately 38% from the age of 20 to Estimations of individual variations of density of macular pigment vary in different publications 3-11 in the range of about 40% to 50% about the average. This density may vary as a result of diet, 12 heavy smoking, 13 and possibly ethnicity/geographical location. 14 Due to polymorphism, the peak spectral sensitivity of the cones varies between observers; the shift is estimated to be between 2 nm and 9 nm according to different publications Most of the data relate to the L cones, although some indications exist of polymorphism in the M cones 15,19,25,27 and of a small (<1 nm) shift in the S cones. 28 The relative amounts of L and M cones vary on average within a 4-fold range 29,30, although this kind of variability is not expected to have any effect on colour matching. 31 Variation in the effective optical density of the cones, determined by the length of the outer cone segment and its orientation, were found 32 to contribute to the variability of 2 colour matching functions (CMFs). 33 From analysis of the Stiles and Burch 10 colour matching dataset, it has been suggested 28 that this density varies with a standard deviation of about in a correlated manner in all three photopigments presumably as the

6 6 result of the lengths of the outer segments of all receptors varying to the same degree. Variations in a spectral filter forming an integral part of the cone outer segments could account for some of the individual variations as well, 32 although the authors note that there is no hard evidence of the existence of such a filter. The conditions in which colorimetry is applied in the graphic arts industry are almost always different from the ones in symmetric or quasi-symmetric *34 colour matching experiments in which the variations of colour matching properties are typically studied. In this industry the stimuli are often spatially separated, their sizes vary, and the viewing geometry is not fixed. Compared with the vast amount of accumulated knowledge about the causes and magnitudes of individual variability in colour matching, available research on its implications in conditions relevant to practical colorimetry is almost non-existent. Large variations in Davidson & Hemmendinger (D&H) colour rule judgements are known, which could be partly correlated with the observer s age; 35 these studies could provide an indication of the expected variability in judgments of small adjoining reflective samples. In applications involving comparisons of display and surface colours, i.e. in cross-media colour matching, the stimuli are never adjoining. The few reports of experiments on cross-media colour matching are largely contradictory: according to one, observer metamerism poses no practical problem, 38 while others indicate significant discrepancies between the judgments of different observers, 39,40 reporting individual variation to be on average 2.7 CIELAB units, with maximum as large as 19.7 units. * A quasi-symmetric colour matching setup is an asymmetric setup in which the visual system can be reasonably assumed to behave similarly to the symmetric one; classical bipartite field colour matching is a quasi-symmetric one. Extensive discussion of colour matching configurations can be found in Chapter 5 of reference 34

7 7 The existence of large individual variations in CMFs has motivated the development of statistical models of the uncertainty of colour matching, 41,42 which eventually led to the development of the CIE Standard Deviate Observer (SDO). 43,44 However, the applicability of these uncertainty models to any conditions other than those of symmetric and quasi-symmetric colour matching experiments has never been shown. The CIE SDO itself has failed to be adopted by industry, which could have happened for one or both of the following reasons: a) the standard does not represent the real variations in colour matching 40,45 or, b) it is not needed. The present study was designed to bridge the gap between theory and practice for one particular colour matching setup, relevant mostly to the graphic arts industry: matching the colour of a computer display to an object colour. The questions we ask are: Do individual variations in colour matching functions have any appreciable implications in this setup? How can individual variations in cross-media colour matching be modelled and accounted for? Thus, we report a study in applied colorimetry rather then in a basic colour and vision research. We study and characterise the practical implications of the phenomenon of observer metamerism, rather then the phenomenon itself, and report data and conclusions which can be directly used by field practitioners while, as a by-product, also providing some speculations regarding the underlying vision processes.

8 8 Experimental Rationale The design of the experiment was motivated by the aim of characterising a real-world setup typical of the graphic arts industry, with all its inherent uncertainties,. Thus, we used commercially available industry-standard computer displays and a standard graphic arts viewing cabinet as stimuli generators to achieve a level of metamerism similar to that in practical application. We arranged these as accepted by graphic arts practitioners. Finally, as in the industry, the observers were fully aware of the origins of the stimuli: displays and surface stimuli were clearly identifiable. We are conscious of the possibility of adaptation differences between self-luminous displays and object-colour stimuli, and deal with the subject of adaptation in a separate publication. 46 While maintaining all the uncertainties typical of industrial application, we kept the rest of the uncertainties at the minimum possible in order to allow meaningful data analysis. Thus, we conducted the experiment in as strictly controlled conditions as possible in terms of stimuli configuration and illumination although we realise that such a strict control is often not attainable in industry. The setup The setup (Figure 1) consisted of a viewing cabinet (VeriVide DTP-60) and two computer displays (LaCIE BlueEye IV CRT and LaCIE 321 LCD). The cabinet provided a fluorescent illuminant with a correlated colour temperature of approximately 6000 K. The inner surface of the cabinet was covered with black velvet; the light source was not

9 9 visible. The spectral power distributions of the displays primaries are illustrated in Figure 2. Figure 3 illustrates a metameric match between both monitors and a neutral surface sample with respect to the CIE 1964 Standard Colorimetric Observer. Lighting booth CRT display Test stimulus LCD display Observer Figure 1. Scheme of the experimental setup w/sr/m w/sr/m λ λ A) B) Figure 2. Spectral power distribution functions of the monitors primaries A) LaCIE 321 (LCD); B) LaCIE BlueEye IV (CRT) W/sr/m λ Figure 3. SPD of the grey sample displayed on the LCD and CRT monitors, matching in colour the grey paint sample in the viewing booth for the CIE 1964 Standard Observer. Grey line: paint sample; black solid line: LCD display; black dashed line: CRT display

10 10 Ten paint patches mounted on grey cards produced test stimuli: two achromatic and eight chromatic ones, chosen so they span the CIELAB a*b* plane in hue angle steps of approximately 45 (Figure 4, Table 2) b* a* Figure 4. a*b* projection of CIELAB coordinates of paint samples used as test stimuli L* a* b* White Grey Yellow Brown Magenta Purple Blue Cyan Dark green Bright green Background Table 1. CIELAB coordinates of the paint samples used in the experiment as test stimuli. Calculated from spectroradiometric measurements taken in the cabinet, for the cabinet illuminant and the CIE 1964 Standard Colorimetric Observer. The monitors were arranged at both sides of the viewing cabinet, so that the surface planes of each monitor and of the cabinet were at angles of 45 to each other. The distance between the observer s eyes and the monitors and cabinet was approximately 80 cm. The observers were instructed to turn their head fully to the cabinet or monitor, so

11 11 that the observational angle with all stimuli was normal. It was not possible for the observer to see both monitors simultaneously; however, when looking at one of the monitors the observer could see the cabinet with peripheral vision, and vice versa. The observers wore black shirts during the experiment in order to avoid reflections of their clothing from the monitors surfaces. No light sources operated in the laboratory apart from the two displays and the viewing cabinet. The sizes of all stimuli (monitors and paint sample) corresponded to a viewing angle of 6 at the experimental viewing distance, surrounded by a grey background of approximately The maximum luminance of both monitors was set to 120 cd/m 2. The viewing cabinet was adjusted so that the luminance of the white paint sample was approximately 110 cd/m 2. Eleven observers took part in the experiment: eight males and three females, aged 32 years on average distributed as follows: three observers aged between 24 and 27 years; five observers aged between 31 to 35 years, and three aged between 36 and 38 years. All were colour science postgraduate students experienced in making colour judgements and in performing psychophysical tasks. The observers were screened for colour vision deficiencies by Ishihara pseudoisochromatic plates, 47 a Farnsworth-Munsell 100 Hue Test (FMH), 48 a D&H Color Rule 35 and a device similar to it a Munsell Matchpoint Rule, while all the tests were done in the same viewing cabinet as was used in the colour matching experiment. All the observers passed the Ishihara screening, and scored high in the FMH test without any confusion patterns. With the colour rule tests, however, there were two observers who consistently made matches which were different from the mean of the group. However, in the subsequent analysis of the experimental data, it appeared that these observers made cross-media matches which were not statistically different

12 12 from the group in all colours but neutrals and, in one case, yellow. Therefore the two observers data was not excluded from the analysis. We discuss the subject of the effectiveness of colour-deficiency tests in predicting an observer s ability to make crossmedia matches in more detail elsewhere. 49 Each observer made five repeated matches of each of the ten stimuli, on both displays, using a two-stage procedure: 1. Matching the background. At the beginning of their first session, the observers adjusted the background on both monitors to match in colour the grey background in the viewing cabinet. During this adjustment, a white paint patch was placed in the cabinet. The observer adjusted both the patch and the grey background simultaneously, beginning from black in both monitors, alternating between the two until the entire patch-background stimulus looked identical to the one in the cabinet. At the beginning of each of the following sessions, the observers checked that the background on the monitors still matched that in the cabinet, and did appropriate adjustments if it did not. 2. Establishing the colour match. Each of the paint samples in turn was placed in the viewing cabinet, and the colour of the patch on monitors was reset to black. The observers then altered the colour of the black patch on each of the monitors to match the appearance of the paint sample. All the matches were complete (3D) colour matches the two sides of the match had identical chromaticness and lightness even though the observer was aware that one side was a paint sample in a booth and the other was a self-luminous display.

13 13 The first stage of the above procedure may seem somewhat unusual: the common approach to standardising the viewing conditions would be to set the backgrounds on both monitors to have the same CIE XYZ coordinates as the one in the cabinet, and to present this background to all observers. However, the colour of the monitor background which matches the one in the cabinet for the Standard Observer (i.e. both having the same CIE XYZ values), will not necessarily match for a real observer, and we do not have a means of evaluating the perceptual magnitude of this mismatch. Thus, if the common procedure is implemented, the backgrounds might match to the CIE Standard Observer but mismatch for some or all real observers, thus making the matches subject to possible appearance and adaptation effects. Our procedure aims to achieve individualised standardisation of the conditions. The assumption is that, after the procedure is carried out, the backgrounds of both monitors will visually match that in the cabinet for each individual observer, although not necessarily for the Standard Observer, and that adaptation effects due to the background colour will thus be the same in all three stimuli. In the second stage, the observers established an asymmetric match between the patch on the monitor and the paint sample in the cabinet. The match began always from black, thus observers did not have clues to the correct adjustment. The observers were instructed to begin the matching with the LCD monitor; this choice is arbitrary, with the sole purpose of standardising the conditions for all observers. Once the match between the LCD and the viewing cabinet was established, observers turned over to the CRT monitor and adjusted its colour to match the same paint sample. The observer kept on alternating between the two monitors until all three stimuli the two monitors and the paint sample looked identical. This process was repeated within each session for each of the ten test

14 14 stimuli. The first match in every session was white, during which the background colour match was also verified. The order of the remaining nine stimuli was randomised in each of five sessions of every observer. A Minolta CS-1000 telespectroradiometer (TSR) was used throughout this study for taking radiometric measurements of the stimuli. The performance of this instrument in resolving the SPD of narrow-band lights was evaluated by comparing its measurements of the transmittance of nine 10 nm bandwidth interference filters spanning the visual spectrum with ones taken at 1 nm intervals by a Bentham TSR, equipped with a Bentham D300 single monochromator with 1 nm bandwidth and with a Bentham DH-3 detector, calibrated against an SRS8 luminance gauge (NPL traceable) and a CL-Hg mercury lamp (NIST/NBS). The mean wavelength error at the filters peaks was 1 nm with maximum of 2 nm. The mean difference between the areas under the transmittance curves of the same filter taken with the two instruments was 3.5%. Radiometric measurements of the matches on both monitors were taken on the same day upon completion of the observation sessions. The paint samples in the viewing cabinet were monitored on a daily basis also by radiometric measurements. Hence, all the results reported herein are based on direct measurements of the stimuli, and are independent of the characterisation and calibration state of the monitors. Specification of variability of judgments Due to the relevance of this study to practical colorimetry, we express our results in units and metrics that are known and intuitively understood by colorimetry practitioners.

15 15 Colour stimuli in this paper are specified by their CIELAB L*a*b* coordinates 50 calculated for the CIE 1964 Standard Colorimetric Observer 51 and the viewing cabinet illuminant. The variability of the individual judgments is evaluated using the method pioneered by Wright, 52 whereby matches made by different observers are plotted in the diagram of a reference observer (CIE 1964). For every data point, the distance from the mean match is representative of the colour difference that the reference observer would see when presented with the test sample and the individual observer s match. Full statistical specification of variability in CIELAB space takes the form of a 3 3 covariance matrix. As a summary, it is possible to express it in familiar units of colour difference as the Mean Colour Difference From Mean (MCDM). 53 If C i is a set of n 3D vectors containing CIELAB measurements of the same colour stimulus, the dispersion of these values about the mean is computed as MCDM = n i= 1 E ( Ci, C) n (1) where ΔE() is any chosen CIELAB-based formula, and C is the mean vector of CIELAB values. The calculation of MCDM as an alternative to full covariance matrix analysis assumes perceptual uniformity of the chosen colour difference formula: that the standard deviation is identical in all the directions, i.e. the distribution of colours about the mean is spherical in the micro-space defined by the E formula in the region of C. However, the CIELAB

16 16 space has a well-known problem of non-uniformity: equal distances have different perceptual meaning in different locations in the space. No alternative Euclidian colourdifference space exists; however, an advanced, non-euclidean colour difference formulae 54 has been proposed: CIEDE2000, or ΔE 00. In the course of the data analysis, we soon realised that ΔE 00 is a better descriptor of our results than ΔE ab. An example in support of ΔE 00 is Figure 5, where the mean intraobserver variations are illustrated. In Figure 5A), the bars show MCDM calculated with the ΔE ab formula; the values vary with test colour in a range of approximately units for both displays. In Figure 5 B), the bars show MCDM calculated with ΔE 00 ; the heights are nearly identical, with a range of only units MCDM MCDM White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green Test colour Test colour A) B) Figure 5. Intra-observer variability for each test colour. A) CIELAB units B) CIEDE2000 units. Black: LCD, Grey: CRT. The intra-observer variability in our experiment is governed by the ability of a single observer to detect colour differences between the paint and the monitor stimuli, and to minimise these differences until they are not detectable. This process is governed by the observer s colour discrimination limitations: where no difference is discriminable no

17 17 adjustments need to be made and the match can be accepted. These discrimination limitations, or the criteria that observers use in match-mismatch decisions, are likely to be independent of the test colour: there is no reason to assume that larger in perceptual terms colour differences will be tolerated in some colours than in others. This is what is meant by perceptual uniformity, and what the results calculated by the ΔE 00 formula illustrated in Figure 5 express: the variability of matches within individual observers data is constant throughout the perceptually-uniform colour space. This also means that the formula is applicable to viewing conditions significantly different from ones utilised in the course of its development. Thus, in this publication, the variability values are reported in units of ΔE 00 (also denoted as CIEDE2000) values unless otherwise stated. The statistical analysis and calculation of confidence ellipses was done using the full covariance matrix specification. The CIEDE2000 formula was used in the full four-term form. Calculation of lightness differences was done by setting the hue and chroma differences to zero; calculation of chromaticness differences was done by setting lightness differences to zero. Results and discussion Intra- and inter-observer variability Intra-observer variability characterises the ability of a single observer to repeat the same match; we evaluated it using the data from the five repeated matches made by each observer for each test stimulus. Inter-observer variability characterises differences in matches made by different observers; we evaluated it from the variations between the mean matches of all eleven observers.

18 18 Expectedly, colour matches made by different observers vary more than repeated matches made by individuals. Unexpectedly, this difference is almost entirely due to variations in lightness matching. As illustrated in Figure 6, this effect is pronounced in the LCD and in the CRT results to the same degree. 3.0 MCDM00(a*b*) MCDM(L*) White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green A) B) 3.0 MCDM(a*b*) MCDM(L*) White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green White Grey Yellow Brown Magenta Purple Blue Cyan Dark Green Bright Green C) D) Figure 6. Comparison of intra- and inter-observer variability in dimensions of chromaticness and lightness. A) Chromaticness, LCD; B) Lightness, LCD; C) Chromaticness, CRT; D) Lightness, CRT. Black bars: intra-observer; grey bars: inter-observer. This is surprising, because the variations between observers in our setup were believed to result from observer metamerism, which, in turn, is mostly due to variations in optical properties of the lens and macular pigment. These variations affect mostly the response of the S cones, and have almost no effect on lightness; thus the behaviour observed here is the complete opposite of that expected. In order to investigate this finding further, we computed two sets of covariance matrices: one representing the mean intra-observer variability combining the results from both monitors, and another representing the inter-

19 19 observer variability between the eleven observers, again combining the results from both monitors. These were used to construct 95% confidence ellipses in the CIELAB a*b* chromaticity diagram. Both sets of ellipses are superimposed in Figure 7. With the exception of yellow, the ellipses corresponding to the same test stimuli almost coincide, illustrating that inter- and intra-observer variability in the a*b* plane are qualitatively and quantitatively nearly identical b* a* Figure 7. 95% confidence ellipses in a*b* plane constructed using combined covariance matrices for both monitors. Thick line: intra-observer; thin line: inter-observer. The ellipses are scaled up 5 their real size. This suggests that the inter-observer variability in colour matches in our experimental conditions might not be the result of observer metamerism, for if it were, it would have properties and magnitude substantially different from the intra-observer variability. To state this differently: the factors governing the observer variability in matching spatially separated display and surface colours seem to render the contribution of variations in the

20 20 observers colour matching functions statistically insignificant. This conclusion implies that any model or index of metamerism for change in observer, such as the CIE SDO, 43 is bound to fail when applied to the prediction of inter-observer disagreement in industrial cross-media colour matching because the inter-observer variation is not governed the inter-observer variations in colour matching properties. Hence, it is of interest to try to model the variability that we would expect to have if it was the result of observer metamerism, and to compare it with our experimental results. Comparison with Stiles and Burch dataset Colour matching can be mathematically modelled if the spectral power distribution (SPD) functions of the primary lights and of the test light, and the colour matching functions (CMFs) of the observer are known. In our case, this model would result in an SPD function of the light emitted by the monitor which matches the light reflected by the paint sample for the observer represented by the CMFs. When applied to a set of CMFs belonging to a group of observers, the spread of matches thus constructed would correspond to the magnitude of observer metamerism within this group for a particular metameric pair. Let Q(λ) be the spectral power distribution of the light reflected from the paint sample, R(λ), G(λ) and B(λ) be the SPDs of the monitor primaries, and r ( λ ), g ( λ ) and b ( λ ) be the CMFs; all given in the nm range in 1 nm steps. The tristimulus values of Q(λ) with respect to colour matching functions r ( λ ), g ( λ ) and b ( λ ) are given by

21 21 Q Q Q 780 λ = λ = λ = 380 ( λ ) ( λ ) R = r Q ( λ ) ( λ ) G = g Q ( λ ) ( λ ) B = b Q (2) Tristimulus values of each of the monitor primary lights with respect to the same set of CMFs are calculated similarly: R R R 780 λ = λ= λ = 380 ( λ) ( λ) R = r R ( λ) ( λ) G = g R ( λ) ( λ) B = b R (3) Expressions for the other monitor primaries, G(λ) and B(λ) are similar. Having the tristimulus values of the paint-sample stimulus and of the monitor primaries, the tristimulus values Q(λ) in the tristimulus space defined by the monitor primaries R(λ), G(λ) and B(λ) are given by 1 R R R R G B RQ, M GQ, M BQ, M RQ GQ B Q RG GG B = G RB GB B B (4) where the subscript M in the result vector stands for Monitor. Tristimulus values R Q,M, G Q,M and B Q,M are, by definition, the multipliers of the SPDs of the monitor primaries. Thus, the SPD of the light emitted by the monitor that matches stimulus Q(λ) for an observer having CMFs r ( λ ), g ( λ ) and b ( λ ) is given by

22 22 ( λ ) ( λ ) ( λ ) ( λ ) Q = R R + G G + B B (5) M Q, M Q, M Q, M This modelling assumes that cross-media colour matching is governed by the laws of trichromatic colour matching and is additive. If the inter-observer variabilities in the experimental data and the modelled data are markedly different then these assumptions must be incomplete and the matching in our experiment is not governed strictly by equality of cone signals, and the experimental inter-observer variability is not primarily the result of observer metamerism. Using the described procedure, we constructed, for each paint sample, a set of 47 SPDs for each monitor, each of which would match the colour of the paint sample for one of the 47 individual observers in the Stiles and Burch 55 dataset., We converted the resulting SPDs into CIELAB values, and subjected them to analysis similarly to our own experimental data. The MCDM values are illustrated in Figure MCDM White Grey Yellow Brown Magenta Purple Blue Cyan Dark green Light green Test colour Figure 8. MCDM (CIEDE00) within the modelled colour matching set using Stiles and Burch 47 observers CMF. Black: LCD; grey: CRT. The original data is for 49 observers; two observers were excluded from the analysis due to missing entries The authors wish to thank P. Trezona for providing the set of original NPL colour matching data protocols.

23 23 The mean MCDM values are 0.51 and 0.55 CIEDE2000 units for LCD and CRT respectively, with maximums at 1.16 and 1.25 units for the white test colour in both cases. A breakdown into lightness and chromaticness showed that, as anticipated, observer metamerism has almost no effect on lightness matching. Therefore, it makes sense only to compare the modelled colour matching data with our experimental data in chromaticness. The mean modelled variability is significantly smaller than ours: 0.52 versus 1.24 on average for both displays. The difference is not homogeneous: the variability values for neutrals are very similar, while for the rest of the colour centres the differences are very large. We visualise the comparison of the two sets by examination of confidence ellipses in the a*b* plane (Figure 9). Figure 9. 95% confidence ellipses in the a*b* plane constructed from eleven observers mean matches, superimposed with ellipses constructed for 47 observers CMFs from the Stiles and Burch dataset A) LCD monitor; B) CRT monitor. Experimental matches: grey; Stiles and Burch dataset: black.

24 24 If the Stiles and Burch colour matching dataset is representative of our group of observers, and if the variability of matches made by our observers was governed solely by observer metamerism, our experimental ellipses should have been not substantially different from the Stiles and Burch ones. However, not only are the Stiles and Burch dataset ellipses significantly smaller, but in many cases their shapes and orientations are markedly different. Large differences between the two sets of ellipses can signify one of three possibilities: 1) observer metamerism is an insignificant contributor to variability of cross-media matches, 2) variations in the Stiles and Burch dataset are not representative of variations that exist in the colour matching functions of the colournormal population or 3) the colour matching functions of our observers varied more and in a different manner than those of the colour-normal population. Although we believed the second possibility to be unlikely, we decided to test it as follows. Comparison with physical model of observer metamerism If the variations within the Stiles and Burch set of CMFs are not representative of variations in the colour-normal population this could be due to, for example, mathematical treatment of the original colour matching data, 40 or an unrepresentative pool of observers. Although we have shown elsewhere that the variability in the Stiles and Burch dataset could be reproduced even within a smaller group of observers, 56 it is still of interest to test this possibility by modelling our colour matching experiment without the use of any experimentally-derived CMFs, but using only knowledge of the physiology and optics of the eye.

25 25 Quantal colour matching is guided by the laws of physical optics. Upon entering the eye the light is filtered by the lens and the macular pigment, and is absorbed by the photopigment of the cones. Each of these stages can be mathematically modelled if the light absorbing properties of these substances are known. Knowledge of ranges and distributions of variation of each of the eye elements among colour-normals can be used to introduce a pseudorandom noise which would model the inter-individual variations in colour matching properties. The result is a set of artificially-generated cone fundamental functions, variation within which is representative of variations within the colour-normal population. The modelling process consists of the following stages: 1. Start with a set of standard cone fundamental functions (CFFs) 2. Convert the CFFs to cone absorptance spectra using standard values for lens, macular pigment and photopigment densities 3. Assign new values to the lens, macular pigment and photopigment densities, chosen from a pseudorandomly generated pool of values, all of which are within the limits chosen for the model (Table 2), and are distributed according to the chosen distribution (t-distribution in our case). 4. Convert the cone absorptance to CFF while replacing the standard values by the pseudorandomly-generated ones. The procedure described below is partly based on the formulae published in the CIE TC 1-36 report. 57 Let l ( λ ), m( λ ) and s ( λ ) be the set of CFFs, and D lens (λ) and D mac (λ) be the lens and the macular pigment density spectra respectively. The cone fundamental values are

26 26 corrected for the effect of macular pigment and lens absorption, and are converted to quantum spectra: l C m s C ( λ) C ( λ) ( λ) l = T m = T s = T ( λ) ( ) ( λ ) ( λ) ( λ) ( ) 1 k λ λ lc 1 k λ 1 k λ λ sc mc (6) T is the total transmittance of the prereceptoral filters lens and macular pigment: T ( λ ) ( D ( λ ) + D ( λ )) lens mac = 10 (7) and k lc, k mc, k sc are normalising factors: k k k lc mc sc = max = max = max 1 ( lc ( λ )) 1 ( mc ( λ )) 1 ( sc ( λ )) (8) Calculate the cone absorptance spectra from the corrected fundamentals: ( ) ( ) = log 1 t lc ( ) k α ( ) = log( 1 t mc ( )) ( ) = log( 1 t sc ( )) k α λ λ l l l α λ λ m m mα α λ λ s s sα k (9) Here t i (i = l, m, s) is

27 27 t i Dmax, i = 1 10 (10) and k is a normalising factor: k k k lα mα sα = max = max = max 1 ( αl ( λ )) 1 ( αm ( λ )) 1 ( αs ( λ )) (11) Within limits described below, assign new values to D lens (λ) and D mac (λ), and the absorptance functions α i (i = l, m, s) and shift the wavelength scale to account for a new peak sensitivity wavelength. With the new values assigned, reverse the above calculation procedure to arrive at new cone fundamental functions. The CFFs corrected for prereceptoral absorption are given by l C, new m s C, new C, new ( λ ) ( λ) ( λ ) 1 10 = = = 1 10 αl, new ( λ ) klα Dmax, l, new αm, new ( λ ) kmα Dmax, m, new α s, new ( λ ) ksα Dmax, s, new (12) Here, the subscript new indicates the randomly modified values: α i,new (i = l, m, s) are the cone absorptance spectra shifted on the wavelength scale, and D max,i,new is the modified peak cone maximum density. Lastly, reverse the prereceptoral filtering correction:

28 28 l new m s ( λ) new new ( λ) ( λ) l = T C, new new m = s = Qk lc T ( λ) C, new new Qk T mc C, new new Qk sc ( λ) ( λ) (13) lnew ( λ ), mnew ( λ ) and s λ ( ) λ are the new CFFs, T new (λ) is the new total transmittance of the prereceptoral filters lens and macular pigment, calculated with randomly modified lens and macular pigment density values D lens,new (λ) and D mac,new (λ): T new ( λ) ( Dlens, new ( λ) + Dmac, new ( λ) ) = 10 (14) We used the Stockman and Sharpe 58,59 CFFs for 10, with their estimation of cone peak density of 0.38, 0.38 and 0.3 for L, M and S, respectively. We also used the Bone et al. 10 macular pigment density with the peak at 0.095, and the Stockman and Sharpe 59 lens density estimation. The limits within which the model parameters were varied are given in Table 2. Model parameter Variations in location of peak sensitivity of M and L cones Variation of peak cone density Variations ±2 nm σ=0.045 Variations of macular pigment peak density (relative standard deviation) Variations of lens peak density (relative standard deviation) Table 2. Values of variations used in modelling of observer metamerism. 45% 25% Cone maximum density was assumed to vary in a correlated manner in all three types of cones. The type of distribution for the random value generation in all the model elements

29 29 was Student t-distribution. A set of 50 cone fundamental functions generated by the above procedure is illustrated in Figure 10. Figure 10. Set of 50 cone fundamental functions generated using the optical model of variability of colour matching described in the text. We used this set to simulate our colour matching experiment with the paint samples and LCD and CRT monitors primaries in the same way that we used the Stiles and Burch (S&B) data above (Eqs. (2)-(5)). We converted the resulting 50 spectra to CIELAB values. The variability within the simulated set in MCDM terms (CIEDE2000) is illustrated in Figure 11, where it is compared with the corresponding values calculated for the S&B colour matching dataset. The same data are illustrated in the form of 95% confidence ellipses in the a*b* plane in Figure 12.

30 30 MCDM(00) MCDM(00) White Grey Yellow Brown Magenta Purple Blue Cyan Dark green Light green White Grey Yellow Brown Magenta Purple Blue Cyan Dark green Light green Test colour Test colour A) B) Figure 11. Variability within the set of simulated cone fundamental functions compared with the corresponding variability in the Stiles and Burch dataset. A) LCD; B) CRT. Grey: simulated CFF; black: Stiles and Burch dataset. A) B) Figure % ellipses in a*b* plane, constructed from the simulated CFF, compared with the corresponding Stiles and Burch dataset ellipses. A) LCD; B) CRT. Black: Simulated CFF; grey: Stiles and Burch dataset. The ellipses are scaled up 5 their real size. The Stiles and Burch dataset is the result of a colour matching experiment carried out by colour-normal observers. The simulated set is the result of mathematical modelling based on approximate knowledge of variations that exist in the eye optical path, mean density

31 31 estimations and number of gross simplifications about the construction of the eye optical and sensory system. Considering these circumstances, the correspondence between the two sets of data is remarkable: in MCDM terms, the values are within 14% of each other for the LCD data and within 30% for the CRT data. The largest discrepancies are for the neutral and green colours on the CRT monitor, for which MCDM values for the simulated data are significantly smaller than for the S&B data. The 95% a*b* confidence ellipses illustrate that the correspondence is not only quantitative but also qualitative. The orientation and sizes of the LCD ellipses are very similar; in some cases the ellipses of the two sets practically coincide. Even for the CRT ellipses, where the correspondence in sizes is poorer than in LCD, the correspondence in relative shape and orientation is still high. In previous studies of observer metamerism, the color matching functions of the Sties- Burch observers have generally been assumed to be representative of those of the colournormal population. The significant similarity between the results of our simulation based on the Stiles and Burch dataset and our simulation based on an optical model of observer metamerism supports this. Under the further assumption that our group of observers is also representative of the colour normal population, and considering the significant differences between the results of both simulations and our experimental results, we conclude that observer metamerism does not have a significant contribution to the variability of cross-media colour matches in cross-media colour matching.

32 32 Colour difference formulae and variability of colour-matching The short ellipses radii in Figure 7 are almost parallel to the chroma lines, and the long radii are parallel to the hue lines with the exception of blue, where CIELAB has the well known blue hue inconstancy problem. These features are known to characterise the perceptual non-uniformity of Euclidian colour differences in the CIELAB a*b* plane: the sensitivity is highest to hue (h*) differences and lowest to chroma (C*) differences. Advanced, non-euclidian colour-difference formulae have been developed 54,60 to correct for this non-uniformity. As Figure 6(A) illustrates, our experimental observer variability is nearly constant for all colours when expressed in the units of the CIEDE2000 colour difference formula, suggesting that this metric can be used to describe the features of our intra-observer variability. Comparison between our data and the prediction of the formula can be done using the same method of comparing the confidence ellipses in the a*b* plane. One set of ellipses will be that of the mean of eleven observers and both monitors. Another will be the set of loci of constant CIEDE2000 colour difference drawn around the colour centres which coincide with the mean observers matches. Figure 13 illustrates the construction of the locus of constant CIEDE2000 difference. Point A with known coordinates ( a * A coordinates ( a * B * b A ) is the colour centre. The task is to calculate the * b B ) of point B, which is situated on the line passing through A and having angle of α with the a* axis, and such that the colour difference between A and B equals D CIEDE2000 units:

33 33 ( ) E00 A,B = D (15) First, the coordinates of point R are calculated, so that it would lie on the line connecting A and B at the distance of one a*b* unit from A, i.e. ( R) Ea* b* A, = 1 (16) We have: * * R A ( ) a = a + cos α (17) * * R A ( ) b = b + sin α (18) Next the CIEDE2000 colour difference between A and R is calculated: ( ) ( ) E00 A, R = CIEDE2000 A, R (19) Finally, the coordinates of B are calculated as * * B A ( α ) a = a + cos * r (20) * * B A ( α ) b = b + sin * r (21) Where r is equal to D r = E (22) ( A R) 00, Carrying out similar calculations for a number of angles spanning the range results in series of points, all of which are situated at D units of CIEDE2000 colour

34 34 difference from A. We computed covariance matrices for the resulting sets of values, and used them to construct 95% confidence ellipses as usual. The result is shown in Figure 14. Figure 13. Calculation of loci of constant colour difference. See text for details. Figure 14. Combined 95% inter-observer ellipses for both monitors, superimposed with ellipses of constant CIEDE2000 colour difference equal to 1 with parametric coefficients [1 3 1]. Black: experimental ellipses; grey: CIEDE2000 ellipses.

35 35 The fit between the two sets is very good, with some pairs of ellipses almost coinciding (magenta, purple and cyan). The largest difference is between the ellipses for the blue test colour. The parametric coefficients k L, k C and k H in the CIEDE2000 formula were set so visual evaluation showed a good fit. Computational methods exist 61 which allow optimising the parametric coefficients in order to achieve minimum possible mean colour difference between the two sets of ellipses. However, due to the different scope of our study, as well as to a relatively small amount of data and thus a rather approximate nature of the fitting, employing these methods did not seem appropriate. Rather, fitting by visual evaluation sufficed to reach the conclusion that the inter-observer chromaticness variability in our experimental conditions can be modelled by one unit of colour difference calculated with the CIEDE2000 formula, with the chroma parametric coefficient k C set to 3 (i.e. CIEDE2000(1:3:1)). The CIEDE2000 formula was developed based on experiments with non-metameric adjacent stimuli. Rich et al suggested 62 that the orientation of colour-difference ellipses is similar in aperture and surface colour viewing modes for non-metameric adjacent samples. Similarity between our results and CIEDE2000 formula prediction allows extending this statement by suggesting that colour difference ellipse orientation is independent of the extent of spatial separation between stimuli, while sizes of ellipses increase with increasing spatial separation as indicated by rather large parametric coefficient for chroma k C.

36 36 Conclusions The existence of variations in colour matching functions of colour-normal observers, and their consequence observer metamerism is long established and well studied. As any colour match between computer monitor and reflective object is metameric, it seemed reasonable to assume that the inter-observer variations in cross-media colour matches are governed by observer metamerism, and could be modelled by application of models of uncertainty of colour matching 42,44,63,64. However, the CIE Standard Deviate Observer, which was based on these models and on Stiles and Burch colour matching data set, 55 was not adopted by the industry, and has been shown experimentally to underestimate the inter-observer variations. 40,45. The suggested explanations for this failure were exclusion of some of the S&B observers from the analysis which led to the development of SDO, 45 and improper mathematical treatment of the original colour matching data 40. The option that was not suggested previously is that models of variability of symmetric metameric colour matching can be inapplicable to the conditions of asymmetric matching in some typical industrial situations such as soft proofing. A trichromatic colour match is a cone-level event: in conditions of a symmetric colour matching experiment, if signals from three types of cones are identical then the lights which trigger them will match in colour, whatever their spectral power distribution is. In the conditions of quasi-symmetric colour match strict trichromacy can reasonably be assumed to hold in a small bipartite field. 34 It has been suggested that as the size of the bipartite field is increased observers begin to compare signals from postreceptoral chromatic channels rather then cone signals themselves. 65 These postreceptoral signals

37 37 may be influenced by more than simply the signals from the cones in the two areas being compared. In the conditions of strict trichromacy, variability of colour matching properties in the colour-normal population is ultimately characterised psychophysically, by establishing the variability within a set of colour matching functions measured by the pool of observers representative of this population. Moreover, given the knowledge about variability of each of the elements in the eye s optical path, the variability of colour matching can be modelled mathematically. Provided that the knowledge about the eye s properties is complete, the result of the mathematical modelling should be identical to the result of the colour matching experiment with human observers. Both methods of modelling the observer metamerism the psychophysical and the mathematical will successfully predict the variations of matches made by colournormal observers in conditions of symmetric or quasi-symmetric colour matching. Mechanisms operating in asymmetric colour matching are unknown, but they do not seem to be those of direct comparison of cone signals. 66 However, these are the conditions in which the colorimetry is usually applied in graphic arts, where the stimuli are almost always spatially separated. If the mechanisms governing this kind of matching are not the same as those governing quasi-symmetric colour matching, neither of the two methods would successfully predict the spread of judgments made by observers. Colour matching functions can be used to predict the match, but the variability of colour matching functions cannot be used to predict the range of mismatches made by different