The LLAB (l:c) colour model

A new colour model, named LLAB(l:c) is derived. It includes two parts: the BFD chromatic adaptation transform derived by Lam and Rigg, and a modified CIELAB uniform colour space. The model's performance was compared with the other spaces and models using the LUTCHI Colour Appearance Data Set. The results show that LLAB(l:c) model is capable of precisely quantifying the change of colour appearance under a wide range of viewing parameters such as light sources, surrounds/media, achromatic backgrounds, sizes of stimuli, and luminance levels. It had a similar performance as that of the Hunt colour appearance model. The LLAB(l:c) model was also tested using various colour difference datasets. The model gave a similar performance as the state-of-the-art colour difference formulae such as CMC, CIE94, and BFD. This performance is considered to be very satisfactory, and the model, therefore, should be considered for field trials in applications such as colour specification, colour difference evaluation, cross-image reproduction, gamut mapping, prediction of metamerism and colour constancy, and quantification of colour-rendering properties. The model does not give predictions for chroma (as distinct from colourfulness), or for brightness, and it does not include any rod response. © 1996 John Wiley & Sons, Inc.     

Regression analysis to determine the optimum colour tolerance level for instrumental shade sorting

An investigation of the correlation between visual colour assessment and instrumental colour acceptance determination using regression analysis has been carried out. Three colour-difference equations, CIELAB, CMC(2:1) and CIE94(2:1:1), were studied in order to determine which is the best for generating a uniform colour space/microspace for allocating the colour population in shade sorting. Determination of optimum colour tolerance for further shade sorting was also undertaken. Some 1320 pairs of dyed samples distributing around 20 shade standards were measured instrumentally and also evaluated visually by a panel of 32 observers. Percentage rejection was plotted against colour difference and different mathematical regression relationships were then imposed. As a result, both CMC and CIE94 showed better correlation between the two colour assessment methods than the CIELAB colour-difference equation. Consequently, optimum colour tolerance limits were determined for subsequent development of shade sorting, with the findings being equally applicable to colour acceptance (shade passing).     

BFD (l:c) colour-difference formula Part 1ndashDevelopment of the formula

The available experimental data relating to small colour differences between pairs of surface colours have been combined together into sets including perceptibility results and acceptability results. Supplementary experiments have been carried out to enable all the previous visual results to be brought on to a common scale, and to provide extra information when this was considered necessary. A new colour-difference formula, BFD(l:c), has been developed using the combined experimental results. Various aspects of colour differences have been considered in turn to decide the form of formula required, and the constants in the formula have been optimised using the combined perceptibility and acceptability results. The new formula is similar in structure to the CMC(l:c) formula in most respects. However, it was found that a new term was required to take account of the fact that when chromaticity discrimination ellipses calculated from experimental results are plotted in a b space, they do not all point towards the neutral point. The experimental results were not very consistent with respect to possible tilting of discrimination ellipsoids relative to the xy plane. Overall it seems that any such tilting is quite small and in the direction implicit in the CMC and BFD formulae. Experimental results based on both acceptability and perceptibility judgements form part of the same overall pattern except for the weighting of lightness differences relative to hue and chroma differences.     

Investigation of parametric effects using small colour differences

This experiment was carried out to investigate some viewing parameters affecting perceived colour differences. It was divided into eight phases. Each phase was conducted under a different set of experimental conditions including separations, neutral backgrounds, and psychophysical methods. Seventy‐five wool sample pairs were prepared corresponding to five CIE colour centers. The mean colour difference was three CIELAB units. Each pair was assessed by a panel of 21 observers using both the gray scale and pair comparison psychophysical methods. The assessments were carried out using the three different backgrounds (white, mid‐gray, and black) and a hairline gap between the samples. Assessments on the gray background were repeated using a large (3‐inch) gap between the samples. It was found that the visual results obtained from both psychophysical methods gave very similar results. The parametric effect was small, i.e., the largest effect was only 14% between the white and gray background conditions. These visual data were also used to test four colour‐difference formulae: CIELAB, CMC, BFD, and CIE94. The results showed that three advanced colour‐difference formulae performed much better than CIELAB. There was a good agreement between the current results and those from earlier studies. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 331–343, 1999     

Evaluation of the reliability of metameric indices using visual assessment

Fifty-five metameric sample pairs were prepared using computer-predicted recipes from six different colour centres using cotton knit fabric. The colour difference of each sample pair was measured spectrophotometrically and was assessed visually by a panel of observers against a grey scale under three illuminants: reference illuminant D₆₅, test illuminant A and TL84. In general, there was a positive agreement between observers' assessments although there was some variation due to the spread of ages. The results of illuminant-specific special indices, CMC(2:1), were better than others, which included CIELAB, CMC(1:1), CIE94(1:1:1) and CIE94(2:1:1). In general, the performance of these five special indices was acceptable. The results of illuminant-independent general indices failed to show any significant correlation. The effect of residual colour difference under the reference illuminant affected the performance of the special indices to a certain degree, but this was not true of general indices.     

Testing uniform colour spaces and colour‐difference formulae using printed samples

A grey‐scale psychophysical experiment was carried out for evaluating colour differences using printed colour patches. In total, 446 pairs of printed samples were prepared surrounding 17 colour centers recommended by the CIE with an average δE of 3 units. Each pair was assessed 27 times by nine observers. The visual results were used to test some selected more advanced colour‐difference formulae and uniform colour spaces. The results showed that CIELAB and OSA performed the worst, and the advanced formulae and spaces gave quite satisfactory performance such as CIEDE2000, CIE94, DIN99d, CAM02‐UCS, and OSA‐GP‐Eu. The colour discrimination ellipses were used to compare with those of the earlier studies. The results showed that they agreed well with each other. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Performance of lightness difference formulae

There are large variations between different previously published lightness difference experimental data sets. Two hundred and eight pairs of matt and glossy paint samples exhibiting mainly lightness differences were accumulated. Each pair was assessed about twenty times by a panel of fourteen observers using the grey scale method. The results were used to derive a new lightness difference formula (CII), and to a large extent, a possible new CIE lightness difference formula (CMC99). Both formulae were found to be more accurate than the typical deviation of an individual assessment from the mean of a panel of 20 observers, and outperformed the existing formulae using the present data set. The new CMC99 lightness difference formula is integrated into the new CIE colour difference equation CIEDE2000. The results also showed that special attention should be paid to measuring very dark samples. This is caused by poor instrument repeatability and inter-instrument agreement in this colour region.     

Some aspects of the visual scaling of large colour differences

The formulation of a metric to provide numbers that correlate with visually perceived colour differences has proved a very difficult task. Most early experimental work was concerned with just-perceptible colour differences. Later the concept of perceptibility was expanded to acceptability, it being argued that many industrial tolerances were larger than just-perceptible. This led naturally to the concept of large colour differences and the question as to whether the current CIE colour-difference formulae, specified as appropriate for just-perceptible differences, can be applied to larger differences than those concerned with, for instance, colour matches experienced in the fabric dyeing industry. This article investigates the application of four colour-difference formulae to visual scaling of large colour differences between photographically prepared reflection colour samples at approximately constant lightness. It is shown that the scaling of colour differences depends on the directions of hue and chroma differences of a test sample when compared with a reference. It is also shown that, of the four candidate colour-difference metrics, the modified CIE 1976 L*a*b* colour difference, referred to as CIE1994 or , correlates best with visual scaling. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 298–307, 1997     

Colour-difference Measurements in Relation to Visual Assessments in the Textile Field

Two sets of dyeings, each containing six samples, showing slight colour variations about a standard were prepared on bright viscose rayon satin and milled wool cloth, respectively. The two standards were centred in the green with luminance factors of about 10%, and were intended to be approximate and non-metameric matches. In each case the six colourvariations were chosen to be essentially in pairs: brighter-duller; stronger-weaker; andtwo showing a hue difference. In all cases the differences were isomeric about the standard and ranged from one to eight traces. According to industrial procedures and under illumination conforming to BS 950:1967, 32 observers in four organisations assessed visually the colour differences from standard in each set, and the colour differences were measured on 23 different instruments throughout seven organisations, largely on Colormaster and Color-Eye tristimulus colorimeters, but also on other types of colorimeters and on three spectrophotometers. The instrumental results, obtained in the CIE system and with reference to Illuminant C., were converted to single-number colour-difference values by the use of six typical formulae, including the 1964 CIE recommended formula. Reasonable, but not completely satisfactory, agreement was found between observers and between instruments, but the correlation of visual and instrumental results provided by the formulae was poor. Some improvement in instrumental performances should be possible, and a modified method of correlation is needed, which can be achieved satisfactorily for the limited number of colours considered here. However, further work is obviously required.     

BFD (l:c) colour-difference formula Part 2-Performance of the formula

The available experimental data relating to small colour differences between pairs of surface colours have been combined together into two sets including perceptibility results (CP) and acceptability results (CA). A new colour-difference formula, BFD(\:c) has been developed using the combined experimental results. For small colour differences, particularly when perceptibility judgements are involved, the new formula represents a substantial improvement over other fomulae. For large colour-differences the new formula is close to the best available formula. Different 1 values are required for perceptibility and acceptability judgements, and for large colour differences, but c=1 in all cases. The BFD formula gives the best possible results obtainable with currently available data. Analysis shows that results from different studies, including those based on perceptibility and acceptability judgements, are compatible in many respects. Discrepancies that were detected seemed to be due to experimental error, or problems in scaling the visual results. However, there are major differences between the results for small differences between surface colours and those implicit in the Munsell system and MacAdam ellipses.     

Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods

The objectives of this work were to develop a comprehensive visual dataset around one CIE blue color center, NCSU‐B1, and to use the new dataset to test the performance of the major color difference formulae in this region of color space based on various statistical methods. The dataset comprised of 66 dyed polyester fabrics with small color differences ($\Delta E_{{\rm ab}}^* < 5$ ) around a CIE blue color center. The visual difference between each sample and the color center was assessed by 26 observers in three separate sittings using a modified AATCC gray scale and a total of 5148 assessments were obtained. The performance of CIELAB, CIE94, CMC(l:c), BFD(l:c), and CIEDE2000 (K_L:K_C:K_H) color difference formulae based on the blue dataset was evaluated at various K_L (or l) values using PF/3, conventional correlation coefficient (r), Spearman rank correlation coefficient (ρ) and the STRESS function. The optimum range for K_L (or l) was found to be 1–1.3 based on PF/3, 1.4–1.7 based on r, and 1–1.4 based on STRESS, and in these ranges the performances of CIEDE2000, CMC, BFD and CIE94 were not statistically different at the 95% confidence level. At K_L (or l) = 1, the performance of CIEDE2000 was statistically improved compared to CMC, CIE94 and CIELAB. Also, for NCSU‐B1, the difference in the performance of CMC (2:1) from the performance of CMC (1:1) was statistically insignificant at 95% confidence. The same result was obtained when the performance of all the weighted color difference formulae were compared for K_L (or l) 1 versus 2. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2011     

Small and Moderate Colour Differences

In nineteen regions of colour space groups of about 30 samples, differing by small to moderate amounts from one designated as ‘the standard’ were generated by offset printing. Twenty observers estimated the perceived size of each of these differences twice, using cateogry scaling - the judgements were not based on acceptability. The samples were placed, in turn, adjacent to the standard on a middle gray surround, subtended 4d? on the retina, were illuminated with semidiffuse fluorescent light, simulating daylight at about 45d? incidence, and viewed along the normal. The visual data were converted from an ordinal to an interval scale. The samples were measured by abridged spectro-photometry, and CIE coordinates, obtained by integration using the spectral-power distribution of the illumination source and the 1931 2d? standard observer. Colour differences were calculated by eleven formulae and correlated with the visual interval-scale results. The usual low correlation coefficients were found. The data are analysed colour by colour and significant differences are noted. Collectively, the Adams Chromatic Value (ANL AB 40), Saunderson-Milner, and CIE 1976 L*a*b* formulae gave better performances.     

Evaluation of daylight simulators. Part 2; Assessment of the quality of daylight simulators using actual metameric pairs†

This paper discusses two methods for evaluating the quality of daylight simulators, namely the band‐value method specified in British standard BS 950 and the CIE metamerism index method. Six daylight simulators of various types and manufacturers were used for the assessment and a psychophysical experiment was conducted to evaluate the two methods. A range of 70 metameric pairs was assessed by a panel of observers under each of the six simulators and the reliability of their visual results was examined in terms of observer accuracy and repeatability. The visual results were also compared for each pair of simulators to reveal how the results could be affected by using different simulators. The effectiveness of four colour difference formulae was tested using the visual results. Finally, four methods were developed using two statistical measures of performance factor, band‐value deviation and CIE metamerism index for evaluating the quality of daylight simulators.     

Euclidization of the first quadrant of the CIEDE2000 color difference system for the calculation of large color differences

The calculation of colour distances in the first quadrant of the CIEDE2000 space can be realized now after the author succeeded in working out such calculations in the CIE94 and CMC space in preceeding articles. The new system is presented and then the Euclidean line element is established, from which terms are derived for the new coordinates of lightness, hue, and hue angle. The calculations of colour distances are carried out with the new Euclidean coordinates according to a well‐known method and are demonstrated by examples guided by CIE94 and CMC distances from the preceeding articles. Finally, proposals are given for the eventual improvement of the CIEDE2000 formula. © 2005 Wiley Periodicals, Inc. Col Res Appl, 31, 5–12, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20168     

Geometric relations between scales of small colour differences

Varying magnitude of colour differences from threshold up to moderate size in painted sample pairs at five CIE colour centers was estimated by grey scale assessment. Painted samples were produced for constant step width along the main axes of previously determined threshold (x,y,Y)‐ellipsoids with lightness variation at constant (x,y)‐chromaticity starting with threshold length and enlarging it five times for moderate magnitude of colour difference. Pairs were formed for linear extensions along axes and for diagonal combinations at equal step width between axes. The model under test assumes additive linear scale extension in constant proportions of the threshold (x,y,Y)‐ellipsoid for increasing magnitude of perceived colour difference and correlates perceptual main colour characters with main ellipsoid axes. Both assumptions were falsified to some degree: in general, magnitude of colour difference varies differently, though close to linear, and slightly subadditive for the three axes and for the different colour centers; the short (x,y)‐ellipse axis in some cases is not correlated with a perceptual hue vector component, and the main lightness direction sometimes is tilted in relation to the (x,y)‐plane. Three colour‐difference formulae do not provide better global predictions than the local (x,y,Y)‐ellipsoid formulae. The results may be used for more detailed modeling of colour‐difference formulae and for tolerance settings at different ranges of colour difference. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 78–92, 1999     

Uniform colour spaces based on the DIN99 colour‐difference formula

Several colour‐difference formulas such as CMC, CIE94, and CIEDE2000 have been developed by modifying CIELAB. These formulas give much better fits for experimental data based on small colour differences than does CIELAB. None of these has an associated uniform colour space (UCS). The need for a UCS is demonstrated by the widespread use of the a*b* diagram despite the lack of uniformity. This article describes the development of formulas, with the same basic structure as the DIN99 formula, that predict the experimental data sets better than do the CMC and CIE94 colour‐difference formulas and only slightly worse than CIEDE2000 (which was optimized on the experimental data). However, these formulas all have an associated UCS. The spaces are similar in form to L*a*b*. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 282–290, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10066     

Interrelation of the Swiss Colour Atlas (SCA-2541) and the Munsell Color Order System

The CIE tristimulus values of measured Swiss Colour Atlas samples were converted to Munsell notations using a colour notation conversion program. A selected subset of SCA-2541 sample points was chosen: the samples on the fully populated regularly spaced hues 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60. The resulting Munsell notations were plotted onto Munsell Value-Chroma and Hue-Chroma planes and analysed for regularity of spacing and hue distribution around the achromatic axis. An earlier article has detailed the interrelation between the Natural Color System (NCS) and the Munsell Color Order System using similarly constructed charts. Comparison is made with the sample spacing of the NCS and SCA-2541 points when mapped into Munsell colour space, to determine similarities and differences between these two geometrically similar systems; both are double cones forming equilateral triangular constant hue planes. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 111–120, 1997     

The CRI‐CAM02UCS colour rendering index

A new colour rendering index, CRI‐CAM02UCS, is proposed. It predicts visual results more accurately than the CIE CIR‐R_a. It includes two components necessary for predicting colour rendering in one metric: a chromatic adaptation transform and uniform colour space based on the CIE recommended colour appearance model, CIECAM02. The new index gave the same ranks as those of CIE‐R_a in the six lamps tested regardless the sample sets used. It was also found that the methods based on the size of colour gamut did not agree with those based on the test‐sample method. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Evaluation of colour‐difference formulae for different colour‐difference magnitudes

Most of the colour‐difference formulae were developed to fit data sets having a limited range of colour‐difference magnitudes. Hence, their performances are uncertain when applying them to a range of colour differences from very small to very large colour differences. This article describes an experiment including three parts according to the colour‐difference magnitudes: large colour difference (LCD), small colour difference (SCD), and threshold colour difference (TCD) corresponding to mean ΔE values of 50.3, 3.5, and 0.6, respectively. Three visual assessment techniques were used: ratio judgement, pair comparison, and threshold for LCD, SCD, and TCD experiments, respectively. Three data sets were used to test six colour‐difference formulae and uniform colour spaces (CIELAB, CIE94, CIEDE2000, CAM02‐SCD, CAM02‐UCS, and CAM02‐LCD). The results showed that all formulae predicted visual results with great accuracy except CIELAB. CIEDE2000 worked effectively for the full range of colour differences, i.e., it performed the best for the TCD and SCD data and reasonably well for the LCD data. The three CIECAM02 based colour spaces gave quite satisfactory performance. © Wiley Periodicals, Inc. Col Res Appl, 2012