A colour-difference formula for surface colours under illuminant A

The available experimental data for small colour differences between surface colours under illuminant A have been analysed in a manner similar to that used earlier for the comparable results under daylight. Chromaticity discrimination ellipses were calculated from the results for each colour centre. The size of the ellipses varied with chromaticity in an irregular manner suggesting that the visual results for the different centres were effectively on different scales. New experiments, carried out using a grey scale method for the visual assessments, allowed the relative sizes of ellipses to be adjusted. After adjustment the size of the ellipses varied much more systematically with chromaticity. Similar adjustments allowed all the results to be combined together and used to develop a new colour-difference formula suitable for assessments under illuminant A. Values of ΔE from the new formula gave a better fit to the visual results than those from other formulae. Earlier formulae were intended to be used with results for daylight. Using chromatic adaption formulae to transform the illuminant A results to illuminant D₆₅ improved the agreement, but the results were still not as good as those obtained with the new formula.     

The impact of viewing conditions on observer variability for cross‐media colour reproduction

This study investigates observer metamerism in cross‐media colour reproduction (CMCR) between monitor and physical colours. An LCD display was placed inside a viewing cabinet. The cabinet had a mid‐grey interior. Observers were asked to match a colour displayed on the monitor to a printed colour patch, which was also inside the viewing cabinet in two configurations, one consisting of two samples separated by a hairline gap (Configuration 1), and the other consisting of two samples separated by a large gap (Configuration 2). Eleven observers were asked to first match the background colour and then 10 test colours for each configuration, and this was repeated five times. The observers’ variability results showed little difference between inter‐ and intra‐variability, and between the two configurations. Comparing the observers’ results with the CIE 1964 standard colorimetric observer, Configuration 1 and Configuration 2 each showed similar agreement. In both configurations, the results of observer variability were smaller than those obtained by Oicherman et al. in 2008. In addition, each configuration's results showed better agreement with the CIE standard colorimetric observer than Oicherman et al.'s results. This implies that both configurations, one with two samples having a hairline gap and with two samples separated by a large gap in a viewing cabinet, could be recommended for future CMCR systems. However, if choosing between the two, then Configuration 2 is recommended rather than Configuration 1.     

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.     

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.     

Color discrimination results from a CRT device: Influence of luminance

In this article, we report new color discrimination ellipsoids calculated from two normal observers, using a CRT device and five values of luminance at each of the five centers recommended by the CIE in 1978 (Col Res Appl 1978;3:149–151). Our main goal was to test the weighting function for lightness adopted by the CIE94 color‐difference model (CIE Publication 116, 1995). Although some of the experimental conditions employed here (CRT monitor, small size of the visual field, and controlled exposure time) did not fit those recommended by this model, our results support the weighting function for lightness proposed by CIE94. The only robust trends observed in the ellipsoids obtained were a confirmation of Weber's law and a decrease in the area of the x, y chromaticity ellipses, when the luminance of each reference stimulus increased towards the one of the surround. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 38–44, 1999     

Synthetic reflectance curves by additive mixing

A method of producing a reflectance curve for a given set of CIE tristimulus values, based on additive mixing of red, green and blue primaries, is described. Smooth data representing colours having good colour constancy are obtained. The method is computationally efficient, even when a large number of data points is required.     

The quantification of small visual colour differences

The Shademaster system, developed at UMIST, was used to explore the use of on-screen colour in order to assess the reliability of the CMC(l:c) formula as a measurement of small colour differences. Differences limited to almost pure hue, chroma and lightness changes around nine colour centres were judged by a group of ten observers. Each colour difference pair was presented on-screen in the form of a divided tile. The colour difference between each pair was measured using a Bentham telespectroradiometer and by a method using reverse transformation of RGB to CIE coordinates. The resultant measurements were used to determine the visibility of a particular colour difference, how that visibility varied from colour to colour and how it varied in different directions (i.e. hue, chroma or lightness). The data obtained from the judgements were used to construct perceptibility boundaries around each colour centre.     

Mathematical approach for predicting non‐negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non‐negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non‐linear optimization problem. By solving the non‐linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non‐negativity constraint for the TSVs of the corresponding colours. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011     

Optimal yarn colour combination for full‐colour fabric design and mixed‐colour chromaticity coordinates based on CIE chromaticity diagram analysis

It is challenging for textile designers to achieve full‐colour effects in woven fabric using a limited set of coloured yarns. The common problems encountered during full‐colour fabric design include an insufficient number of colours and a failure to match the fabric colour with the desired colour. Using the theories of primary colours and optical colour mixing, we examine the mixed‐colour distribution of primary colour yarns on the basis of the CIE 1976 chromaticity diagram (CIE u′v′). In our experiment, dope‐dyed polyester filament yarns were selected as raw materials. Eight kinds of gradually varied weave structures and four types of primary colour combination were adopted in order to make different types of full‐colour fabric colour chart. Spectrophotometer and DigiEye colour measurement systems were selected to measure the reflectance and colour value of the fabric samples. By comparing the colour distribution of mixed fabrics in the CIE u′v′ diagram, the relationship between the primary colour combinations and the colour distribution of mixed fabrics is discussed. Of RGB, CMY, NCS, and RGBCMY combinations, only RGBCMY resulted in a relatively complete and large colour gamut. Moreover, the colour positions of mixed fabrics in the CIE u′v′ diagram were almost all distributed on or near the connecting line of the primary colour coordinates. The specific colour position of mixed fabrics in the CIE u′v′ diagram were mainly determined by the proportion of primary colours on the fabric surface. In this way, a new method for computing colour position in the CIE u′v′ diagram is introduced.     

On the colours dichromats see

Dichromatic colour vision is commonly believed to be a reduced form of trichromatic colour vision (referred to as the reductionist principle). In particular, the colour palette of the dichromats is believed to be a part of the colour palette of the trichromats. As the light‐colour palette differs from the object‐colour palette, the dichromatic colour palettes have been derived separately for light‐colours and object‐colours in this report. As to light‐colours, the results are in line with the widely accepted view that the dichromatic colour palettes contain only two hues. However, the dichromatic object‐colour palettes have proved to contain the same six component colours which constitute the trichromatic object‐colour palette (yellow, blue, red, green, black and white). Moreover, all the binary and tertiary combinations of the six component colours present in the trichromatic object‐colour palette also occur in the dichromatic object‐colour palettes. Yet, only five of the six component colours are experienced by dichromats as unitary (unique) object‐colours. The green unitary colour is absent in the dichromatic object‐colour palettes. The difference between the dichromatic and trichromatic object‐colour palettes arises from the fact that not every combination of the component‐colour magnitudes occurs in the dichromatic object‐colour palettes. For instance, in the dichromatic object‐colour palettes there is no colour with the strong green component colour. Furthermore, each achromatic (black or white) component colour of a particular magnitude is combined with the only combination of the chromatic components. In other words, the achromatic component colours are bound with the chromatic component combinations in dichromats. © 2012 Wiley Periodicals, Inc. Col Res Appl, 39, 112–124, 2014     

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     

A study of colour emotion and colour preference. Part I: Colour emotions for single colours

This article classifies colour emotions for single colours and develops colour‐science‐based colour emotion models. In a psychophysical experiment, 31 observers, including 14 British and 17 Chinese subjects assessed 20 colours on 10 colour‐emotion scales: warm–cool, heavy–light, modern–classical, clean–dirty, active–passive, hard–soft, tense–relaxed, fresh–stale, masculine–feminine, and like–dislike. Experimental results show no significant difference between male and female data, whereas different results were found between British and Chinese observers for the tense–relaxed and like–dislike scales. The factor analysis identified three colour‐emotion factors: colour activity, colour weight, and colour heat. The three factors agreed well with those found by Kobayashi and Sato et al. Four colour‐emotion models were developed, including warm–cool, heavy–light, active–passive, and hard–soft. These models were compared with those developed by Sato et al. and Xin and Cheng. The results show that for each colour emotion the models of the three studies agreed with each other, suggesting that the four colour emotions are culture‐independent across countries. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 232–240, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20010     

A comprehensive model of colour appearance for related and unrelated colours of varying size viewed under mesopic to photopic conditions

CIE has recommended two previous appearance models, CIECAM97s and CIECAM02. However, these models are unable to predict the appearance of a comprehensive range of colours. The purpose of this study is to describe a new, comprehensive colour appearance model, which can be used to predict the appearance of colours under various viewing conditions that include a range of stimulus sizes, levels of illumination that range from scotopic through to photopic, and related and unrelated stimuli. In addition, the model has a uniform colour space that provides a colour‐difference formula in terms of colour appearance parameters. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 293–304, 2017     

Memory for the color of non‐monochromatic lights

The aim of this work was to explore the limits of memory for the hue of coloured illumination using nonspectral colours. Eighty‐four undergraduate optometry students with normal colour vision as assessed by the Ishihara 38 plate test, were given 10 s to memorize the hue of a luminous surface (luminance 120 cd m^?2), subtending 22 by 18 degrees in an otherwise unlit room. The sample hue was one of 12 samples with chromaticity spaced evenly every 30 degrees around a hue circle in the CIE UCS diagram. The circle, radius 0.06, was centered at the chromaticity of D65 (u′ = 0.198, v′ = 0.468). The hue was displaced randomly by between 40 and 100 degrees, and the participants were required to use one of two keys to return the hue to its original appearance. The keys changed CIE 1976 hue angle (h_uv) by 1 degree, one in a clockwise and the other in a counterclockwise direction, but left the CIE 1976 saturation (s_uv) and the luminance unchanged. Each participant saw the to‐be‐memorized hue once only and made subsequent adjustments without seeing it again. Four adjustments were made immediately, four after 1 h, and a further four after 1 week. The second and the fourth in each set of four were preceded by a clockwise displacement of hue angle and the remaining two by an anticlockwise displacement. The CIE 1976 UCS chromaticity of the standard and the chromaticity of the very first adjustment performed immediately after the presentation of the standard were separated by 0.0210 (s.d. 0.0178) averaged across hues. One hue (purple) was more readily nameable than the others and was more accurately reproduced. There was no evidence of stable individual differences in observers' memory: observers' accuracy in reproducing one colour was not significantly correlated with their accuracy in reproducing another. Adjustments made after an interval of 1 h were worse than those undertaken immediately, but no better than those performed after 1 week. The variability of hue memory under these conditions was similar to the variability of coloured surfaces under common sources of illumination. © 2006 Wiley Periodicals, Inc. Col Res Appl, 32, 11–15, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20281     

The Gamut of Real Surface Colours

A maximum gamut for real surface colours has been derived from the analysis of the colour coordinates of 4089 samples. The gamut has been derived in both the CIE 1976 L* u* v* colour space and the CIE 1976 L* a* b* colour space. The data are compared with the gamut produced by a typical dye set used in a photographic colour paper, and with the gamut of a typical television-receiver display tube. Comparison with printing inks is difficult because of the large number available, but a large set of ink colours was used in deriving the maximum real-colour gamut.     

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     

Comparison of real colour gamuts using a new reflectance database

A large set of data, comprising the spectral reflectances of real surface colours, has been accumulated. The data comprise 16 groups with different materials and include 85,879 measured spectra. From these data, CIELAB colorimetric coordinates were calculated under CIE illuminant D50 and the CIE 1931 standard colorimetric (2°) observer. Several published colour gamuts including those developed by Pointer and ISO reference colour gamut [ISO Graphic Technology Standard 12640‐3:2007] were compared using the present data set. It was found that the Pointer gamut is smaller than the new real data in most of the colour regions. The results also showed that the ISO reference colour gamut is larger than the new real accumulated data in most regions. The present finding indicates that there is a need to derive a new colour gamut based on the newly accumulated data for common applications. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 442–451, 2014     

Spectral power distributions for the CIE stimuli

The CIE reference colour stimuli, X, Y, and Z, were derived by constructing a triangle outside the R,G,B triangle and outside the area bounded by the spectrum locus and the purple line. By this means, all colours, including monochromatic ones, have positive tristimulus values. The colour‐matching functions are the relative quantities of these stimuli required to be mixed additively to match the equal energy monochromatic colours. The stimuli are not realizable as light sources, and the CIE has not specified their spectral power distributions. There is an infinite number of spectral power distributions whose properties meet the prerequisites for X (X = 100, Y = 0, Z = 0), Y (0, 100, 0), and Z (0, 0, 100), and two possible sets have been calculated by different methods. These curves could be used as primary red, green, and blue lights in additive mixing to produce synthetic reflectance curves, which are useful in the specification of on‐screen colours, and as a means of producing colour constant standards. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 478–482, 2001     

The mapping of a surface of constant visual depth in CIELAB colour space†

Independent visual assessments of depth by a panel of four professional colourists were made on dyeings prepared along eight hue directions in CIELAB colour space. From the assessments made, the variation of lightness with chroma for dyeings of uniform depth was mapped along the hue directions. An algorithm was developed to determine the lightness on the surface for any colour of given chroma and hue angle. Whilst direct comparison with the surface defined by the Christ formula for 1/1 standard depth was not possible, it was found that qualitatively the shapes of the two surfaces were very similar. The Christ formula defined greater increases in lightness with chroma in the yellow and lime‐green regions than the surface obtained in this work, which may be due to an inconsistency of depth of the 1/1 standard depth samples in this region, as indicated by other depth formulae.     

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