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.     

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.     

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     

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.     

Publications Sponsored by the Colour Measurement Committee-VI

A set of gloss-paint samples exhibiting large (10–25 CIE units) colour differences has been prepared. Visual assessments have been made under different viewing conditions. The results substantiate the view that visual assessments vary markedly with the size of sample and, together with earlier work (2), show that assessments also vary with the size of the colour difference. Thus, colour-difference equations can correlate well with visual assessments only for given conditions. Existing equations apply best to conditions very different from those encountered in industry. It should not be too difficult to develop a more suitable equation for industrial use, given sufficient experimental data obtained under appropriate viewing conditions.     

Colour-difference formulae-recent developments

Although a colour-difference formula should, ideally, be based on a colour appearance model, most formulae in common use are empirically based. Of the many proposed, none are completely satisfactory, but advances have been made in recent years. Bryan Rigg considers the reliability of these newer formulae, concentrating on their surprising dissimilarities with regards to lightness differences.     

A comparison of the colour differences computed using the CIE94, CMC(l:c) and BFD(l:c) formulae

The colour differences computed using three advanced formulae have been compared for numerical standard/sample pairs located at regular intervals throughout the colour space. A ratio method was used to compare the values obtained, so that the regions of the colour space where the greatest disagreements occur could be identified. The level of disagreement between the BFD and the CIE94 formulae was generally lower then that between the CMC and CIE94 formulae. In the latter case, the greatest level of disagreement covered a large part of the colour space, concentrated especially in the orange region. It is recommended that studies of the performance of these formulae in relation to visual assessments are made, for real standard/sample pairs located in this region.     

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.     

Instrumental methods for assessing colour fastness. Part 2 — Staining

In Part 1 of this paper, different fastness formulae for change in colour were compared. In the present report, the same methodology was used to compare different staining formulae. A set of experimental results was used to test the performance of various staining formulae. The constant grade contours for each formula were also calculated. Their patterns were compared and their differences were identified.     

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     

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     

Predicting visual similarity between colour palettes

This work is concerned with the prediction of visual colour difference between pairs of palettes. In this study, the palettes contained five colours arranged in a horizontal row. A total of 95 pairs of palettes were rated for visual difference by 20 participants. The colour difference between the palettes was predicted using two algorithms, each based on one of six colour-difference formulae. The best performance (r² = 0.86 and STRESS = 16.9) was obtained using the minimum colour-difference algorithm (MICDM) using the CIEDE2000 equation with a lightness weighing of 2. There was some evidence that the order (or arrangement) of the colours in the palettes was a factor affecting the visual colour differences although the MICDM algorithm does not take order into account. Application of this algorithm is intended for digital design workflows where colour palettes are generated automatically using machine learning and for comparing palettes obtained from psychophysical studies to explore, for example, the effect of culture, age, or gender on colour associations.     

Investigating the effect of texture on the performance of color difference formulae

To predict the perceived color differences, the effect of the surface texture on the performance of the color difference formulae was investigated. To this end, knitted polyester fabrics with eight different textures were prepared. The fabrics were dyed by seven dyestuffs in five different depths. The selected pairs from the five samples with different depths in each hue covered small to large color differences. The assessed pair of samples had the same texture and hue, but different depths. A panel of 23 observers assessed the color differences of the pairs by gray scale method. The results showed that for the textile samples with different texture structures, the CIEDE2000 (2:1:1) performed the best followed by CMC (2:1:1), CIE94 (2:1:1), and CIELAB with approximately same performance. In addition, the magnitude of color difference influenced the ability of the formulae to predict the visual assessments and the best performance obtained for medium color differences. The comparison between eight different texture groups indicated that the texture structures of the pairs significantly affected the performance of the color difference formulae. For instance, the PF/3 measures obtained for the eight texture groups by CIEDE2000 (2:1:1) color formula could be varied between 21.98 and 33.37 PF/3 units. © 2009 Wiley Periodicals, Inc., Col Res Appl, 2010.     

European practices and philosophy in industrial colour-difference evaluation

A survey has been made of the use and methods of Instrumental colour difference measurement in quality control of colour within Europe. Several colour differnce formulae are in use. The performances of the most used formulae, namely CIELAB, CMC, BFD, M&S, and Datacolor, are compared. The degree of implementation of colour difference measurement in the textile, leather, automobile, and coatings industries is summarised. The use of new computer graphics to ensure continuity of colour from batch to batch and the alternative methods of colour sorting to minimise colour differences between batches are described.     

Modification to the JPC79 Colour–difference Formula

The JPC79 colour–difference formula has represented a substantial improvement over earlier formulae and is being applied successfully in industrial shade passing. Modifications are described which overcome certain problems and, to some extent, simplify the formula. With available experimental data, the modified version performed even better than the original formula. Perceptibility data are fitted better by increasing the JPC79 lightness weighting by a factor of two. The new formula, designated CMC (: c), has the best overall performance of any formula so far published.     

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     

The ULAB colour space

A new colour space, named ULAB, is developed. It is derived from the CIELAB colour space and can be converted to and from CIELAB. Unlike modified CIELAB colour‐difference formulae, ULAB incorporates corrections for lightness, chroma, and hue differences into its colour coordinates. For the small magnitude colour difference data, it shows the performance as good as more complicated formulae such as CIEDE2000. ULAB shows another chance of developing a colour space approximately more uniform than CIELAB. © 2013 Wiley Periodicals, Inc. Col Res Appl, 40, 17–29, 2015     

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.     

Comparison of instrumental methods for assessing colour fastness. Part 1 — Change in colour

Different instrumental methods for assessing change in colour are described. A set of experimental results were used to test the performance of the various formulae and to illustrate the lack of agreement between them and visual results. Each method is based on a different colour-difference formulae. The differences between the formulae are illustrated by plotting constant AE contours for each of the formulae for various colour centres. The areas of colour where the formulae differ most from each other have been identified. The differences between the methods in some areas were very large, up to a factor of five in terms of ΔE, or two full grades of fastness.     

Methods for quantifying metamerism. Part 1ndashVisual assessment

This work forms part of the Society of Dyers and Colourists' CMC Working Group 1 project on metamerism and colour constancy. The aim of the project is to derive reliable indices for predicting metamerism and colour constancy. Some 76 metamers were prepared by dyeing wool with acid dyes. Two experiments were conducted to quantify the degree of metamerism using a grey-scale method. In the first experiment each metamer's colour difference was assessed against a grey scale by a panel of observers under seven light sources. The second experiment was carried out under three sources: D₆₅, A and TL₈₄. Each observer assessed not only the total colour difference as in the first experiment but also the separate lightness, chroma, and hue components. Observer variations were investigated in terms of observer precision, and within-and between-observer errors. Cross-over wavelengths for each metamer were also examined. It was found that intersections tend to converge on three wavelengths for almost all metamers used here, in agreement with previous findings.