Are chroma tolerances dependent on hue‐angle?

Relationships between suprathreshold chroma tolerances and CIELAB hue‐angles have been analyzed through the results of a new pair‐comparison experiment and the experimental combined data set employed by CIE TC 1–47 for the development of the latest CIE color‐difference formula, CIEDE2000. Chroma tolerances have been measured by 12 normal observers at 21 CRT‐generated color centers L*₁₀ = 40, C*_ab,10 = 20 and 40, and h_ab,10 at 30° regular steps). The results of this experiment lead to a chroma‐difference weighting function with hue‐angle dependence W_CH, which is in good agreement with the one proposed by the LCD color‐difference formula [Color Res Appl 2001;26:369–375]. This W_CH function is also consistent with the experimental results provided by the combined data set employed by CIE TC 1–47. For the whole CIE TC 1–47 data set, as well as for each one of its four independent subsets, the PF/3 performance factor [Color Res Appl 1999;24:331–343] was improved by adding to CIEDE2000 the W_CH function proposed by LCD, or the one derived by us using the results of our current experiment together with the combined data set employed by CIE TC 1–47. Nevertheless, unfortunately, from the current data, this PF/3 improvement is small (and statistically nonsignificant): 0.3 for the 3657 pairs provided by CIE TC 1–47 combined data set and 1.6 for a subset of 590 chromatic pairs (C*_ab,10>5.0) with color differences lower than 5.0 CIELAB units and due mainly to chroma. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 420–427, 2004; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/col.20057     

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     

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.     

A shift of the perceptual attributes of color due to the manifestation of the simultaneous contrast effect on a display

This research shows the effect of simultaneous contrast on a design solution that generates it, and it also shows how its manifestation affects the shift of perception attributes of the observer's color. In the conducted research, 55 subjects had to harmonize the primary stimuli from the reproduction obtained with the help of digital printing technology, with the primary stimuli presented on two computer screens. As a visual harmonization technique, simultaneous binocular harmonization was used. The primary stimuli were made achromatic, with a 50% Raster Tone value (RTV), and are surrounded by achromatic secondary stimuli whose values increase in steps from 10% RTV up to 100% RTV. A shift in the perceptual attributes of color has been shown with the help of the CIEDE2000 system. Using ANOVA with repeated-measures and Fisher's post hoc analysis, statistically significant differences were found between the perceived means of shift in the ΔC₀₀ chroma and ΔL₀₀ lightness on defined samples on both computer screens, while in the case of the ΔH₀₀ hue, no statistically significant differences were observed. The research also determined colorimetric differences in the ΔE₀₀ color difference. Moreover, the student's t test was used to determine that the effect is stronger when manifested on the Lenovo computer than on the Asus computer screen (P < .05).     

The perception of static colored noise: Detection and masking described by CIE94

We present psychophysical data on the perception of static colored noise. In our experiments, we use the CIE94 color difference formula to quantify the noise strength and for describing our threshold data. In Experiment 1 we measure the visual detection thresholds for fixed pattern noise on a uniform background color. The noise was present in one of three perceptual color dimensions lightness (L*), chroma (C*), or hue (h). Results show that the average detection threshold for noise in L* is independent of hue angle and significantly lower than that for noise in C* or h. Thresholds for noise in C* and h depend on hue angle in an opponent fashion. The measured detection thresholds, expressed in terms of the components ΔL*/k_LS_L, ΔC*/k_CS_C, and ΔH*/k_HS_H that build up the CIE94 color difference formula are used to tune CIE94 to our experimental conditions by adjusting the parametric scaling factors k_L, k_C, and k_H. In Experiment 2, we measure thresholds for recognizing the orientation (left, right, up, down) of a test symbol that was incremental in L*, C*, or h, masked by supra‐threshold background noise levels in L*, C*, or h. On the basis of the CIE94 color difference formula we hypothesized (a) a constant ratio between recognition threshold and noise level when the test symbol and background noise are in the same perceptual dimension, and (b) a constant recognition threshold when in different dimensions. The first hypothesis was confirmed for each color dimension, the second however, was only confirmed for background noise in L*. The L*, C*, h recognition thresholds increase with increasing background noise in C* or h. On the basis of some 16,200 visual observations we conclude that the three perceptual dimensions L*, C*, and h require different scaling factors (hue dependent for C* and h) in the CIE94 color difference formula, to predict detection threshold data for color noise. In addition these dimensions are not independent for symbol recognition in color noise. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 178–191, 2008     

Testing CIELAB‐based color‐difference formulas

The CMC, BFD, and CIE94 color‐difference formulas have been compared throughout their weighting functions to the CIELAB components ΔL*, ΔC*, ΔH*, and from their performance with respect to several wide datasets from old and recent literature. Predicting the magnitude of perceived color differences, a statistically significant improvement upon CIELAB should be recognized for these three formulas, in particular for CIE94. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 49–55, 2000     

Evaluation of the crispening effect using CRT‐displayed colour samples

In this study, the crispening effect was clearly observed when 38 neutral‐coloured sample pairs with only lightness differences were assessed under 5 neutral backgrounds of different lightness values. The sample pairs are CRT‐based colours, and they are selected along the CIELAB L* axis from 0 to 100. The magnitude of colour difference of each pair is 5.0 CIELAB units. The visual assessment results showed that there is a very large crispening effect. The colour differences of the same pair assessed under different backgrounds could differ by a factor of up to 8 for a sample pair with low lightness. The perceived colour difference was enlarged when the lightness of a sample pair was similar to that of the background. The extent of crispening effect and its quantification are discussed in this investigation. The performances of five colour‐difference equations were also tested, including the newly developed CIEDE2000. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 374–380, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20045     

Comparison of the metrics between the CIELAB and the DIN99 uniform color spaces using dental resin composite material values

The sizes for the perceptible or acceptable color difference measured with instruments vary by factors such as instrument, material, and color‐difference formula. To compensate for disagreement of the CIELAB color difference (ΔE^*_ab) with the human observer, the CIEDE2000 formula was developed. However, since this formula has no uniform color space (UCS), DIN99 UCS may be an alternative UCS at present. The purpose of this study was to determine the correlation between the CIELAB UCS and DIN99 UCS using dental resin composites. Changes and correlations in color coordinates (CIE L*,a*, and b* versus L₉₉, a₉₉, and b₉₉ from DIN99) and color differences (ΔE^*_ab and ΔE₉₉) of dental resin composites after polymerization and thermocycling were determined. After transformation into DIN99 formula, the a value (red–green parameter) shifted to higher values, and the span of distribution was maintained after transformation. However, the span of distribution of b values (yellow–blue parameter) was reduced. Although color differences with the two formulas were correlated after polymerization and thermocycling (r = 0.77 and 0.68, respectively), the color coordinates and color differences with DIN99 were significantly different from those with CIELAB. New UCS (DIN99) was different from the present CIELAB UCS with respect to color coordinates (a and b) and color difference. Adaptation of a more observer‐response relevant uniform color space should be considered after visual confirmation with dental esthetic materials. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 168–173, 2006     

Evaluation of performance of various color‐difference formulae using an experimental black dataset

The objective of this study was to develop a specific visual dataset comprising black‐appearing samples with low lightness (L* ranging from approximately 10.4 to 19.5), varying in hue and chroma, evaluating their visual differences against a reference sample, and testing the performance of major color difference formulas currently in use as well as OSA‐UCS‐based models and more recent CAM02 color difference formulas including CAM02‐SCD and CAM02‐UCS models. The dataset comprised 50 dyed black fabric samples of similar structure, and a standard (L*= 15.33, a* = 0.14, b* = ?0.82), with a distribution of small color differences, in ΔE^*_ab, from 0 to approximately 5. The visual color difference between each sample and the standard was assessed by 19 observers in three separate sittings with an interval of at least 24 hours between trials using an AATCC standard gray scale for color change, and a total of 2850 assessments were obtained. A third‐degree polynomial equation was used to convert gray scale ratings to visual differences. The Standard Residual Sum of Squares index (STRESS) and Pearson's correlation coefficient (r), were used to evaluate the performance of various color difference formulae based on visual results. According to the analysis of STRESS index and correlation coefficient results CAM02 color difference equations exhibited the best agreement against visual data with statistically significant improvement over other models tested. The CIEDE2000 (1:1:1) equation also showed good performance in this region of the color space. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 589–598, 2014     

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     

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.     

CIE94-a new colour-difference formula*

The Commission Internationale de I'Eclairage (CIE) has recently published a new colour-difference formula, called CIE94, for use in industrial pass/fail colour-difference work. It is based in CIELAB colour space but on the CMC(l:c) colour-difference formula. In this paper the history behind the development of the new formula is outlined, before the formula itself is described and compared with the CMC(l:c) formula. The role of future work in this area is briefly reviewed and the attitude of the Society's Colour Measurement Committee to CIE94 is outlined.     

Different transformation methods between CIELAB coordinates and Munsell hue

This research aims to convert CIE L*C*_abh_ab coordinates into corresponding Munsell hues. Different transformation methods for colour mapping from CIELAB colour space to Munsell hues are proposed. Polynomial equations that predict Munsell hue from CIELAB h_ab suffer from poor performance as there is no direct one‐to‐one mapping. Polynomial methods that predict Munsell hue from all three L*C*_abh_ab values also show limited performance. However, a distance‐weighted look‐up‐table model based upon the CIEDE2000 colour‐difference equation is able to predict Munsell hue to an accuracy of 1 unit of root mean square error. All transformation methods in this paper were developed using CIE illuminant C and the 2° standard observer conditions and were based on 2729 Munsell renotation colour samples.     

Vector-based modelling of colour difference: a pilot study of the DE2000 colour difference model

A novel approach to colour difference modelling is presented whereby for any given CMC (1:1) or CIE DE2000 ∆E, ∆C, ∆H, and ∆L colour difference, the equivalent CIE XYZ, L*a*b*, and L*C*h coordinate changes are derived by optimising the input RGB stimuli from which they are all calculated. Single-dimension L or C or H difference loci expressed in DE2000 difference units are thus generated, and the additive equivalence of tristimulus values is likewise projected forward onto each locus and also onto a set of CIE DE2000 three-unit ellipse boundaries. Using the datasets thus generated, it is then shown firstly that the derived ellipses have well-defined semi-axes, which explain the detailed orientation of the MacAdam ellipses in x,y,Y space. Unit CIE DE2000 difference is confirmed as a successful quantifying constant of visual difference over a wide range of chroma, hue, and lightness differences. As a constant, CIE DE2000 unit difference is shown to have a significantly variable value at high and low chroma: evidence is established for systematic changes in both chroma and hue difference sensitivity. A hitherto unresolved non-linearity is revealed in the C* dimension of L*C*h space that is not replicated in the CIE DE2000 model. The derived difference loci appear to specify physically reproducible experimental stimuli that could be used in the estimation of visual difference magnitude. Overall, the data derived by the new approach and presented in this paper increase the probability that a true vector model of the visual difference response may eventually be derived.     

On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines

There is reasonable agreement between the orientation of the major axes of the a*b* tolerance ellipses in the blue region and the slope of the tritanopic confusion lines passing through their centers. This agreement includes some experimental facts such as the approximate constant orientation of the ellipses when the luminance of the center changes and the clockwise rotation of the major axis of the ellipses when the luminous source D65 is replaced by A. However, the tilts predicted by the tritanopic lines do not follow the pattern proposed by the CIEDE2000 color‐difference formula; in particular, for the blue‐green centers with hue angles lower than 255°, the high tilts predicted by the tritanopic lines are quite different. From 132 ellipses previously reported, we found that the orientations of the 17 ellipses in the blue region (255° < h < 320°) were similarly predicted by both CIEDE2000 and the tritanopic confusion lines (average error of 12.2° in absolute value). © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 180–184, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10053     

Improving k La determination in fungal fermentation,taking into account electrode response time

An alternative way for determining the oxygen mass transfer coefficient, k_La, based upon the traditional dynamic method, is proposed. The oxygen material balance equation in the liquid phase is integrated after insertion of the oxygen probe response time (first order type), and k_La values are determined by employing Marquardt's algorithm, considering as a weighting factor the model's sensitivity with respect to k_La. Bench‐scale fermentations of Aspergillus awamori, performed under different agitation (300–700 rpm) and aeration conditions (0.2–0.6 vvm), were utilized for calculating k_La values (0.0283–0.0874 s⁻¹), employing three methods: two so‐called traditional, the gas balancing and the dynamic methods, and the one proposed here. The latter method is shown to be as reliable as the aforementioned methods but is easier to apply when the oxygen level in the reactor is above the critical value. © 2000 Society of Chemical Industry     

Evaluation of colour difference formulae

Values obtained by using five colour difference formulae in a set of 106 pairs of textile samples are compared with visual assessments. These included not only total colour difference, but also their psychophysical components (lightness, chroma and hue differences). Visual data used for the comparisons are the average from more than eight observers' assessments, carried out under standardised conditions by means of the grey scale method. Linear regression calculations show that the new CIEDE2000 formula gives similar results to the CMC(2:1) formula, with the differences between correlation coefficients not being statistically significant. The application of performance factors helps to ascertain the superiority of these two formulae over the other three tested. This is valid not only for total colour difference, but also for its individual components.     

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     

Mass transfer properties of bubble columns suspending immobilized glucose oxidase gel beads for gluconic acid production

The volumetric gas-liquid oxygen transfer coefficient, k_L a, and the liquid–solid coefficient, k_S, were measured in a 6.7 L external loop airlift bubble column (ELBC), a 2.5 L internal loop airlift (ILBC) and a 2.5 L normal bubble column (NBC) by the steady state method proposed previously using the oxidation of glucose with air catalyzed by glucose oxidase, GO. For an improved and simultaneous determination of k_L a and k_S, GO was entrapped in calcium alginate gel beads together with fine palladium particles instead of catalase to decompose the hydrogen peroxide produced. The gas holdup, ?_G, in each type of bubble column and the liquid circulation velocity, u_L, governing ?_G in the ELBC were also measured to correlate the data on k_La according to the previous correlations proposed for a larger scale of the ELBC, ILBC and NBC. The data on k_L a, k_S, ?_G and u_L (only for the ELBC) in the reaction system were compared to each other for the three types of bubble columns. The results are well predicted by the previous correlations.     

Colour metrics for image edge detection

Image edge detection based on low-level feature is usually performed on gray-scale images. Some methods have been developed for edge detection on colour images based on low-level feature, but they are not consistent with human colour perception. This research provides a new algorithm for edge detection based on the “HyAB” large-colour-difference formula. This algorithm uses Sobel operators for gradient-magnitude calculations and Canny methods for localizing edge points. The performance of the new algorithm is qualitatively compared with Sobal and Canny methods using some challenging colour images. The results indicate that gradient magnitudes are best calculated using the HyAB colour-difference formula, and that CIELAB and CIEDE2000 differences are not suitable for this purpose. Definition of gradient magnitudes according human perception is essential in applications such as quality control of fabric printing, calculation of disruptive colouration, and so on. The new algorithm is successful in accuracy and fine edge detection in comparison with the Sobel and Canny methods. The new method is quantitatively compared with state-of-the-art methods using three datasets including BSDS500, MBDD, and BIPED. The correctness and accuracy of annotations of images in datasets have an important effect on results. The new method does not reach scores better than deep-learning-based methods, but it is simple and does not need training. It could probably have better results with improving noise-suppression.