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

Simple color appearance model (sCAM) based on simple uniform color space (sUCS)

A new color appearance model named sCAM has been developed, including a uniform color space, sUCS. The model has a simple structure but provides comprehensive functions for color related applications. It takes input from either XYZ D65 or signals from an RGB space. Their accuracy has been extensively tested. sUCS performed the best or second-best to the overall 28 datasets for space uniformity and the 6 datasets for hue linearity comparing the state of the art UCSs. sCAM also performed the best to fit all available one- and two-dimensional color appearance datasets. It is recommended to have field tests for all color related applications.

Parametric effects in color-difference evaluation

An experiment was conducted to investigate three parameters affecting color-difference evaluation on a display: 4 sample sizes (2°, 4°, 10°, and 20°), 2 color-difference magnitudes (4 and 8 CIELAB units), and 2 separations (inclusion or exclusion of the separation line between two colors in a pair). Sample pairs surrounding 5 CIE recommended color centers were prepared. In total, 1120 sample pairs of colors were assessed 20 times using the grey-scale method. The experimental results were used to reveal various parametric effects and to verify the performance of different color matching functions (CMFs) and four color difference formulae and uniform color spaces. It was found that there was little difference in terms of ΔE values calculated using different CMFs for all the color models tested. A parametric formula was proposed to predict three parametric effects for sample pairs having no-separation line: 1) differences in sample size, 2) media (surface and self-luminous colors), and 3) color-difference magnitudes.

Optimizing Parametric Factors in CIELAB and CIEDE2000 Color-Difference Formulas for 3D-Printed Spherical Objects

The current color-difference formulas were developed based on 2D samples and there is no standard guidance for the color-difference evaluation of 3D objects. The aim of this study was to test and optimize the CIELAB and CIEDE2000 color-difference formulas by using 42 pairs of 3D-printed spherical samples in Experiment I and 40 sample pairs in Experiment II. Fifteen human observers with normal color vision were invited to attend the visual experiments under simulated D65 illumination and assess the color differences of the 82 pairs of 3D spherical samples using the gray-scale method. The performances of the CIELAB and CIEDE2000 formulas were quantified by the STRESS index and F-test with respect to the collected visual results and three different optimization methods were performed on the original color-difference formulas by using the data from the 42 sample pairs in Experiment I. It was found that the optimum parametric factors for CIELAB were kL = 1.4 and kC = 1.9, whereas for CIEDE2000, kL = 1.5. The visual data of the 40 sample pairs in Experiment II were used to test the performance of the optimized formulas and the STRESS values obtained for CIELAB/CIEDE2000 were 32.8/32.9 for the original formulas and 25.3/25.4 for the optimized formulas. The F-test results indicated that a significant improvement was achieved using the proposed optimization of the parametric factors applied to both color-difference formulas for 3D-printed spherical samples.

Design of highly perceptible dual-resonance all-dielectric metasurface colorimetric sensor via deep neural networks

Colorimetric sensing, which provides effective detection of bio-molecular signals with one's naked eye, is an exceptionally promising sensing technique in that it enables convenient detection and simplification of entire sensing system. Though colorimetric sensors based on all-dielectric nanostructures have potential to exhibit distinct color variations enabling manageable detection due to their trivial intrinsic loss, there is crucial limitation that the sensitivity to environmental changes lags behind their plasmonic counterparts because of relatively small region of near field-analyte interaction of the dielectric Mie-type resonator. To overcome this challenge, we proposed all-dielectric metasurface colorimetric sensor which exhibits dual-resonance in the visible region. Thereafter, we confirmed with simulation that, in the elaborately designed dual-Lorentzian-type spectra, highly perceptible variations of structural color were manifested even in minute change of peripheral refractive index. In addition to verifying physical effectiveness of the superior colorimetric sensing performance appearing in the dual-resonance type sensor, by combining advanced optimization technique utilizing deep neural networks, we attempted to maximize sensing performance while obtaining dramatic improvement of design efficiency. Through well-trained deep neural network that accurately simulates the input target spectrum, we numerically verified that designed colorimetric sensor shows a remarkable sensing resolution distinguishable up to change of refractive index of 0.0086.

Bayesian approach for developing threshold color-difference models by the strip-pair comparison method

A Bayesian approach alternative to the one used in the strip-pair comparison method for developing threshold color-difference models is presented in this paper. Strip-pair comparison method is based on the construction of color-control strips made of pairs of patches put in contact and ordered by increasing the CIELAB color difference. Observers are required to indicate the number of the pair of patches in every strip for which they begin to perceive a just noticeable color difference. Frequency data obtained, from repeating several times the visual assessment, is recorded to build a Bayesian multinomial logistic regression model, which allows the determination of the coefficients of the color discrimination ellipsoids. The results of the Bayesian approach agree closely with the results obtained to validate strip-pair comparison method for the same theoretical frequency data. The main advantage of the Bayesian approach over many other methods is that it allows a direct analysis of the statistical variability of the estimated parameters by means of confidence intervals and other measures of statistical variability.

Testing uniform colour spaces using colour differences of a wide colour gamut

An experimental dataset, WCG, was assembled. The set includes 416 pairs of samples that surround 28 colour centres and covers a wide colour gamut. The data were used to test the performance of seven colour-difference models, CIELAB, CIEDE2000, CAM16-UCS, DIN99d, OSAGP, and ICTCP, Jzazbz. Colour discrimination ellipses were also fitted to compare the uniformity of the colour spaces. Different versions of the models were derived to improve the fit to the data, including parametric factors, kL, kC, and a power factor. It was found that the kL optimised CAM16-UCS, DIN99d, OSAGP models significantly outperformed the other colour models. In addition, the magnitude of the colour difference had an impact on visual assessment.

Assessment of Camouflage Effectiveness Based on Perceived Color Difference and Gradient Magnitude

We propose a new model to assess the effectiveness of camouflage in terms of perceived color difference and gradient magnitude. The “image color similarity index” (ICSI) and gradient magnitude similarity deviation (GMSD) were employed to analyze color and texture differences, respectively, between background and camouflage images. Information entropy theory was used to calculate weights for each metric, yielding an overall camouflage effectiveness metric. During the analysis process, both spatial and color perceptions of the human visual system (HVS) were considered, to mimic real-world observations. Subjective tests were used to compare our proposed method with previous methods, and our results confirmed the validity of assessing camouflage effectiveness based on perceived color difference and gradient magnitude.

Color difference evaluation for wide-color-gamut displays

With the emerging demand for wide-color-gamut displays, an issue has been raised in which the commonly used color difference formulae or uniform color spaces that were derived based on the data produced in the relatively smaller color gamut could be unreliable for predicting color differences in the highly saturated color regions. A psychophysical experiment was carried out for evaluating color difference at a luminance level of 310cd/m² on a wide-color-gamut display with an approximate DCI-P3 color gamut. Twelve color centers were selected to cover the entire gamut boundary. There were 192 pairs of samples over 12 color centers judged by 18 observers using the greyscale psychophysical method. The data set was used to test the performance of six uniform color spaces and color difference equations, CIELAB, CIEDE2000, CAM02-UCS, J_za_zb_z, IC_TC_P, and nIC_TC_P, a newly revised IC_TC_P formula. The color discrimination ellipses were used to test local and global uniformity of color spaces and compared with previous studies. The results revealed that all formulae improved their performance to have a mean lightness parametric factor of about 0.5. CAM02-UCS significantly outperformed the others in overall, local, and global uniformity. The high-quality visual data set is recommended to evaluate or to derive color difference formulae for WCG applications in the future.

Goniochromatic assessment of gray scales for color change

The dependence of color differences on the illumination and viewing directions for two widely used gray scales for color change (SDCE and AATCC) was evaluated through measuring the spectral bidirectional reflectance distribution function (BRDF) by a gonio-spectrophotometer of metrological quality. Large incidence and viewing angles must be specially avoided using these gray scales because, in these conditions, color differences vary considerably from those established in ISO 105-A02 and ASTM D2616-12. While the visual appearance of the SDCE and AATCC gray scales for color change is similar, our results indicate that their goniochromatic properties are different. Finally, some recommendations regarding observation distance and illumination angle are given to correctly use these gray scales for visual experiments.

Color-difference formula for evaluating color pairs with no separation: ΔENS

All color-difference formulas are developed to evaluate color differences for pairs of stimuli with hairline separation. In printing applications, however, color differences are frequently judged between a pair of samples with no separation (NS) because they are printed adjacently on the same piece of paper. A new formula, ΔE_NS, has been developed for pairs of stimuli with NS. An experiment was conducted to investigate the effect of different color-difference magnitudes using sample pairs with NS. 1012 printed pairs with NS were prepared around 11 CIE recommended color centers. The pairs, representing four color-difference magnitudes of 1, 2, 4, and 8 CIELAB units were visually evaluated by a panel of 19 observers using the gray-scale method. Comparison of the present data based on pairs with NS, and previously generated data using pairs with hairline separation, showed a clear separation effect. A new color-difference equation for the NS viewing condition (ΔE_NS) is proposed by modifying the CIEDE2000 formula. The separation effect can be well described by the new formula. For a sample pair with NS, when the CIEDE2000 color difference is less than 9.1, a larger color difference leads to a larger lightness difference, but has no effect on the chromatic difference. When the CIEDE2000 color difference is greater than 9.1, the effect is the opposite. The new formula is recommended for future research to evaluate its performance in appropriate applications.

Performance of select color-difference formulas in the blue region

The main objective of this work was to test the performance of major formulas for assessment of small suprathreshold color differences in the blue region. The models examined include CIELAB color space based equations, including CIELAB, CIE94, CIEDE2000, CMC (l:c), BFD (l:c), and formulas based on more uniform color spaces, such as DIN99d, CAM02-SCD, CAM02-UCS, OSA-GP, and OSA-Eu in comparison against data obtained via visual assessments. For this purpose, a dataset around the CIE high-chroma blue color center, hereafter called NCSU-B2, was developed. The NCSU-B2 dataset comprised 65 textile substrates and a standard, with a mean ΔE(ab)* color difference of 2.72, ranging from 0.54-5.72. Samples were visually assessed by 26 subjects against the reference gray scale in three separate trials with at least 24 h between assessments. A total of 5070 assessments were obtained. The standardized residual sum of squares (STRESS) index was used to examine the performance of various formulas for this dataset, as well as a previously developed NCSU-B1 low-chroma blue dataset [Color Res. Appl. 36, 27, 2011], and blue centers from other established visual datasets. Results show that formulas based on more recent uniform color spaces provide better agreement with perceptual data compared with models based on CIELAB space.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Performance of CIE LAB-Based Color Difference Formulae under Different Viewing Conditions

In order to investigate the performance of color difference formulae under different viewing conditions 144 pairs of sample around 17 color centers were designed and printed, and then assessed visually under four different viewing condition. STRESS values between the visual color difference and calculated color difference by five CIELAB-based color difference formulae CIELAB, BFD, CMC, CIE94, CIEDE200 were calculated. The result shows that the formulae have the similar performance but CIE94 is the best in all viewing conditions and CIELAB and BFD are the worst. All the color difference formulae have the best performance under illuminant D65 with illuminance of 1000 lx and gray background

Generalization of color-difference formulas for any illuminant and any observer by assuming perfect color constancy in a color-vision model based on the OSA-UCS system

The most widely used color-difference formulas are based on color-difference data obtained under D65 illumination or similar and for a 10° visual field; i.e., these formulas hold true for the CIE 1964 observer adapted to D65 illuminant. This work considers the psychometric color-vision model based on the Optical Society of America-Uniform Color Scales (OSA-UCS) system previously published by the first author [J. Opt. Soc. Am. A 21, 677 (2004); Color Res. Appl. 30, 31 (2005)] with the additional hypothesis that complete illuminant adaptation with perfect color constancy exists in the visual evaluation of color differences. In this way a computational procedure is defined for color conversion between different illuminant adaptations, which is an alternative to the current chromatic adaptation transforms. This color conversion allows the passage between different observers, e.g., CIE 1964 and CIE 1931. An application of this color conversion is here made in the color-difference evaluation for any observer and in any illuminant adaptation: these transformations convert tristimulus values related to any observer and illuminant adaptation to those related to the observer and illuminant adaptation of the definition of the color-difference formulas, i.e., to the CIE 1964 observer adapted to the D65 illuminant, and then the known color-difference formulas can be applied. The adaptations to the illuminants A, C, F11, D50, Planckian and daylight at any color temperature and for CIE 1931 and CIE 1964 observers are considered as examples, and all the corresponding transformations are given for practical use.

A perceptually tuned watermarking scheme for color images

Transparency and robustness are two conflicting requirements demanded by digital image watermarking for copyright protection and many other purposes. A feasible way to simultaneously satisfy the two conflicting requirements is to embed high-strength watermark signals in the host signals that can accommodate the distortion due to watermark insertion as part of perceptual redundancy. The search of distortion-tolerable host signals for watermark insertion and the determination of watermark strength are hence crucial to the realization of a transparent yet robust watermark. This paper presents a color image watermarking scheme that hides watermark signals in most distortion-tolerable signals within three color channels of the host image without resulting in perceivable distortion. The distortion-tolerable host signals or the signals that possess high perceptual redundancy are sought in the wavelet domain for watermark insertion. A visual model based on the CIEDE2000 color difference equation is used to measure the perceptual redundancy inherent in each wavelet coefficient of the host image. By means of quantization index modulation, binary watermark signals are embedded in qualified wavelet coefficients. To reinforce the robustness, the watermark signals are repeated and permuted before embedding, and restored by the majority-vote decision making process in watermark extraction. Original images are not required in watermark extraction. Only a small amount of information including locations of qualified coefficients and the data associated with coefficient quantization is needed for watermark extraction. Experimental results show that the embedded watermark is transparent and quite robust in face of various attacks such as cropping, low-pass filtering, scaling, media filtering, white-noise addition as well as the JPEG and JPEG2000 coding at high compression ratios.

Investigations of suprathreshold color-difference tolerances with different visual scales and different perceptual correlates using CRT colors

In order to investigate the performance of suprathreshold color-difference tolerances with different visual scales and different perceptual correlates, a psychophysical experiment was carried out by the method of constant stimuli using CRT colors. Five hue circles at three lightness (L*=30, 50, and 70) and chroma (C*ab=10, 20, and 30) levels were selected to ensure that the color-difference tolerances did not exceed the color gamut of the CRT display. Twelve color centers distributed evenly every 30 degrees along each hue circle were assessed by a panel of eight observers, and the corresponding color-difference tolerances were obtained. The hue circle with L*=50 and C*ab=20 was assessed with three different visual scales (DeltaV=3.06, 5.92, and 8.87 CIELAB units), which ranged from small to large visual scales, while the remaining hue circles were observed only with the small visual scale. The lightness tolerances had no significant correlation with the hue angles, while chroma and hue tolerances showed considerable hue angle dependences. The color-difference tolerances were linearly proportional to the visual scales but with different slopes. The lightness tolerances with different lightness levels but the same chroma showed the crispening effect to some extent, while the chroma and hue tolerances decreased with the increment of the lightness. For the color-difference tolerances with different chroma levels but the same lightness, there was no correlation between the lightness tolerances and the chroma levels, while the chroma and hue tolerances were nearly linearly proportional to the chroma levels.

Performance of recent advanced color-difference formulas using the standardized residual sum of squares index

The standardized residual sum of squares (STRESS) index was used to reevaluate four experimental datasets employed during the development of CIEDE2000, the current CIE recommended color-difference formula. This index enables statistical inferences not achievable by other metrics used commonly for performance evaluation. It was found that CIEDE2000 was statistically superior at a 95% confidence level to either CIE94, the previous recommended equation by the CIE, or the simple Euclidean distance in CIELAB, DeltaE*ab. Recent formulas based on the CIECAM02 color-appearance space and chroma-compressed variants of CIELAB were also evaluated and found to have only slightly reduced performance compared with CIEDE2000. These formulas have the advantage of simplicity and easier interpretation when used for quantifying color accuracy. Finally, each experimental dataset was evaluated separately rather than weight averaged as used during the development of CIEDE2000. Significant differences were found between datasets, suggesting that combining datasets may obscure important differences and that the practice of parameter optimization during formula development using combined data is likely suboptimal.

Measurement of the relationship between perceived and computed color differences

Using simulated data sets, we have analyzed some mathematical properties of different statistical measurements that have been employed in previous literature to test the performance of different color-difference formulas. Specifically, the properties of the combined index PF/3 (performance factor obtained as average of three terms), widely employed in current literature, have been considered. A new index named standardized residual sum of squares (STRESS), employed in multidimensional scaling techniques, is recommended. The main difference between PF/3 and STRESS is that the latter is simpler and allows inferences on the statistical significance of two color-difference formulas with respect to a given set of visual data.

Influence of random-dot textures on perception of suprathreshold color differences

We have analyzed the way in which simulated textures made of random dots influence visual suprathreshold color tolerances. We considered 32 textures created by a systematic variation of the following variables: size, number, and color of the dots. Each texture was mapped on the five centers recommended by the International Commission on Illumination (CIE) in 1978 [Color Res. Appl.3, 149 (1978)]. A panel of five experienced observers determined the experimental tolerances using a CRT color monitor by the method of adjustment. At our observation distance, neither small differences in dot size (1 or 4 pixels) nor sparse number of dots (less than 20% of the surface of the sample) changed the tolerances found for homogeneous samples. For the textures that led to statistically significant differences with respect to homogeneous samples, the parametric factors of CIEDE2000 and CIE94 color-difference formulas were fitted. These simulated textures consistently reduced the color difference perceived in a pair or, equivalently, increased the tolerances, mainly (but not only) lightness tolerance. The results demonstrate that it is not simple to provide a unique set of parametric factors for all the potential textures.

Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas

CIELAB-based color-difference formulas are used to improve the prediction of visually perceived color differences through the introduction of various corrections to CIELAB. In our study we analyze the relative importance of these corrections. From the combined dataset employed for the development of CIEDE2000, we found that the improvement of CIE94 over CIELAB was considerably greater than that of CIEDE2000 over CIE94. Chroma-difference correction was the most important correction in both CIE94 and CIEDE2000. With an arbitrary value of 100 assigned to this correction, the score of the hue-difference correction in CIE94 was 21, and the scores of the four remaining corrections in CIEDE2000 were as follows: hue difference, 29; rotation term, 8; lightness difference, 8; and gray correction, 6. At 95% confidence level each of the corrections introduced in CIEDE2000 or CIE94 was statistically significant for the whole combined dataset, in agreement with the results reported by CIE TC 1-47 and 1-29. For the combined dataset, the differences between CMC and CIEDE2000 were found to be statistically significant at 95% confidence level, but the differences between CMC and CIE94 were not. From subsets of the combined dataset it was concluded that further analyses of the lightness-difference and gray corrections proposed by CIEDE2000 would be desirable, using new experimental data.

Digital color imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.

Chromaticity-discrimination thresholds with aperture and object colors: experimental results and predictions of some recent color-difference formulas

Threshold-discrimination ellipses were obtained by three normal observers, at five color centers, by the use of two experimental devices, which provided light-surface colors, and the same method and experimental conditions. The ellipses obtained for each center in both devices were quite similar when the sample distributions were appropriate and slightly smaller for object color than for aperture color. The ellipses predicted by three recent color-difference formulas based on the CIE uniform color space (CIELAB) were compared with those experimentally obtained by us as well as by other researchers who analyzed a greater number of color centers. The color-difference formula proposed by the CIE Technical Committee 1-29 [Color Res. Appl. 18, 137 (1993)] provides the best prediction of the semiaxis relationship for all the experimental datasets used, confirming their good performance in previous works [Appl. Opt. 33, 8069 (1993)], although the differences with respect to the experimental results are higher than those attributable to the interobserver variability.

Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset

The Rochester Institute of Technology-Dupont dataset [Color Res. Appl. 16, 297-316 (1991)] has been used to analyze the uniformity of seven color metrics, developed after CIELUV and CIELAB, with methods similar to those previously applied to several other classical datasets [J. Opt. Soc. Am. A 9, 1247-1253 (1992)]. Significant performance improvements over CIELAB were found with several CIELAB-based metrics, mainly with the model recently proposed by Commission Internationale de L'Eclairage Technical Committee 1-29 [Color Res. Appl. 18, 137-139 (1993)]. Several significant differences found between some pairs of metrics became insignificant when we selected from the Rochester Institute of Technology-Dupont dataset pairs of samples with only chromaticity differences.