Measurement of the relationship between perceived and computed color differences

Bridging instrumental and visual perception with improved color difference equations: A multi-center study

OBJECTIVES

This multicenter study aimed to evaluate visual-instrumental agreement of six color measurement devices and optimize three color difference equations using a dataset of visual color differences (∆V) from expert observers.

METHODS

A total of 154 expert observers from 16 sites across 5 countries participated, providing visual scaling on 26 sample pairs of artificial teeth using magnitude estimation. Three color difference equations (ΔE*ab, ∆E00, and CAM16-UCS) were tested. Optimization of all three equations was performed using device-specific weights, and the standardized residual sum of squares (STRESS) index was used to evaluate visual-instrumental agreement.

RESULTS

The ΔE*ab formula exhibited STRESS values from 18 to 40, with visual-instrumental agreement between 60 % and 82 %. The ∆E00 formula showed STRESS values from 26 to 32, representing visual-instrumental agreement of 68 % to 74 %. CAM16-UCS demonstrated STRESS values from 32 - 39, with visual-instrumental agreement between 61-68 %. Following optimization, STRESS values decreased for all three formulas, with ΔE' demonstrating average visual-instrumental agreement of 79 % and ∆E00 of 78 %. CAM16-UCS showed average visual-instrumental agreement of 76 % post optimization.

SIGNIFICANCE

Optimization of color difference equations notably improved visual-instrumental agreement, overshadowing device performance. The optimzed ΔE' formula demonstrated the best overall performance combining computational simplicty with outstanding visual-instrumental agreement.

New Insights into Wine Color Analysis: A Comparison of Analytical Methods to Sensory Perception for Red and White Varietal Wines

The Glories method and CIE L*a*b* color space are poorly correlated in the light red high-saturation color area. Non-uniformities in the CIE L*a*b* color space have led to the CIEDE2000 formula, while the Euclidean color distance is still used in wine research. In this study, 112 white and red wines were examined to compare the Glories method, CIE L*a*b, and human perception using monovarietal wines from different grape varieties. The objective of this study was to investigate which of the two methods and which parameter of each method better aligned with human perception. The visual color threshold was re-evaluated with the CIEDE2000 formula and triangle testing. CIE L*a*b* more closely matched the human perception, elevating the use of CIE L*a*b* over the use of the Glories method. Visual color thresholds were better expressed with CIEDE2000 but still varied depending upon the color area in the CIE L*a*b* color space.

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.

Brightness Prediction of Large Color Gamut Laser Display Devices

A brightness-perceived color appearance model tailored for large gamut display devices, exemplified by laser displays, was investigated. Psychophysical experiments on the brightness matching of 30 color stimuli with achromatic white light were conducted by 16 observers. The analysis compares the performance of a number of existing color appearance models and equivalent luminance models in predicting brightness. None of the models performed acceptably due to a severe underestimation of the Helmholtz-Kohlrausch (H-K) effect. A modified model of perceived brightness based on CAM16, taking into account the H-K effect, is proposed. Evaluated by psychophysical experiments, the proposed model exhibits a superior performance compared to the preceding models, especially within the extensive color gamut range stipulated by BT.2020. The results help to optimize the design of laser displays with a wide color gamut and high perceived brightness.

A Novel Method for Calibration of Digital Soil Images Captured under Irregular Lighting Conditions

Soil color is commonly used as an indicator to classify soil and identify its properties. However, color-based soil assessments are susceptible to variations in light conditions and the subjectivity of visual evaluations. This study proposes a novel method of calibrating digital images of soil, regardless of lighting conditions, to ensure accurate identification. Two different color space models, RGB and CIELAB, were assessed in terms of their potential utility in calibrating changes to soil color in digital images. The latter system was determined to be suitable, as a result of its ability to accurately reflect illuminance and color temperature. Linear regression equations relating soil color and light conditions were developed based on digital images of four different types of soil samples, each photographed under 15 different light conditions. The proposed method can be applied to calibrate variations in the soil color obtained by digital images, thus allowing for more standardized, objective, and accurate classification and evaluation of soil based on its color.

On the Quantification of Visual Texture Complexity

Complexity is one of the major attributes of the visual perception of texture. However, very little is known about how humans visually interpret texture complexity. A psychophysical experiment was conducted to visually quantify the seven texture attributes of a series of textile fabrics: complexity, color variation, randomness, strongness, regularity, repetitiveness, and homogeneity. It was found that the observers could discriminate between the textures with low and high complexity using some high-level visual cues such as randomness, color variation, strongness, etc. The results of principal component analysis (PCA) on the visual scores of the above attributes suggest that complexity and homogeneity could be essentially the underlying attributes of the same visual texture dimension, with complexity at the negative extreme and homogeneity at the positive extreme of this dimension. We chose to call this dimension visual texture complexity. Several texture measures including the first-order image statistics, co-occurrence matrix, local binary pattern, and Gabor features were computed for images of the textiles in sRGB, and four luminance-chrominance color spaces (i.e., HSV, YC_bC_r, Ohta’s I₁I₂I₃, and CIELAB). The relationships between the visually quantified texture complexity of the textiles and the corresponding texture measures of the images were investigated. Analyzing the relationships showed that simple standard deviation of the image luminance channel had a strong correlation with the corresponding visual ratings of texture complexity in all five color spaces. Standard deviation of the energy of the image after convolving with an appropriate Gabor filter and entropy of the co-occurrence matrix, both computed for the image luminance channel, also showed high correlations with the visual data. In this comparison, sRGB, YC_bC_r, and HSV always outperformed the I₁I₂I₃ and CIELAB color spaces. The highest correlations between the visual data and the corresponding image texture features in the luminance-chrominance color spaces were always obtained for the luminance channel of the images, and one of the two chrominance channels always performed better than the other. This result indicates that the arrangement of the image texture elements that impacts the observer’s perception of visual texture complexity cannot be represented properly by the chrominance channels. This must be carefully considered when choosing an image channel to quantify the visual texture complexity. Additionally, the good performance of the luminance channel in the five studied color spaces proves that variations in the luminance of the texture, or as one could call the luminance contrast, plays a crucial role in creating visual texture complexity.

Metrics of color-difference formula improvement

Metrics of color-difference formula improvement (i.e., standardized residual sum of squares and Pearson product moment correlation) are shown to convey the same information. Furthermore, each metric has two computational forms that assume different linear data models, specifically, with or without an ordinate intercept. It is essential to choose a computational form that matches the data model. We recommend explicitly declaring whether or not the data have been centered, i.e., by subtracting the mean value from each datum, to match the intercept-free data model. Statistical testing of the metrics assumes independent, normally distributed randomness of residuals from the data model, and homogeneous variance. Procedures consistent with these assumptions include robust statistical tests, homogenizing data transformations, and meta-analysis.

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.

No-reference image quality metrics for color domain modified images

Predicting the quality of natural images without using a reference image has always been a challenging task. Numerous approaches have been proposed in the past, but they mainly focused on spatial and frequency domain degradations like blur, noise, and compression. Image quality metrics (IQMs) in literature perform with quite a high accuracy for such types of degraded images. However, their performances are not good on the images modified in the color domain. In this study, psychophysical experiments were conducted to assess the quality of the color domain images. A new dataset was developed for this purpose. Additionally, a second dataset consisting of color domain modified images from the three previously published datasets were used in the psychophysical experiments. The newly developed dataset was then used to develop three IQMs based on absolute values, relative values, and statistical analysis of image color appearance attributes. Their performances were then evaluated together with five spatial domain IQMs from the literature using cross-database evaluation methodology. The results showed that the color-domain IQMs outperformed the other models. The absolute and relative attributes-based models, when combined, achieved the best performance. The present results suggest that more effort is needed to improve the performance of color domain IQMs for image quality estimation.

Effect of observer age and stimulus size on the performance of CIE color matching functions

Both observer age and size of stimulus as characterized using the field of view (FOV) are two important parameters to affect the color matching functions (CMFs) of human observers. They are also included in the cone fundamental and CMFs models that were recently proposed by the International Commission on Illumination (CIE) in 2006. In contrast to the great number of studies investigating the performance of CMFs in characterizing color matches and mismatches using different primary sets, few study investigated the effect of CMFs in characterizing these two factors. In this study, we carefully designed a series of test stimuli in five colors, which had different magnitudes of calculated color difference to the corresponding reference stimulus using the CIE 2006 CMFs model. The stimuli were presented in two FOVs (i.e., 8.6° and 2.9°). A group of young and senior observers were asked to judge which of the two test stimuli appeared to be similar to the reference stimulus, which was a forced choice. The color differences calculated using the CIE 1931 2° and 1964 10° CMFs were found to have higher correlations to the visual color differences judged by the senior and young observers respectively, regardless of the actual FOVs used in the experiment. In addition, though the CIE 2006 CMFs with the different parameter settings always had better performance in predicting the perceived color differences, they failed to characterize the effect of observer age and stimulus size. Also, the experiment results did not support the CIE's recommendation of using the 10° CMFs for stimuli with an FOV greater than 4° and the 2° CMFs for those smaller than 4°.

Influences of shape, size, and gloss on the perceived color difference of 3D printed objects

In order to study the influence and mechanisms of color differences using 3D-shaped objects, 440 pairs of 3D samples surrounding five CIE color centers (gray, red, yellow, green, and blue) with the variations of gloss, size, and shape were prepared by a Sailner 3D color printer, and their color differences were assessed by 26∼45 observers using the gray-scale method. The new color difference data were used to investigate the parametric effects (gloss, 3D shape, and size) on the perceived color difference. Results indicate that, for 3D objects, high gloss and small size objects (2 cm) raise smaller visual color differences than matte and large size objects (4 cm), and the visual color difference of spheres is larger than that of the cone and cylinder sample pairs. The chromaticity ellipses indicated that the glossy samples with different shapes will arouse fairly different visual perceptions, especially for sphere and cylinder samples.

Towards an image-based brightness model for self-luminous stimuli

Brightness is one of the most important perceptual correlates of color appearance models (CAMs) when self-luminous stimuli are targeted. However, the vast majority of existing CAMs adopt the presence of a uniform background surrounding the stimulus, which severely limits their practical application in lighting. In this paper, a study on the brightness perception of a neutral circular stimulus surrounded by a non-uniform background consisting of a neutral ring-shaped luminous area and a dark surround is presented. The ring-shaped luminous area is presented with 3 thicknesses (0.33 cm, 0.67 cm and 1.00 cm), at 4 angular distances to the edge of the central stimulus (1.2°, 6.4°, 11.3° and 16.1°) and at 3 luminance levels (90 cd/m², 335 cd/m², 1200 cd/m²). In line with the literature, the results of the visual matching experiments show that the perceived brightness decreases in presence of a ring and the effect is maximal at the highest luminance of the ring, for the largest thickness and at the closest distance. Based on the observed results, an image-based model inspired by the physiology of the retina is proposed. The model includes the calculation of cone-fundamental weighted spectral radiance, scattering in the eye, cone compression and receptive field post-receptor organization. The wide receptive field assures an adaptive shift determined by both the adaptation to the stimulus and to the background. It is shown that the model performs well in predicting the matching experiments, including the impact of the thickness, the distance and the intensity of the ring, showing its potential to become the basic framework of a Lighting Appearance Model.

CAM18sl brightness prediction for unrelated saturated stimuli including age effects

Modelling the influence of age on the perception of brightness of visual stimuli is an important topic for indoor and outdoor lighting. As people get older, the transmittance of the ocular media becomes lower, especially in the blue wavelength region. This paper reports on an experimental study aiming to evaluate how the brightness perception of red and blue stimuli is affected by the age of the observer. A matching experiment has been set up in which both young (25 years old on average) and older (70 years old on average) adult observers had to match the brightness of a blue stimulus with the brightness of a red stimulus, both surrounded by a dark background (unrelated stimuli). A significant difference in brightness perception between the two groups of observers was found. In particular, older people report a decrease in brightness perception for the blue stimuli compared to younger people. The results show that the brightness correlate of the colour appearance model CAM18sl (applied with zero luminance background) adequately predicts the matching results of young observers, but failed to predict the results obtained by the older observers. As CAM18sl is built on cone fundamentals which include the transmittance of the ocular media and consider the age of the observer as an input parameter, the authors developed the idea to substitute the cone fundamentals for a young observer by the cone fundamentals for a 70 years old observer. This updated CAM18sl performed very well for the older observer as well, on condition that the transmittance of the ocular media is isolated and kept out of the normalization of the cone fundamentals.

Memory colors and the assessment of color quality in lighting applications

Due to their potential use as an internal reference, memory colors may provide an excellent approach for the color rendition evaluation of white light sources in terms of predicting visual appreciation. Because of certain limitations in the design of existing memory-related color quality measures, a new metric based on the outcome of a series of recently conducted memory color appearance rating experiments is proposed in this work. In order to validate its predictive performance, a meta-correlation analysis on a comprehensive set of preference rating data collected from literature is performed. Results indicate that the new metric proposal outperforms established color quality measures and is capable of correctly predicting the rank order of light sources in different lighting scenarios. The future inclusion of this new metric into a comprehensive lighting quality model may serve as a valuable tool for the lighting designer to create optimally lit environments for humans that do not only support the visual task fulfillment but also increase the users' well-being and emotional comfort by rendering the perceived space in such a way that it complies with the people's inherent memory references.

Optimization of the method for color measurement and color-difference calculation of holographic prints with light pillars

To determine the methods of color measurement and color-difference calculation for holographic prints with light pillars, 94 pairs of holographic prints constituted by 17 different products were collected. A set of color-difference comparison experiments was organized by 64 observers with normal color vision, and a total of 86 groups of visual judgments were gathered. The CIELAB and CIEDE2000 color-difference values were calculated on the basis of the analysis of the microstructures of gratings distributed on the holographic paper. The performances of the original formulas were evaluated in terms of the standardized residual sum of squares index, and then they were optimized considering the power function effects (a, b factors) together with a contribution from lightness (k_L factor). Meanwhile, the color-difference threshold of the holographic prints was estimated with a goal to minimize the number of wrong decision in the visual experiment; therefore, the values were set as 2.50 and 2.00 for the original CIELAB and CIEDE2000 with the consistency of 91.5% and 98.9%, respectively. The results can also provide guidance to evaluate the color quality of the holographic prints with light pillars in the packaging and printing industries.

Color-difference evaluation for 3D objects

A psychophysical experiment using 3D printed samples was conducted to investigate the change of perceived color differences caused by two different illuminations and two 3D sample shapes. 150 pairs of 3D printed samples around five CIE color centers [Color Res. Appl. 20, 399-403, 1995], consisting of 75 pairs of spherical samples and 75 pairs of flat samples, with a wide range of color differences covering from small to large magnitude, were printed by an Mcor Iris paper-based 3D color printer. Each pair was assessed twice by a panel of 10 observers using a gray-scale psychophysical method in a spectral tunable LED viewing cabinet with two types of light sources: diffuse lighting with and without an additional overhead spotlight. The experimental results confirmed that the lighting conditions had more effect on the perceived color difference between complex 3D shapes than between 2D objects. The results for 3D and 2D objects were more similar under only diffuse lighting. Current 3D results had good correlations with previous ones [Color Res. Appl. 24, 356-368, 1999; J. Opt. Soc. Am. A 36, 789-799, 2019] using 2D samples with large color differences, meaning that color-difference magnitude had more effect on perceived color differences than sample shape and lighting. Considering ten modern color-difference formulas, the best predictions of the current experimental data were found for CAM02-LCD formula [Color Res. Appl. 31, 320-330, 2006]. For current results, it was also found that predictions of current color-difference formulas were below average inter-observer variability, and remarkable improvements were found by adding power corrections [Opt. Express 23, 597-610, 2015].

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.

ZCAM, a colour appearance model based on a high dynamic range uniform colour space

A colour appearance model based on a uniform colour space is proposed. The proposed colour appearance model, ZCAM, comprises of comparatively simple mathematical equations, and plausibly agrees with the psychophysical phenomenon of colour appearance perception. ZCAM consists of ten colour appearance attributes including brightness, lightness, colourfulness, chroma, hue angle, hue composition, saturation, vividness, blackness, and whiteness. Despite its relatively simpler mathematical structure, ZCAM performed at least similar to the CIE standard colour appearance model CIECAM02 and its revision, CAM16, in predicting a range of reliable experimental data.

Color reproduction method based on neural networks and visual matching

A new method is proposed to build up a color reproduction model based on neural networks and visual matching. Training data were obtained from a visual matching experiment and the commonly used CIECAM02 model to set up a link between the device parameters and human color perception. The process of training neural networks is presented. An experiment simulating an office environment was conducted, together with a user study, to verify the performance of the proposed method in identifying and reproducing color.

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.

Strip-pair comparison method for building threshold color-difference model: theoretical model validation

This paper presents a method for developing color-difference models near a threshold, based on the serial exploration method described by Torgerson [Theory and Methods of Scaling; Wiley & Sons (1958); Chap. 7], involving the construction of color-control strips of patches arranged in arrays of 2 × n, where n is the number of pairs in the strip. The patches in the lower row should be calorimetrically identical, while the color of the patches in the upper row should vary progressively in constant steps of CIELAB color difference along selected color space vector directions. Prospective observers are instructed to indicate the patch pair number for which they begin to perceive a slight color difference between corresponding patches. The frequency data obtained from the observers was used to build a threshold color-difference model. The intention was to validate the method with theoretical data to determine the effect of the precision with which the strips are constructed, on the accuracy of the estimated parameters. Theoretical frequency data was generated using the CIE94 color difference formula, whose associated color discrimination ellipsoid parameters are very easy to determine, associated with a hypothetical logistic psychometric curve for different color centers. The proposed method allows to determine color discrimination parameters with a precision nearby 4% and an accuracy of 3% with respect to the simulated theoretical parameters, for color samples generated with a standard deviation of ΔEab∗=0.2 of the superimposed error around the ideal color difference of pairs of patches.

Parametric effects by using the strip-pair comparison method around red CIE color center

The strip comparison method, based on the serial exploration method described by Torgerson [Theory and Methods of Scaling; Wiley & Sons (1958); Chap. 7], for the development of near-threshold color difference models was presented and validated with theoretical data by the authors in a previous work. In this study, we investigate parametric effects derived from the use of the strip comparison method on chromaticity-discrimination ellipses around the red CIE color center. The results obtained led to the conclusion that the strip comparison method has little effect on the parameters of the chromaticity-discrimination ellipses determined by the pair comparison method when pairs of patches in the strips are separated by a black line 0.5 mm thick or are separated by 3 mm spacing on a white background and also correlates well with the parameters reported by other authors using the pair comparison method at the threshold.

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.

Parametric effects on the evaluation of threshold chromaticity differences using red printed samples

Results from different authors showed deviations of radial orientation in the a^*-b^* plane (tilt) for the major axes of chromaticity-discrimination ellipses centered around the International Commission on Illumination (CIE) red color center [Color Res. Appl.3, 149 (1978)CREADU0361-2317], which are not considered by most of the current advanced color-difference formulas (e.g., CIEDE2000). We performed a visual experiment using red printed samples in order to test the influence of the separation between samples (gap) on the mentioned tilt. Our results confirm a counterclockwise tilt of fitted a^*-b^* ellipses with a magnitude of approximately 36° for samples with no separation, which is similar to that detected by other authors, and a reduction of the mentioned tilt owing to the separation of the samples. We detected a tilt of approximately 22° for samples with a black gap of 0.5 mm and a tilt of approximately 25° for samples with a white gap of 3 mm. Notably, the uncertainty of previous values given by the corresponding credibility intervals of 95% posterior probability is approximately ±8° of the mean values. Finally, we study the performance of the most widely used color-difference formulas in the graphic arts sector using our current experimental results, and conclude that the performance of the CAM02-SCD and CAM02-UCS color-difference formulas is significantly better than that of the CIEDE2000 formula.

Color appearance model for self-luminous stimuli

A model for brightness and hue perception of self-luminous stimuli surrounded by a self-luminous achromatic background has been developed based on a series of visual experiments. In the model, only the absolute spectral radiance values of the stimulus and background are used as input. Normalized cone excitations are calculated using the 10° Commission Internationale de l'Éclairage (CIE) 2006 cone fundamentals. A von Kries chromatic adaptation transform applied in the CIE 2006 cone space is adopted, and luminance compression and adaptation due to the self-luminous background are included by using a Michaelis-Menten function. Model parameters are determined by fitting the model to the experimental visual data obtained for brightness, hue, and the amount of color versus neutral. The model is validated with additional experimental data. An absolute brightness scale expressed in "bright" is proposed.

Comparison of two color-difference formulas using the Bland-Altman approach based on gingiva color space

The objectives of this study were to determine the relationship between the results provided by the classical CIELab (ΔE_ab*) and the CIEDE2000 (ΔE00) formulas and the gingival color space using the Bland and Altman limits of agreement, to use this relationship to establish the equivalences between the gingival color thresholds of perceptibility of both formulas, and to evaluate whether the relationship between ΔE_ab* and ΔE00 is modified depending on the axis in which the changes occur. The means of the L*, a*, and b* coordinates of the 21 gingiva porcelain samples (Heraceram, Heraeus Kulzer Mitsui Chemical Groups) were used and the differences in color were calculated in 210 pairs of samples using the CIELab (ΔE*ab) and CIEDE2000 (ΔE00) color-difference formulas. The results obtained with these formulas were compared and the limits of agreement after a logarithmic transformation of the data were obtained. The relationship between both formulas was ln ΔE₀₀ = - 0.22 + ln ΔE_ab*. The results obtained with the CIELab formula were between 1.01 (95% confidence interval 0.98-1.03) and 1.54 (95% confidence interval 1.52-1.59) times higher than those obtained with the CIEDE200 formula. In the gingiva color space, the scale factor between the CIEDE2000 and CIELab values changes from 0.63 to 1.02, such that providing an accurate scale factor between both values proves difficult. The pairs with the highest ratio were those where the difference in color was mainly due to changes in lightness, whereas the pairs with the smallest ratio were those where the difference in color was mainly due to changes in the blue-yellow or green-red axes.

CIE 2017 color fidelity index Rf: a better index to predict perceived color difference?

The CIE General Color Rendering Index Ra is currently widely and internationally used to assess the ability of white light sources to render colors. But over the past decades, there has been increasing evidence of its limitations. As a result of several years of scientific work, the Commission Internationale de l'Eclairage (CIE) published in April 2017 an updated calculation method. To reduce misinterpretation by users and make a clear distinction with the other aspects of color quality, the color rendering index was renamed color fidelity index (CIE-Rf). Before proposing this index as a new international standard for color fidelity prediction, there is a need for validation. This paper presents a psychophysical experiment designed to address this aim. Twelve observers evaluated color differences of 16 color samples under eight pairs of light sources. 3000K and 4000K light-emitting diodes and fluorescent sources with CIE-Rf values ranging from 64 to 94 were investigated. Results show that the prediction of color differences is significantly better in CAM02-UCS color space than in CIE U^*V^*W^* or CIELAB, whatever the color matching functions. A high correlation was found between perceived color differences and CIE-Rf. This psychophysical experiment did not make it possible to detect significant differences with the other tested color fidelity indices (CIE-Ra, CQS-Qf, CRI2012, CRI-CAM02UCS, and IES-Rf). However, there are some signs of an improvement of the prediction by CIE-Rf in comparison to CIE-Ra. To increase, in further works, the chance to detect potential significant differences between color fidelity indices, some modifications of the experimental protocols are suggested.

White appearance of a tablet display under different ambient lighting conditions

In comparison to the great efforts made on the enhancement of image quality for tablet displays, little attention has been paid on the concept of white point. Given the increasing popularity of the light sources with chromaticities off the Planckian locus and color-tunable LED lighting, it is important to investigate human's white perception of tablet display under different ambient lighting conditions. This study investigated the white appearance of a tablet display under 17 ambient lighting conditions, including a dark condition, seven conditions with chromaticities on the Planckian locus, and nine conditions with chromaticities off the Planckian locus, (i.e., D_uv = + 0.02, -0.02, and -0.04). It was found that both the white appearance boundary defined by the fitted one-standard-deviation error ellipse and the whitest stimulus rated by the observers or identified by the bivariate Gaussian distribution were different under the various ambient lighting conditions. The optimization based on the whitest stimulus under each ambient lighting condition suggested a lower degree of chromatic adaptation under the conditions with a lower Correlated Color Temperature (CCT). For the conditions with a same CCT, a D_uv of -0.02 was found to provide a higher degree of chromatic adaptation than D_uv values of + 0.02 and -0.04.

Perceptually uniform color space for image signals including high dynamic range and wide gamut

A perceptually uniform color space has been long desired for a wide range of imaging applications. Such a color space should be able to represent a color pixel in three unique and independent attributes (lightness, chroma, and hue). Such a space would be perceptually uniform over a wide gamut, linear in iso-hue directions, and can predict both small and large color differences as well as lightness in high dynamic range environments. It would also have minimum computational cost for real time or quasi-real time processing. Presently available color spaces are not able to achieve these goals satisfactorily and comprehensively. In this study, a uniform color space is proposed and its performance in predicting a wide range of experimental data is presented in comparison with the other state of the art color spaces.

Study of chromatic adaptation using memory color matches, Part II: colored illuminants

In a previous paper, 12 corresponding color data sets were derived for 4 neutral illuminants using the long-term memory colours of five familiar objects. The data were used to test several linear (one-step and two-step von Kries, RLAB) and nonlinear (Hunt and Nayatani) chromatic adaptation transforms (CAT). This paper extends that study to a total of 156 corresponding color sets by including 9 more colored illuminants: 2 with low and 2 with high correlated color temperatures as well as 5 representing high chroma adaptive conditions. As in the previous study, a two-step von Kries transform whereby the degree of adaptation D is optimized to minimize the DEu'v' prediction errors outperformed all other tested models for both memory color and literature corresponding color sets, whereby prediction errors were lower for the memory color set. Most of the transforms tested, except the two- and one-step von Kries models with optimized D, showed large errors for corresponding color subsets that contained non-neutral adaptive conditions as all of them tended to overestimate the effective degree of adaptation in this study. An analysis of the impact of the sensor space primaries in which the adaptation is performed was found to have little impact compared to that of model choice. Finally, the effective degree of adaptation for the 13 illumination conditions (4 neutral + 9 colored) was successfully modelled using a bivariate Gaussian in a Macleod-Boyton like chromaticity diagram.

Study of chromatic adaptation using memory color matches, Part I: neutral illuminants

Twelve corresponding color data sets have been obtained using the long-term memory colors of familiar objects as target stimuli. Data were collected for familiar objects with neutral, red, yellow, green and blue hues under 4 approximately neutral illumination conditions on or near the blackbody locus. The advantages of the memory color matching method are discussed in light of other more traditional asymmetric matching techniques. Results were compared to eight corresponding color data sets available in literature. The corresponding color data was used to test several linear (von Kries, RLAB, etc.) and nonlinear (Hunt & Nayatani) chromatic adaptation transforms (CAT). It was found that a simple two-step von Kries, whereby the degree of adaptation D is optimized to minimize the DEu'v' prediction errors, outperformed all other tested models for both memory color and literature corresponding color sets, whereby prediction errors were lower for the memory color sets. The predictive errors were substantially smaller than the standard uncertainty on the average observer and were comparable to what are considered just-noticeable-differences in the CIE u'v' chromaticity diagram, supporting the use of memory color based internal references to study chromatic adaptation mechanisms.

Method to determine the degrees of consistency in experimental datasets of perceptual color differences

We propose a fuzzy method to analyze datasets of perceptual color differences with two main objectives: to detect inconsistencies between couples of color pairs and to assign a degree of consistency to each color pair in a dataset. This method can be thought as the outcome of a previous one developed for a similar purpose [J. Mod. Opt.56, 1447 (2009)JMOPEW0950-034010.1080/09500340902944038], whose performance is compared with the proposed one. In this work, we present the results achieved using the dataset employed to develop the current CIE/ISO color-difference formula, CIEDE2000, but the method could be applied to any dataset. Specifically, in the mentioned dataset, we find that some couples of color pairs have contradictory information, which can interfere in the successful development of future color-difference formulas as well as in checking the performance of current ones.

Visual and instrumental correlation of sparkle by the magnitude estimation method

Most real surfaces and objects show variations in appearance with viewing and illumination directions. Besides angular dependency, they also show spatial variation in color, i.e., they exhibit some sort of texture. Of the surfaces we see, surfaces colored by special-effect pigments produce several complex visual effects, like change in color and lightness with viewing and illumination angles, and effects like sparkle and gloss on other textures. In the last two decades, different commercial devices have appeared to help ensure the proper characterization of materials with special-effect pigments. However, the instrumental characterization of sparkle is currently available only by a commercial device integrated into a multi-angle spectrophotometer. As it is difficult to find complete open original studies about the sparkle effect for designing and calibrating this commercial instrument, the main objective of this work was to check whether a good visual and instrumental correlation exists between the sparkle that the observer perceives and the sparkle value provided by the device using some subsets of goniochromatic samples with different types of special-effect pigments and colors. Visual assessments were made by a conventional magnitude estimation method in a directional lighting booth, which belonged to the same company owner of the sparkle instrument, in different geometries and at distinct illuminance levels. The results revealed that there was a good visual correlation of the sparkle grade value. By separately analyzing the factors used in its instrument algorithm, such as sparkle intensity and sparkle area values, it was clearly shown that the correlation was not good or simply did not exist. Consequently, and perhaps in regards to the choice of new special-effect pigments, such as synthetic mica and other future ones, we generated herein even more questions about current mathematical algorithms, and only recognized calculating this texture effect at the industrial level.

Bayesian approach to color-difference models based on threshold and constant-stimuli methods

An alternative approach based on statistical Bayesian inference is presented to deal with the development of color-difference models and the precision of parameter estimation. The approach was applied to simulated data and real data, the latter published by selected authors involved with the development of color-difference formulae using traditional methods. Our results show very good agreement between the Bayesian and classical approaches. Among other benefits, our proposed methodology allows one to determine the marginal posterior distribution of each random individual parameter of the color-difference model. In this manner, it is possible to analyze the effect of individual parameters on the statistical significance calculation of a color-difference equation.

Brightness prediction of different sized unrelated self-luminous stimuli

In a series of magnitude estimation experiments, the effect of the size of a circular stimulus varying from 1° to 30° field of view on the perception of brightness has been investigated for unrelated self-luminous stimuli. A clear, hue independent, size effect on brightness was found. Based on a simple modification of the recently developed Color Appearance Model CAM15u, the brightness of different sized unrelated self-luminous stimuli was adequately predicted. The modified brightness prediction performs much better than existing predictions and has been validated by a separate validation experiment.

Experimental driven modelling of the color appearance of unrelated self-luminous stimuli: CAM15u

Based on an extensive magnitude estimation experiment, a new color appearance model for unrelated self-luminous stimuli, CAM15u, has been designed. With the spectral radiance of the stimulus as unique input, the model predicts the brightness, hue, colorfulness, saturation and amount of white. The main features of the model are the use of the CIE 2006 cone fundamentals, the inclusion of an absolute brightness scale and a very simple calculation procedure. The CAM15u model performs much better than existing models and has been validated by a validation experiment. The model is applicable to unrelated self-luminous stimuli with an angular extent of 10° and a photopic, but non-glare-inducing, luminance level.

Power functions improving the performance of color-difference formulas

Color-difference formulas modified by power functions provide results in better agreement with visually perceived color differences. Each of the modified color-difference formulas proposed here adds only one relevant parameter to the corresponding original color-difference formula. Results from 16 visual data sets and 11 color-difference formulas indicate that the modified formulas achieve an average decrease of 5.7 STRESS (Standardized Residual Sum of Squares) units with respect to the original formulas, signifying an improvement of 17.3%. In particular, for these 16 visual data sets, the average decrease for the current CIE/ISO recommended color-difference formula CIEDE2000 modified by an exponent 0.70 was 5.4 STRESS units (17.5%). The improvements of all modified color-difference formulas with respect to the original ones held for each of the 16 visual data sets and were statistically significant in most cases, particularly for all data sets with color differences close to the threshold. Results for 2 additional data sets with color pairs in the blue and black regions of the color space confirmed the usefulness of the proposed power functions. The main reason of the improvements found for the modified color-difference formulas with respect to the original color-difference formulas seems to be the compression provided by power functions.

Comprehensive model for predicting perceptual image quality of smart mobile devices

An image quality model for smart mobile devices was proposed based on visual assessments of several image quality attributes. A series of psychophysical experiments were carried out on two kinds of smart mobile devices, i.e., smart phones and tablet computers, in which naturalness, colorfulness, brightness, contrast, sharpness, clearness, and overall image quality were visually evaluated under three lighting environments via categorical judgment method for various application types of test images. On the basis of Pearson correlation coefficients and factor analysis, the overall image quality could first be predicted by its two constituent attributes with multiple linear regression functions for different types of images, respectively, and then the mathematical expressions were built to link the constituent image quality attributes with the physical parameters of smart mobile devices and image appearance factors. The procedure and algorithms were applicable to various smart mobile devices, different lighting conditions, and multiple types of images, and performance was verified by the visual data.

Chromaticity of unique white in object mode

The chromaticity of unique white viewed in object mode and under dark adapted conditions was investigated for 3 luminance levels (200, 1000 and 2000 cd/m(2)) using two experimental methods: unique white setting and rating. The results of the two methods were found to agree well. Both showed quite large observer variation and an apparent shift of the average unique white (across observers) towards colder correlated color temperatures as the stimulus luminance was dropped from 2000 cd/m(2) to 200 cd/m(2), although no such trend was observable at the individual observer level. Unique white was shown to encompass a region in color space, mostly located below the blackbody locus at around 6000 K. The low and high color temperature ends of the CIE class A and B white regions tend to respectively over- and slightly underestimate the size of the chromaticity area perceived as white by the dark adapted average observer. However, the agreement along a direction approximately perpendicular to the blackbody locus was quite good. Finally, the unique white ratings were modeled by a bivariate Gaussian function, resulting in a simple empirical metric to predict the degree of neutrality of any object stimulus viewed under dark adapted conditions.

Scaling perceived saturation

Two psychophysical experiments were conducted at North Carolina State University (NCSU) and Rochester Institute of Technology (RIT) to obtain replicated perceived saturation data from color normal observers on the order of one unit of saturation. The same 37 Munsell sample sheets, including up to four references that had similar perceived saturation but different hue, were used in both experiments. Different assessment methods included presenting either four references simultaneously or only one reference at a time to observers and obtaining judged saturation magnitudes for the given Munsell samples. Four saturation models comprising Sab*, Suv*, CIECAM02, as well as Richter/Lübbe, were tested. CIECAM02 gave the best prediction of saturation for data obtained at NCSU while Sab* outperformed other models for the RIT data. For the combined dataset, Sab*, the Richter/Lübbe, and CIECAM02-based saturation models exhibited comparable performances. The Standardized Residual Sum of Squares index was used to measure the inter- and intra-observer variability and goodness of fit. Inter- and intra-observer variability of assessments was smaller than or comparable to those reported for the typical color difference evaluation experiments.

Predicting the brightness of unrelated self-luminous stimuli

In a magnitude estimation experiment, twenty observers rated the brightness of several unrelated, self-luminous stimuli surrounded by a dark background. The performance of a number of existing vision models, color appearance models and models based on the concept of equivalent luminance in predicting brightness has been investigated. Due to a severe underestimation of the Helmholtz-Kohlrausch effect, none of the models performed acceptable. Increasing the weight of the colorfulness contribution to the brightness attribute in the CAM97u model results in a very good correlation between the model predictions and the visually perceived brightness. Finally the experimental results and the brightness prediction from the modified model CAM97u,m are verified through a matching experiment and a validation magnitude estimation experiment.

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.

Hyperbolic geometry for colour metrics

It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.

Testing the performance of CIECAM02 model using two distinct glossinesses of color printing atlas

Psychophysical experiments have been carried out in which the color appearance of high-gloss and low-gloss color printing atlases was assessed using a magnitude estimation method under three different light sources. A linearity fitting algorithm by the method of least squares was applied to evaluate the correlation between visual experiment data and predicted results through the CIECAM02 model of different glossinesses of color printing atlases. The research result has shown that there was a good correlation between mean visual results and predicted results for hue and lightness of two distinct glossinesses of the color printing atlas. The correlations of hue and lightness between visual experiment data and predicted results were the best and the second best, respectively, under the same light source. Colorfulness was the worst. Meanwhile, high-gloss and low-gloss color printing atlases have been estimated and compared in the viewing conditions of 0°/45°. The result has indicated that the hue of the color printing atlas could not be affected by gloss levels under three light sources. Colorfulness of the color printing atlas almost could not be affected by gloss levels under D65 and TL84 light sources. Lightness of the color printing atlas could be affected by gloss levels under a TL84 light source.

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.

Brightness perception of unrelated self-luminous colors

The perception of brightness of unrelated self-luminous colored stimuli of the same luminance has been investigated. The Helmholtz-Kohlrausch (H-K) effect, i.e., an increase in brightness perception due to an increase in saturation, is clearly observed. This brightness perception is compared with the calculated brightness according to six existing vision models, color appearance models, and models based on the concept of equivalent luminance. Although these models included the H-K effect and half of them were developed to work with unrelated colors, none of the models seemed to be able to fully predict the perceived brightness. A tentative solution to increase the prediction accuracy of the color appearance model CAM97u, developed by Hunt, is presented.

Color-difference evaluation for digital images using a categorical judgment method

The CIELAB lightness and chroma values of pixels in five of the eight ISO SCID natural images were modified to produce sample images. Pairs of images were displayed on a calibrated monitor and assessed by a panel of 12 observers with normal color vision using a categorical judgment method. The experimental results showed that assuming the lightness parametric factor k(L)=1 to predict color differences in images, CIELAB performed better than CIEDE2000, CIE94, or CMC, which is a different result to the one found in color-difference literature for homogeneous color pairs. However, observers perceived CIELAB lightness and chroma differences in images in different ways. To fit current experimental data, a specific methodology is proposed to optimize k(L) in the color-difference formulas CIELAB, CIEDE2000, CIE94, and CMC. From the standardized residual sum of squares (STRESS) index, it was found that the optimized formulas, CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1), performed significantly better than their corresponding original forms with lightness parametric factor k(L)=1. Specifically, CIEDE2000(2.3:1) performed the best, with a satisfactory average STRESS value of 25.8, which is very similar to the 27.5 value that was found from the CIEDE2000(1:1) formula for the combined weighted dataset of homogeneous color samples employed at the development of this formula [J. Opt. Soc. Am. A25, 1828 (2008), Table 2]. However, fitting our experimental data, none of the four optimized formulas CIELAB(1.5:1), CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1) is significantly better than the others. Current results roughly agree with the recent CIE recommendation that color difference in images can be predicted by simply adopting a lightness parametric factor k(L)=2 in CIELAB or CIEDE2000 [CIE Publication 199:2011]. It was also found that the different contents of the five images have considerable influence on the performance of the tested color-difference formulas.