Spectral reflectance reconstruction based on wideband multi-illuminant imaging and a modified particle swarm optimization algorithm.

A method for spectral reflectance factor reconstruction based on wideband multi-illuminant imaging was proposed, using a programmable LED lighting system and modified Bare Bones Particle Swarm Optimization algorithms. From a set of 16 LEDs with different spectral power distributions, nine light sources with correlated color temperatures in the range of 1924 K - 15746 K, most of them daylight simulators, were generated. Samples from three color charts (X-Rite ColorChecker Digital SG, SCOCIE ScoColor paint chart, and SCOCIE ScoColor textile chart), were captured by a color industrial camera under the nine light sources, and used in sequence as training and/or testing colors. The spectral reconstruction models achieved under multi-illuminant imaging were trained and tested using the canonical Bare Bones Particle Swarm Optimization and its proposed modifications, along with six additional and commonly used algorithms. The impacts of different illuminants, illuminant combinations, algorithms, and training colors on reconstruction accuracy were studied comprehensively. The results indicated that training colors covering larger regions of color space give more accurate reconstructions of spectral reflectance factors, and combinations of two illuminants with a large difference of correlated color temperature achieve more than twice the accuracy of that under a single illuminant. Specifically, the average reconstruction error by the method proposed in this paper for patches from two color charts under A + D90 light sources was 0.94 and 1.08 CIEDE2000 color difference units. The results of the experiment also confirmed that some reconstruction algorithms are unsuitable for predicting spectral reflectance factors from multi-illuminant images due to the complexity of optimization problems and insufficient accuracy. The proposed reconstruction method has many advantages, such as being simple in operation, with no requirement of prior knowledge, and easy to implement in non-contact color measurement and color reproduction devices.

Colorimetric Evaluation of a Reintegration via Spectral Imaging-Case Study: Nasrid Tiling Panel from the Alhambra of Granada (Spain).

Color reintegration is a restoration treatment that involves applying paint or colored plaster to an object of cultural heritage to facilitate its perception and understanding. This study examines the impact of lighting on the visual appearance of one such restored piece: a tiled skirting panel from the Nasrid period (1238-1492), permanently on display at the Museum of the Alhambra (Spain). Spectral images in the range of 380-1080 nm were obtained using a hyperspectral image scanner. CIELAB and CIEDE2000 color coordinates at each pixel were computed assuming the CIE 1931 standard colorimetric observer and considering ten relevant illuminants proposed by the International Commission on Illumination (CIE): D65 plus nine white LEDs. Four main hues (blue, green, yellow, and black) can be distinguished in the original and reintegrated areas. For each hue, mean color difference from the mean (MCDM), CIEDE2000 average distances, volumes, and overlapping volumes were computed in the CIELAB space by comparing the original and the reintegrated zones. The study reveals noticeable average color differences between the original and reintegrated areas within tiles: 6.0 and 4.7 CIEDE2000 units for the yellow and blue tiles (with MCDM values of 3.7 and 4.5 and 5.8 and 7.2, respectively), and 16.6 and 17.8 CIEDE2000 units for the black and green tiles (with MCDM values of 13.2 and 12.2 and 10.9 and 11.3, respectively). The overlapping volume of CIELAB clouds of points corresponding to the original and reintegrated areas ranges from 35% to 50%, indicating that these areas would be perceived as different by observers with normal color vision for all four tiles. However, average color differences between the original and reintegrated areas changed with the tested illuminants by less than 2.6 CIEDE2000 units. Our current methodology provides useful quantitative results for evaluation of the color appearance of a reintegrated area under different light sources, helping curators and museum professionals to choose optimal lighting.

Domain and range of the CIECAM16 forward transformation.

The domain and range of the CIECAM16 forward transformation was numerically determined and visualized for CIE standard illuminants, using a linear programming approach that provides the gamuts and colour solids for optimum colours. The effect of the surround, adapting luminance, and luminance of the background on the range of the CIECAM16 forward transformation were individually analyzed, showing that their ranges increased when the surround changed from dark to dim or average, the adapting luminance increased, or the luminance of the background decreased. The proposed methodology for the determination and visualization of the domain and range of the CIECAM16 forward transformation can be used for any illuminant, as well as for CIECAM02, CAM16, CAM02-UCS and CAM16-UCS. The findings of this paper not only solve the long-term unresolved domain and range problems of the CIE colour appearance models, but also find applications in cross-media colour reproduction. Furthermore, it was also found that some non-CIE colours are inside the International Color Consortium Profile Connection Space (ICC PCS), and some CIE colours are not included in that space.

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 Color-Difference Formulas for 3D-Printed Objects.

Based on previous visual assessments of 440 color pairs of 3D-printed samples, we tested the performance of eight color-difference formulas (CIELAB, CIEDE2000, CAM02-LCD, CAM02-SCD, CAM02-UCS, CAM16-LCD, CAM16-SCD, and CAM16-UCS) using the standardized residual sum of squares (STRESS) index. For the whole set of 440 color pairs, the introduction of kL (lightness parametric factor), b (exponent in total color difference), and kL + b produced an average STRESS decrease of 2.6%, 26.9%, and 29.6%, respectively. In most cases, the CIELAB formula was significantly worse statistically than the remaining seven formulas, for which no statistically significant differences were found. Therefore, based on visual results using 3D-object colors with the specific shape, size, gloss, and magnitude of color differences considered here, we concluded that the CIEDE2000, CAM02-, and CAM16-based formulas were equivalent and thus cannot recommend only one of them. Disregarding CIELAB, the average STRESS decreases in the kL + b-optimized formulas from changes in each one of the four analyzed parametric factors were not statistically significant and had the following values: 6.2 units changing from color pairs with less to more than 5.0 CIELAB units; 2.9 units changing the shape of the samples (lowest STRESS values for cylinders); 0.7 units changing from nearly-matte to high-gloss samples; and 0.5 units changing from 4 cm to 2 cm samples.

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].

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.

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.

Spectral Image Processing for Museum Lighting Using CIE LED Illuminants.

This work presents a spectral color-imaging procedure for the detailed colorimetric study of real artworks under arbitrary illuminants. The results demonstrate this approach to be a powerful tool for art and heritage professionals when deciding which illumination to use in museums, or which conservation or restoration techniques best maintain the color appearance of the original piece under any illuminant. Spectral imaging technology overcomes the limitations of common area-based point-measurement devices such as spectrophotometers, allowing a local study either pixelwise or by selected areas. To our knowledge, this is the first study available that uses the proposed CIE (Commission Internationale de l'Éclairage) light-emitting diode (LED) illuminants in the context of art and heritage science, comparing them with the three main CIE illuminants A, D50, and D65. For this, the corresponding colors under D65 have been calculated using a chromatic adaptation transform analogous to the one in CIECAM02. For the sample studied, the CIE LED illuminants with the lowest average CIEDE2000 color differences from the standard CIE illuminants are LED-V1 for A and LED-V2 for D50 and D65, with 1.23, 1.07, and 1.57 units, respectively. The work studied is a Moorish epigraphic frieze of plasterwork with a tiled skirting from the Nasrid period (12th-15th centuries) exhibited in the Museum of the Alhambra (Granada, Spain).

Theoretical consideration on convergence of the fixed-point iteration method in CIE mesopic photometry system MES2.

Currently the fixed-point iteration method with initial guess m0=0.5 is officially recommended by the CIE MES2 system [CIE 191:2010] in order to compute the adaptation coefficient m and the mesopic luminance L m e s . However, recently, Gao et al. [Opt. Express25, 18365 (2017)] and Shpak et al. [Lighting Res. Technol.49, 111 (2017)] have numerically found that the fixed-point iteration method could be not convergent for large values of S/P. Shpak et al. suspected that, to achieve convergence, the S/P ratio cannot be greater than 17. In this paper, a theoretical consideration for the CIE MES2 system is given. Namely, it is shown that the ratio S/P be smaller than a constant C2 (≈18.1834) is a sufficient condition for the convergence of the fixed-point iteration method. In addition, a new initial guess strategy, achieving faster convergence, is proposed.

Improved computation of the adaptation coefficient in the CIE system of mesopic photometry.

New values of parameters a and b are proposed for the CIE system of mesopic photometry MES2 [CIE Publication 191:2010], because from the original values this model may have no solution or multi-solutions. From the new values of parameters a and b it is shown that the CIE MES2 system has a unique solution. The difference however, between the original and the new values of parameters a and b is very small and the changes do not affect previous conclusions based on the MES2 model. To compute such a solution, we propose a Bisection-Newton method which exhibits fast convergence (8 iterations in the worst case), and improves the fixed-point method recommended by the CIE MES2 system, which has convergence problems for high values of the photopic luminance and very high values of the scotopic/photopic ratio. Comparative results for the fixed-point method, the Bisection method, the Newton method, and the Bisection-Newton method, in terms of the number of iterations necessary for convergence and the computation time used, are reported.

Accurate method for computing correlated color temperature.

For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 106 K.

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.

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.

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.

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.

Evaluation of threshold color differences using printed samples.

The performances of uniform color spaces and color-difference formulae for predicting threshold color differences were investigated based on visual assessments of 893 pairs of printed color patches under a D65 source. The average ΔE(ab,10)* of the pairs was 1.1 units. A threshold psychophysical experiment was repeated three times by a panel of 16 observers with normal color vision. The experimental data were used to evaluate nine color-difference formulae and uniform color spaces using the standardized residual sum of squares (STRESS) measure. The results indicated that all formulae and spaces performed very similarly to each other, and outperformed CIELAB for threshold color differences. The chromaticity-discrimination ellipses were used to compare with previous results from small color differences [Color Res. Appl. (2011), doi:10.1002/col.20689], and they agreed with each other, except for the purple color center.

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.

Skin color measurements before and after two weeks of sun exposure.

We performed spectrophotometric measurements of skin reflectance at four body locations (forehead, cheek, neck, and back of hand), before and after two weeks of sun exposure, for 103 first-year college students. Skin reflectance was measured twice at each body location, before and after two weeks of sun exposure, obtaining an average repeatability (mean color difference from the mean) in the range of 0.2-0.5 CIELAB units (D65 illuminant, CIE 1931 standard observer). However, the average skin color differences before and after two weeks of sun exposure were in the range of 3.6-3.9 CIELAB units, considerably higher than measured repeatability, as a consequence of suntanning. Skin color appearance variation was analyzed in the CIELAB color space, and it was found that at all body locations two weeks of sun exposure made lightness L∗ and hue-angle hab significantly decrease, a∗ and chroma Cab∗ significantly increase, and b∗ shows no statistically significant changes (except for hab at the forehead and cheek, and for a∗ at the forehead where no statistically significant changes were found). An W shape for skin spectral reflectance between 520 nm and 600 nm was found at some of the four measured body locations. It was found that the individual typological angle (ITA) defined from L∗ and b∗ performed well in predicting our measured data and a modification of ITA using L∗ and Cab∗ performed even better, with the measured L∗ as reference. The color shifts produced by two weeks of sun exposure in different planes of CIELAB were analyzed for the skin categories established by the ITA index, and compared with the control group data accumulated by Amano et al. (PLoS ONE. 15(12), e0233816)(PLoS ONE 15(2020) e0233816). The measured skin spectra can be useful to the skin color database currently being developed by CIE TC 1-92.

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.