Power functions improving the performance of color-difference formulas

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.

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.

MPED: Quantifying Point Cloud Distortion Based on Multiscale Potential Energy Discrepancy

In this article, we propose a new distortion quantification method for point clouds, the multiscale potential energy discrepancy (MPED). Currently, there is a lack of effective distortion quantification for a variety of point cloud perception tasks. Specifically, in human vision tasks, a distortion quantification method is used to predict human subjective scores and optimize the selection of human perception task parameters, such as dense point cloud compression and enhancement. In machine vision tasks, a distortion quantification method usually serves as loss function to guide the training of deep neural networks for unsupervised learning tasks (e.g., sparse point cloud reconstruction, completion, and upsampling). Therefore, an effective distortion quantification should be differentiable, distortion discriminable, and have low computational complexity. However, current distortion quantification cannot satisfy all three conditions. To fill this gap, we propose a new point cloud feature description method, the point potential energy (PPE), inspired by classical physics. We regard the point clouds are systems that have potential energy and the distortion can change the total potential energy. By evaluating various neighborhood sizes, the proposed MPED achieves global-local tradeoffs, capturing distortion in a multiscale fashion. We further theoretically show that classical Chamfer distance is a special case of our MPED. Extensive experiments show that the proposed MPED is superior to current methods on both human and machine perception tasks. Our code is available at https://github.com/Qi-Yangsjtu/MPED.

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 k_L (lightness parametric factor), b (exponent in total color difference), and k_L + 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 k_L + 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 of extra virgin olive oils enriched with carotenoids from microalgae: influence of ultraviolet exposure and heating

A carotenoid-rich extract containing 2.5 mg/mL of lutein and 3.3 mg/mL of β-carotene from the microalga Scenedesmus almeriensis was added to ten extra virgin olive oils from four Spanish cultivars with differing degrees of ripeness, obtaining carotenoid enriched oils with lutein and β-carotene concentrations of 0.082 and 0.11 mg/mL, respectively. Extra virgin olive oils enriched with carotenoids from microalgae were studied by analyzing the effect on color of three different treatments: ultraviolet exposure, microwave heating and immersion bath heating. The methodology was designed to simulate, in controlled laboratory conditions, the effects of household treatments. Spectrophotometric color measurements were then performed to monitor color changes in the enriched and non-enriched extra virgin olive oil samples. Enriched oils are much more chromatic, darker and redder than natural oils. After 55 days UV irradiation, 40 min microwave heating, and 72 hours thermostatic heating, the average color differences for natural/enriched extra virgin olive oils were 98/117, 15/9 and 57/28 CIELAB units, respectively. In general, increasing temperature and ultraviolet exposure produced higher CIELAB color differences in the non-enriched samples. The addition of microalga extracts to extra virgin olive oils was found to induce some color stability and may constitute a future way of increasing the daily intake of beneficial bioactive compounds such as carotenoids.

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.

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.

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 h_ab significantly decrease, a^∗ and chroma C_ab^∗ significantly increase, and b^∗ shows no statistically significant changes (except for h_ab 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 C_ab^∗ 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.

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].

Complex process of image color correction: a test of a target-based framework

This paper aims at presenting the complexity of the process of image target-based color correction (CC). We present issues encountered from acquisition to rendering using colorimetric traditional tools. Target-based CC can be seen as an optimization problem. We have tested SAT and HUE adaptive fine tuning (SHAFT) an automated framework for target-based CC. A key element of SHAFT is an iterative CIEDE2000 variation comparison between a reference and target image. In this work we replace the standard CIEDE2000 with the Euclidean color-difference formula for small-medium color differences in log-compressed Optical Society of America's Committee on Uniform Color Scales (OSA-UCS) space. Results are presented using both formulae. A discussion on the complexity of scene color departures and correction performances concludes the paper. The effect of real scene complexity is shown and how colors are subject to disordered shifts in the color space. Because of this complexity, the role of the CC method as a different color error minimizer emerges.

Objective colour analysis from digital images as a nuclear forensic tool

A digital colour image may be composed of hundreds of thousands of pixels, every pixel exhibiting a single colour. Each colour can be described as a combination of red, green and blue (RGB) components, of discrete values between 0-255. The RGB data contained within the pixels of an image could, therefore, be used to quantitatively establish the colour of nuclear material powders from digital images, particularly for use in nuclear forensics applications, where there is a need for consistent, objective analysis. This paper sets out a standard method for the photography and analysis of digital images of uranium oxide powder, for the objective quantification of colour by mean RGB values. Eight heat treated (up to 550°C) powder samples of studtite ([(UO₂)(O₂)(H₂O)₂]·2H₂O) were photographed at room temperature and analysed by the RGB method. Hue, saturation and value of the coloured samples were obtained alongside mean RGB values, both of which were used to successfully determine the heating temperatures of unknown specimens of studtite.

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.

Suprathreshold gray scale is implied by thresholds

The inverse of the threshold just noticeable difference (i.e., 1/JND) is proportional to the slope (derivative with respect to visual stimulus luminance) of the suprathreshold gray scale at any stimulus and background luminances. Specifically, the inverse threshold and the gray-scale slope share 81% of their variance over six log units of target luminance; in log-log coordinates, 92% of their variance is shared. The strength of the connection improves when negative or positive contrasts are considered separately. Scientific literature is cited, empirical evidence is presented, results of theoretical calculations are discussed, and applications are described. For instance, suprathreshold gray-scale appearance is important in medical imaging, video rendering, industrial process displays, public information displays (e.g., at airports), military situation displays, heads-up displays, multispectral and other abstract scientific imaging, artistic lighting design (e.g., equal-appearing steps of gray scale), and color coding of text, image segments, or symbols for rapid reliable visual search.

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.