1. Introduction

The current light sources color fidelity evaluation method characterizes the overall similarity of test color sample set (TCSS) color appearance between a test source and reference illuminant, such as CIE-R_a based on eight test color samples (O₈) [1], R_a,2012 based on 17 samples (O₁₇) [2], and CIE-R_f based on 99 color evaluation samples (O₉₉) [3,4]. O_8, O₁₇ and O₉₉ are standard color sample sets (SCSS) corresponding to their color fidelity index (CFI). In addition to uniform distribution in color space, the proposed sample set should has one other important property; that is, good spectral uniformity. it has been shown that both properties are important updates that have a substantial impact on the color fidelity scores [5–7], for example, O₉₉. Although the performance of the TCSS is getting better and better, it is not necessarily suitable for particular scene with particular colors. For example, in an printing art exhibition, the booth including the light source and exhibits is a particular scene, and the color of the exhibits is the particular color. If the color of the samples set used to evaluate the light source fidelity does not include the color of the printing exhibit, the accuracy of the light source evaluation result for the exhibit will be reduced. So, it comes down to how to find a color sample that meets the output characteristics of the printer, which is the focus of this article. It can be seen that light sources’ color fidelity evaluation in specific applications is a developing direction, such as architectural environments, museum lighting scenes and printing industry [6–10]. Moreover, the current research has the problem of inconsistency between objective evaluation and subjective evaluation. How to integrate the existing objective evaluation indexes and the subjective visual experience of the human visual system, and to construct a subjectively and objectively consistent light source color rendering evaluation model is an important problem facing the current lighting field.

To solve these problems, the key elements of color fidelity including test color samples and color difference formula are considered in this paper. If the colors in the scene have much different properties with the TCSS, which may occur with a whole printing image, TCSS will not be an appropriate characterization of the color stimulus, and the color fidelity evaluation results will be less applicable to the specific application. Based on the psychophysical experiment results, the color difference formula of CFI could be further modified, and a color fidelity evaluation model consistent with human vision can be obtained.

The rest of this paper is organized as follows. Section two introduces the method for obtaining the optimized test color samples. Section three analyzes objective performance of the CFIs using OCCS. Section four introduces the psychophysical experiment, as well as the methods and results of subjective and objective evaluation, followed by the conclusion in Section five.

This paper finally forms a complete system of subjective and objective consistency evaluation for specific printing applications. There are the convenience of ICC SCTS data acquisition and the characteristics of the spectrum’s adaptive output with the printing press.

2. Optimized color sample set

For light source of printing, there are some limitations in the relevant color fidelity evaluation research [6], such as output and measurement of a large number of color samples in printing color atlas, complex optimization process of OCSS. To this end, we evaluate color fidelity based on ICC SCTS. In the process of printing production, color management is a very important part to ensure the accuracy of color reproduction. ICC SCTS are the standard color samples for color device characterization in the color management process, mainly including IT8.7/3, ECI and IT8.7/4. In addition, characterization tools also have their own unique sampling data sets, such as TC3.5CMYK in Profilemaker5.0, 378, 530, 917, 1379 and 2989 five data sets [11–12]. It can characterize the device’s color output characteristics well. The design of the ICC SCTS is just the first step in the establishment of ICC profile, which is the necessary file in the color management [12,13]. The output and measurement of ICC SCTS are indispensable links in the printing color management process. As a result, the color sample optimization based on ICC SCTS is convenient for data acquisition. ICC SCTS can well characterize the printing atlas when evaluating the color fidelity of the light sources for printing matter. It is feasible to optimize color samples based on ICC SCTS, which has been verified in the paper. To simplify the optimization process, we build a 6D space including both chromaticity information and spectra information. In this 6D space, the OCSS is obtained by clustering the ICC SCTS. To improve the accuracy and speed of color sample clustering, we use SOMNN [14] clustering analysis instead of AP clustering [15]. The workflow followed in generating the OCSS is summarized in Fig. 1. OCSS should cover the entire hue circle in a defined color space [16–20].

 

Fig. 1. Workflow of OCSS generation

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We first select an appropriate ICC SCTS to optimizing color samples. IT8.7/4 is an extension color targets, it has increased to 1617 types of color blocks, and it is marked as Ω₁₆₁₇. In the color management process of Epson Stylus 7908 ink-jet printer which output the standard color sample Ω₁₆₁₇. And the spectra of samples are measured with the spectrophotometer Eye-One Isis. In color appearance space CAM02-UCS [1], color appearance attributes J’a’b’ of IT8.7/4’s 1617 samples are calculated under illumination D65 and CIE 1964 standard observer function.

Then we obtain sample sets Ω_g and Ω_f, specifically, saturated samples on the 3D gamut enclosure are separated, since the metric performance could be improved by adopting highly-saturated samples [1]. The color sample set Ω_g containing 202 boundary highly-saturated color samples and Ω_f containing 1415 color samples within the color gamut are separated. Subsequently, to avoid metamerisma, 6D color-spectra space with 3D color appearance attribute values J’a’b’ and 3D weighted spectral principal component is constructed. We perform PCA principal component analysis [21–23] on the spectra information, and the first three principal components with different weights are taken as the three spectral dimensions [6]. For all the samples of IT8.7/4, the cumulative contribution coverage of the first three principal components exceeds 99.75%.

SOMNN is a neural network with only input layer and competitive layer, which can perform unsupervised learning clustering on data [24,25]. It does not depend on the selection of initial cluster centers, and is not sensitive to noisy data with better robustness, visualization characteristics. In terms of algorithm complexity, SOMNN must update the inner star weight vector only, and the amount of computation is relatively small. The cluster center obtained by the clustering method SOMNN is the mean data of all color samples, and we take the color sample closest to the mean as the optimized color sample. With SOMNN clustering analysis in 6D space, Ω_g and Ω_f get 16 and 81 clustering centers, which make up O_g and O_f, respectively. The OCSS marked as Θ₉₇ contains 97 (16 + 81) samples.

Θ₉₇ with fewer samples are selected optimally to represent the predictions of ICC SCTS with a faster calculation time and ease of programming. The distribution of Θ₉₇ in the 3D color gamut is shown in Fig. 2. The OCSS would change adaptively with different printing press, but the workflow of acquiring it has formed a fixed system. As motivated by the expectation that the proposed method is suitable for printing matter, SCSS in the existing evaluation method is superseded by Θ₉₇. Such a replacement makes the evaluation method more targeted, and consequently improves its accuracy.

The large number of 97 color samples is not conducive to subjective experiments in terms of time and accuracy. For this reason, we further optimize color samples from Θ₉₇. Regarding Θ₉₇ as a category, the secondary SOMNN clustering is performed on it. The process is the same as above. Finally, eight optimized color samples are obtained, which are marked as Θ₈. The color gamut distribution of them is shown Fig. 2, and the distribution uniformity of Θ₈ in the color space is good.

 

Fig. 2. The 3D distribution of Θ₉₇ and Θ₈

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3. Objective performance analysis of CFIs using OCSS

If the light sources’ fidelity evaluation results are the same or very similar when taking the ICC SCTS and the printing atlas as TCSS, the OCSS optimized from the ICC SCTS will be more convincing to evaluate the color fidelity. To this end, we make the following analysis.

The printing atlas Ω₁₂₈₀₀₀ and Ω₁₆₁₇ are output and measured. Color fidelity indexes of the light sources are calculated by taking them as TCSS. In this paper, three CFIs, CIE R_a, R_a,2012 and CIE R_f, are used to evaluate 1202 light sources. These light sources are from various occasions including clothing sales environment, home environment, museum booth, restaurant lighting environment, office environment, back light billboard and 401 light sources from reference [4]. Light source types cover CIE standard illumination light sources, fluorescent lamps [26], LED lamps [27–31], incandescent lamps, tungsten halogen lamps, high pressure mercury lamps, and their color temperature ranges from 1634 K to 10462 K [32].

The performance between Ω₁₂₈₀₀₀ and Ω₁₆₁₇ is compared by using three metrics Mean Absolute Difference (MAD), Spearman Correlation Coefficient (SCC) and Coefficient of Variation (CV), and the results are listed in Table 1. The calculation formulas are shown as (1) to (4).

Table 1. The correlation index of CFIs between Ω₁₆₁₇ and Ω₁₂₈₀₀₀

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The smaller the MAD and CV values are, the better the correlation between the two sets of data is. And it is the opposite for SCC [33,34]. Using Ω₁₆₁₇ as the TCSS to calculate three CFIs of 1202 light sources, the results are the reference data and marked as R_a-1617/ R_a,2012-1617/R_f-1617. Similarly, the CFIs calculated by Ω₁₂₈₀₀₀ are denoted as R_a-128000/ R_a,2012-128000/R_f-128000.

As is shown in Table 1, the MAD values of the fidelity indexes calculated by Ω₁₂₈₀₀₀ and Ω₁₆₁₇ are all below 2.10, which is relatively small. They can be expected to perform similarly for characterizing color fidelity. The CV values are appropriately represented as a percentage. They float around 1.0, and it is positively correlated with the degree of dispersion between CFIs based on Ω₁₆₁₇ and Ω₁₂₈₀₀₀. SCC values are all greater than 0.985, meaning that when the confidence (Two-sided Test) is 0.01, the CFIs over Ω₁₂₈₀₀₀ can be approximately characterized by the CFIs over Ω₁₆₁₇. By analyzing the results of the three correlation indexes comprehensively, Ω₁₆₁₇ has the best representation of Ω₁₂₈₀₀₀ when calculating CIE R_f, followed by R_a,2012, and finally by CIE R_a. Basing on the above verification, Ω₁₆₁₇ can replace Ω₁₂₈₀₀₀ to optimize color samples.

Considering that the light sources with a terrible CFI have low application rate in various occasions, only light sources with reference CFI ≥ 70 are considered in subsequent analysis. For three types of reference CFIs, the ratios of light sources over the threshold 70 are all more than 90%. The main reason is that the light sources used in this paper are mostly commercially available products and they are expected to perform well. The SCSS of CIE R_a/R_a,2012/CIE R_f is marked as O₈/O₁₇/O₉₉. Taking OCSS Θ₉₇, Θ₈ and O₈/O₁₇/O₉₉ as TCSS, 1202 light sources’ fidelity indexes are calculated. The calculation results are marked as R_a-Θ₉₇, R_a-Θ₈, and R_a-O₈; R_a,2012-Θ₉₇, R_a,2012-Θ₈, and R_a,2012-O₁₇; R_f-Θ₉₇, R_f-Θ₈, and R_f-O₉₉ respectively.

Table 2 presents difference of CFIs between Ω₁₆₁₇ and other sample sets using MAD, CV and SCC values. When considering only CFIs ≥ 70, the MAD between R_a-O₈ and R_a-Ω₁₆₁₇/ R_a,2012-O₁₇ and R_a,2012-Ω₁₆₁₇/ R_f-O₉₉ and R_f-Ω₁₆₁₇ ranges from 4.27 to 20.40; AD_max ranges from 17.93 to 58.33; CV ranges from 3.11 to 13.76; SCC ranges from 0.817 and 0.918. For the improved CFIs (R_a-Θ₉₇ and R_a-Θ₈/ R_a,₂₀₁₂-Θ₉₇ and R_a,₂₀₁₂-Θ₈/ R_f-Θ₉₇ and R_f-Θ₈), the MAD is between 0.06 to 0.36; the maximum value of AD does not exceed 4.31; the maximum value of CV is very small, which is less than 1.00; the SCC are all close to 1.000. Obviously, the worst value of all correlation metrics between R_a-Θ_97/8 and R_a-Ω₁₆₁₇/ R_a,2012-Θ_97/8 and R_a,2012-Ω₁₆₁₇/ R_f-Θ_97/8 and R_f-Ω₁₆₁₇ is better than R_a-O₈ and R_a-Ω₁₆₁₇/ R_a,2012-O₁₇ and R_a,2012-Ω₁₆₁₇/ R_f-O₉₉ and R_f-Ω₁₆₁₇. The CFIs based on Θ₉₇ and Θ₈ are obviously closer to their reference CFIs (R_a-Ω₁₆₁₇/R_a,2012-Ω₁₆₁₇/R_f-Ω₁₆₁₇) than O_8/17/99. The performance of evaluation method whose TCSS replaced by Θ₉₇ will be improved accordingly.

When the MAD values are smaller, the CV values are almost smaller and the SCC values are greater. That is to say, the calculation results of the three analytical metrics have consistency. The performances of R_a,2012-Θ_97/8 and R_f-Θ_97/8 are both better than R_a-Θ_97/8 when evaluating color fidelity of light sources for printing application. And their performances are very close. Compared with previous studies, the calculation accuracy has been further improved [6,15]: the MAD value has increased by an order of magnitude, and the CV value has been further reduced from about 0.8 to 0.2. All of the SCCs values are close to 1.000. The above-mentioned correlation metrics all indicate that Θ₉₇ and Θ₈ both have good applicability to the three color rendering indexes when evaluating the light sources fidelity objectively in the printing application. When there is a similar evaluation effect, the smaller the number of color samples, the better. And section four develops subjective experiments and optimization model focusing on Θ₈, which has a small number of color samples and ideal evaluation results.

Table 2. The AD of CFIs between Ω₁₆₁₇ and other sets

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In order to compare the differences between Θ₉₇/Θ₈ and O₈/O₁₇/O₉₉ more intuitively and meticulously, subsequent analyses are performed using linear regression models. The CFI over Θ₉₇/O₈/O₁₇/O₉₉ is used to predict the CFI over Ω₁₆₁₇, and the prediction result is shown in Fig. 3. The solid black line is the ideal straight line with a slope of one and crossing the origin, and the red dashed line is the linear regression line obtained from the data points. The more discrete the data points are, the greater the difference between the CFI represented by the abscissa and the reference data represented by the ordinate is. As indicated in Fig. 3, the discrete degree of blue dots is the smallest, followed by orange square points, and finally gray triangle points. And the regression lines of the blue dots and orange square points are very close to the ideal black line, which means CFIs over Θ₉₇ and Θ₈ are almost aligned with CFIs over Ω₁₆₁₇. The gray data are very discrete, which shows a very low correlation between CFIs over Ω₁₆₁₇ and CFIs over O₈/O₁₇/O₉₉.

The closer the slope of the regression equation is to 1.00, the better the consistency of Θ₉₇/Θ₈/O₈/O₁₇/O₉₉ and Ω₁₆₁₇ is when evaluating CFIs. The regression lines’ slops of the blue dots and orange square points are both close to 1.00. The slope values for R_a-O₈, R_a,2012-O₁₇ and R_f-O₉₉ are quite different from 1.00, especially for R_a-O₈ and R_a,2012-O₁₇. Their slopes are 0.419 and 0.432 respectively. These results quantitatively show that the consistency between CFIs calculated by the optimized color sample set Θ₉₇/Θ₈ and CFIs calculated by Ω₁₆₁₇ is very good. The SCSS (O₈/O₁₇/O₉₉) does not have such a good consistency with Ω₁₆₁₇.

In almost all cases, CFIs based on O₈/O₁₇/O₉₉ are lower than reference data. This is consistent with the results in the reference [14], which has been verified to may be related to the role of saturated color samples. In addition, the value span of R_a-O₈ is very large when 90<R_a-Ω₁₆₁₇<95, and the difference is greater than ten points, so does R_f-O₉₉ when 85<R_f-Ω₁₆₁₇<90. R_a,2012-O₁₇ is also very discrete, especially when R_a,2012-Ω₁₆₁₇ is around 95, the change value even exceeds 20.

The purpose of this section is to obtain test color samples by optimizing the ICC SCTS in the proposed 6D color-spectra space, and to evaluate the performance of CFIs objectively. After a second optimization, a color sample set Θ₈ was obtained. The Θ₈ would be used for psychophysical experiments, evaluation of subjective and objective consistency, and the modification of color difference in color fidelity index calculations.

 

Fig. 3. Linear regression of CFIs between Ω₁₆₁₇ and other sets

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4. Subjective and objective consistency analysis

This section mainly describes the psychophysical experimental design, subjective and objective consistency analysis, and the modification of color difference on evaluating light sources fidelity.

4.1 Psychophysical experiment setup

Designing an experiment requires definition of the variables, apparatus, procedures, participants and statistical analyses to be conducted, all in order to limit or counteract bias [35].

4.1.1 Light sources

Figure 4 shows the light boxes used in fidelity experiment. The size of the two light boxes is 910 cm*510 cm*430 cm. The light box on the right provides an adjustable light source system LED Cube, which is composed of 15 single-color LED channels. By adjusting the intensity of each channel, the spectrum of the target illuminator can be simulated very closely. This light box has a built-in diffuser, which emits more uniform light and can be used as a reference light source light box in the comparison experiments. The light box on the left is a multi-light source standard observation box, which provides test light sources.

 

Fig. 4. Light boxes

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The inner walls and bottom of the two light boxes are blocked by black cardboard with the same material to eliminate the influence of reflected light. The CIE L*a*b* of the black cardboard was measured with Eye-One Isis. L* value is about 25, a* value is close to 0, b* value is close to -1. It can be considered that the two light boxes have the same background color within the measurement error range.

This psychophysical experiment involves a total of 9 pairs of light sources which include four CCT: 3000 K, 4000 K, 5000 K and 6500 K. Each pair of light sources contains a test and a reference light source, which are marked as F1, F2, F3, F4, LED1, LED2, LED3, LED4, and LED5, respectively. F stands for fluorescent lamp. Their spectral power distribution (SPD) are shown in Fig. 5.

 

Fig. 5. SPD of 9 test light sources

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According to CIE R_f, the SPDs of reference light sources are calculated. These reference SPDs are simulated by the adjustable LED Cube light box which provides the same CCT and illuminance with test light source. Specific parameters are shown in Table 3.

Table 3. Measured photometric and colorimetric properties of the 9 light sources under study

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4.1.2 Observation samples

Θ₈ was output by Epson Stylus Pro 7908 in D65 and CIE 1964 standard observation condition. The size of Θ₈ are all 7.5 cm*7.5 cm. The reflectance factors of the targets used are given in Fig. 6.

 

Fig. 6. Measured spectral reflectance factors (SRF) for Θ₈ used in the experiment.

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4.1.3 Visual assessment

The color fidelity of nine light sources is tested in the experiment. It is easier to evaluate the visual qualities of two targets when they are visible simultaneously, and the pair comparison and gray-scale method are used. The observers were asked to look at the two light boxes, containing identical targets, and to compare the test light source with the reference light source. The color temperature of the reference and test light sources used in this paper is consistent, and the parameters have been given in Table 3. The white field and illuminance are the same, and the environment settings of the two light boxes are the same. Therefore, mixed adaptation viewing conditions are in line with the research content of this paper.

A grey scale including five samples is produced. Each sample in the scale has the same size (7.5cm*7.5 cm) and material. Table 3 lists the J'a'b’ coordinates in CAM02-UCS color space and $\varDelta$J’ and CIE $\varDelta$E values between each step and the darkest grey sample (the standard color sample) under CIE D₆₅.

As shown in Table 4, six neutral samples varying in lightness are marked with grade number. The measured differences increase from grades five to one. The $\varDelta$J’ values agree almost exactly with those of $\varDelta$E values, indicating that all samples are essentially neutral.

Table 4. J*a*b*coordinates, △J’ and △E for grey scale used in experiment

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Fig. 7 illustrates the neutral samples arrangement which are placed in the reference light box. The targets are interchanged in each observing session. The observer is asked to choose a sample from the grey scale alongside the standard, giving a color difference closest to that of the two targets. Each observer is encouraged to give intermediate grades when possible, e.g. a difference of 2.8 indicates that this pair is slightly larger than that between standard and grade 3.

Twenty observers (ten females, ten males) are between 18 and 26 years old, with an average age of 19 years old. Nine of them have professional backgrounds, the others had no such experience. Before the real experiment, a training session is conducted. Each observer pass the Farnsworth D15 color vision tests. The observes assess colour difference via a grey scale as shown in Fig. 7. The observer is asked to choose a sample from the grey-scale (GS) pair, giving a colour difference closest to that of the sample in the test and reference light source. Reference light box always on right side. The experiment under each light source lasts about 15 minutes. Before the start of the every trial, they are given approximately five minutes to accommodate to the dark room and observe the targets. The observation is repeated three for each light source. The total duration of the experiment is about four hours, and it is completed in three-four times.

We present the eight color samples in turn, taking care to make the arrangement of the targets as similar as possible. The aim is that the only parameter to influence the subjects’ judgment should be the lighting. At the start of the experiment, the observers view the color sample target under the reference source and the first test light source (chosen randomly). Then they are asked to give intermediate grades.

 

Fig. 7. Sample arrangement for grey-scale

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4.2 Subjective and objective consistency analysis

The objective color fidelity refers to the index, for example R_a, R_a,2012 and R_f, which calculated by the light sources color fidelity evaluation method or the color fidelity index measured by the instrument. The subjective color fidelity refers to the visual score of the observer on the color fidelity ability of the test light source.

4.2.1 Visual color difference

The GS ratings are obviously not proportional to the difference seen, but their corresponding $\varDelta$E values should be. As is shown in Table 6, a pair with a grey-scale rating GS2 should correspond to about two times of the visual difference for a pair with a GS3 ($\varDelta$E values of 11.9 and 5.8). Hence a standard curve-fitting technique is used to derive third-polynomial equations to correlate accurately between the GS and visual color difference. In order to minimize the influence of other factors on the observer's evaluation, the third-polynomial equations under each reference light source are derived and the equations are shown in Table 5. Subsequently individual observer's grey-scale rating for each pair is transformed to the visual difference (designated as $\varDelta$V).

Table 5. The equations for converting the GS values into visual values under 9 pairs of light sources

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Table 6. Consistency between subjective and objective CIE R_f characterized by SCC and Stress

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4.2.2 Intra-observer difference

It is necessary to analyze the accuracy and repeatability of observer scores. First, we convert each observer's GS rating into visual color difference $\varDelta$V according to the equations in Table 5. The intra-observer difference and the difference between observers are analyzed by calculating Standardized residual sum of squares (Stress) [36]. Stress is a standard statistical measurement method. Refer to formula (5) for the calculation method:

X_i and Y_i are the i-th data in the two groups of data. f is the scale adjustment factor, which makes the groups of data to be compared in the same range. Stress is generally expressed as a percentage representing experimental error. It can be used to compare two sets of data and measure the match degree between two sets of data. For example, when the X_i and Y_i of the two sets of data are completely consistent, Stress is zero. The more the Stress deviates from 0, the greater the deviation of the two sets of data. For example, Stress is 30, which means that there is a 30% difference between X_i and Y_i.

Intra-observer difference, also known as observer repeatability, refers to the consistency between the results of multiple observations of the target by the same observer. This experiment involves nine pairs of light sources and eight color samples. We present the observers with the LED5 a second time, though without informing them that this is the case. For each target, in other words, the observers unknowingly make the comparison between LED5 and the reference source twice. This allow us to check whether anyone has answered randomly, and to make sure that the test is not too complicated. The reproducible results are used to evaluate the internal stability of the observers. At this time, Xi and Yi are the two pairs of visual evaluations and n is eight. The stress values range from 10.43 to 35.42, and only the ninth observer’s difference is more than 30 whose evaluation results are eliminated. The average stress value of 19 intra-observer differences is 16.82.

4.2.3 Difference between observers

The differences between observers, as known as observer accuracy, refers to consistency between the results of different observers observing the same targets. The difference between the visual evaluation results of each observer and the average results of the all observers represents the observer accuracy.

We calculate the Stress values of each observer for every pair of light sources. The average Stress values of nine pairs of light sources is between 24.90 and 49.84, with an average value of 35.42. The average Stress values of 19 observers represent the observer accuracy in each pair of light sources. The results are relatively close, with an average value of 34.97. These results show that the intra-observer differences are smaller than the differences between observers, which is consistent with the theoretically expected result. The differences between observers in this experiment is close to the average difference degree of the gray scale method commonly used internationally, such the value 36 [37,38]. So the obtained visual data is accurate and reliable, and they can be used to evaluate light sources’ fidelity.

4.2.4 Performance evaluation and improvement of fidelity index CIE R_f

The CIE R_f CRI is the latest fidelity index recommended by CIE, and this section analyzes the performance of CIE R_f over O₉₉ and Θ₈ in predicting subjective visual evaluation results.

The CIE R_f values over O₉₉ and Θ₈ of nine test light sources are marked as R_f,9-99 and R_f,9-8. The average subjective evaluation results of all observers for the eight color samples is marked as $\overline {\varDelta V} $. $\overline {\varDelta V} $ is used as the average visual color difference of test color samples in CIE R_f model to calculate the CIE R_f fidelity index R_f,9-8’. The SCC and Stress are calculated to quantitatively analyze the correlation between R_f,9-8’ and R_f,9-99 /R_f,9-8, and the subjective and objective consistency of CIE R_f.

As shown in Table 6, SCC between objective fidelity and subjective visual evaluation R_f,9-8’ ranges from 0.783 to 0.817, and Stress ranges from 5.614 to 7.615. The consistency between the objective fidelity indexes based on O₉₉ and Θ₈. The larger the SCC, or the smaller the Stress values, the better the consistency. The data comparison (0.817 > 0.783, and 5.614 < 7.615) shows that the optimized color samples set Θ₈ can better predict the subjective visual evaluation of the nine test light sources’ fidelity than O₉₉.

In addition, according to the results of psychophysical experiments, the color difference formula in CIE R_f is modified. The mean value of the color difference of the eight color samples under the light source to be objectively calculated is marked as $\overline {\varDelta E}$. A new color difference $\overline {\varDelta E} $’ is obtained by fitting the objectively calculated color difference $\overline {\varDelta E} $ with the visual color difference $\varDelta V$ obtained from psychophysical experiments. The fitting curve is shown in Fig. 8, and the fitting formula is shown in formula 6.

 

Fig. 8. Fitting curve of subjective and objective color difference for 8 color samples

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According to formula 6, the objective color difference values of the eight color samples under the test light source and the reference light source are improved, and the fidelity index R_f is calculated with the improved color difference, which is marked as R_f,₉-8'’. The correlation between the improved R_f,₉-8'’ and the subjective fidelity evaluation result R_f,₉-8’ is analyzed by calculating the SCC and Stress. From the third column of Table 6, it can be seen that after the improvement of the color difference formula, the consistency index SCC value of the subjective and objective evaluation of the eight color samples has increased by about 0.1, and the Stress value has decreased by nearly 3.7 values. It shows that the modification of the objective color difference formula can greatly improve the consistency of the subjective and objective evaluation of the fidelity of the light source.

5. Conclusion

By the SOMNN clustering analysis of the ICC SCTS in a 6D color-spectra space proposed in this paper, 97 optimized color samples are obtained. They can be used to objectively evaluate the fidelity of light sources for printing matter. After that, the 97 color samples are clustered for the second time, and eight optimized color samples are obtained. The eight optimized color samples can be used in the psychophysical experiments. We carry out a psychophysical experiment, in which 20 observers evaluate the visual color difference of the eight optimized color samples under the illumination of nine pairs of test and reference light sources. The performance of subjective and objective evaluation of CFIs including CIE R_a, R_a,₂₀₁₂ and CIE R_f is analyzed. By polynomial fitting of objective color difference and score of psychophysical experiment, the color difference formula of CIE R_f is corrected, and the consistency of subjective and objective consistency evaluation is finally improved. The consistency is analyzed by combining the metrics which are MAD, CV, SCC, and the linear analysis metrics.

The characteristics of this method can be summarized as the following:

In brief, the optimized color samples and proposed method are useable and far superior to the existing one in the objective and subjective color fidelity predictions of light sources for printing application. It is believed that the subjective and objective consistency evaluation based on the optimization of test color samples from ICC SCTS represents an important achievement, as it meets the requirements for specific printing application, and provides printing application with new research methods and ideas.

Appendix:

Schedule 1. Main notations used in this paper

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Funding

Beijing Municipal Education Commission (03150120001/073, 22150121003/038); Beijing Institute of Graphic Communication (Ea202002).

Acknowledgments

Kevin Smet who kindly shared the data of the spectra of Large Set and 401 light sources is greatly acknowledged.

Disclosures

The authors declare no conflict of interest.

Data availability

The data that support the findings of this study are available on request from the corresponding author.

References

1. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng 49(3), 033602 (2010). [CrossRef]  

2. S. J. Schanda, L. Whitehead, and M. R. Luo, “CRI2012: A proposal for updating the CIE color rendering index,” Lighting Research & Technology 45(6), 689–709 (2013). [CrossRef]  

3. A. David, P. T. Fini, K. W. Houser, Y. Ohno, M. P. Royer, K. A. Smet, M. Wei, and L. Whitehead, “Development of the IES method for evaluating the color rendition of light sources,” Opt. Express 23(12), 15888–15906 (2015). [CrossRef]  

4. S. Jost, C. Cauwerts, and P. Avouac, “CIE 2017 color fidelity index Rf: a better index to predict perceived color difference,” J. Opt. Soc. Am. A 35, B202–B213 (2018). [CrossRef]  

5. M. P. Royer, “Comparing Measures of Average Color Fidelity,” Leukos 14(2), 69–85 (2018). [CrossRef]  

6. X. J. Hu, Y. S. Lian, Z. L. Liu, X. F. Wei, and F. X. Liu, “Study of Color Rendering Evaluation Method of Light Sources for Printing Matter,” IEEE Access 8, 5526–5536 (2019). [CrossRef]  

7. K. A. Smet, A. David, and L. Whitehead, “Why color space uniformity and sample set spectral uniformity are essential for color rendering measures,” Leukos 12(1-2), 39–50 (2016). [CrossRef]  

8. M. Smith, “A new method of generating accurate color renderings of architectural spaces,” J. Illum. Eng. Soc. 22(1), 26–32 (1993). [CrossRef]  

9. A. Hurlbert and C. Cuttle, “New Museum Lighting for People and Paintings,” Leukos 16(1), 1–5 (2020). [CrossRef]  

10. D. Nickerson and C. W. Jerome, “Color rendering of light sources: CIE method of specification and its application,” Illum. Eng 60, 262–271 (1965).

11. J. Wang, “Research and Application of Printing Quality Evaluation Model Based on ISO12647-2 Standard,” Shanxi University of Science and Technology (2019).

12. B. Fraser, C Murphy, and F. Bunting, Color Management (Industrial-Strength Production Techniques, 2007).

13. P. Green, J. Holm, and W. Li, “Recent developments in ICC color management,” Color Res. Appl. 33(6), 444–448 (2008). [CrossRef]  

14. A. Ultsch, “Self Organizing Neural Networks perform different from statistical k-means clustering,” Philipps University of Marburg (2020).

15. X. J. Hu, Y. S. Lian, Z. L. Liu, Y. Jin, Y. L. Hu, Y. X. Liu, M. Huang, and Z. X. Lin, “Optimizing selection of the test color sample set for the CIE 2017 color fidelity index,” Opt. Express 28(6), 8407–8422 (2020). [CrossRef]  

16. K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010). [CrossRef]  

17. P. van der Burgt and J. van Kemenade, “About color rendition of light sources: The balance between simplicity and accuracy,” Color Res. Appl. 35(2), 85–93 (2010). [CrossRef]  

18. S. Jost-Boissard, M. Fontoynont, and J. Blanc-Gonnet, “Perceived lighting quality of LED sources for the presentation of fruit and vegetables,” J. Mod. Opt. 56(13), 1420–1432 (2009). [CrossRef]  

19. M. Islam, R. Dangol, M. Hyvärinen, P. Bhusal, M. Puolakka, and L. Halonen, “User preferences for LED lighting in terms of light spectrum,” Lighting Research & Technology 45(6), 641–665 (2013). [CrossRef]  

20. M. Royer, A. Wilkerson, M. Wei, K. Houser, and R. Davis, “Human perceptions of colour rendition vary with average fidelity, average gamut, and gamut shape,” Lighting Research & Technology 49(8), 966–991 (2017). [CrossRef]  

21. T. S. Yan, Y. T. Wen, and W. B. Li, “High-dimensional Data Classification Based on Principal Component Analysis Dimension Reduction and Improved BP Algorithm,” in Proceedings of 2018 International Conference on Communication, Network and Artificial Intelligence (CNAI 2018), pp. 453-457.

22. J. Ma and Y. Y. Yuan, “Dimension reduction of image deep feature using PCA,” Journal of Visual Communication and Image Representation. 63, 102578 (2019). [CrossRef]  

23. Y. Wang, “A Study of Key Technologies in Multispectral Image Color Reproduction,” Xi An University. (2010).

24. A. Ultsch and B. Ultsch, “Self-Organizing Neural Networks for Visualisation and Classification,” Springer, Berlin, Heidelberg (1993).

25. R. L. Xiao, R. X. Cui, M. W. Li, L. F. Chen, Y. C. Ni, and X. H. Lin, “SOMDNCD: Image Change Detection Based on Self-Organizing Maps and Deep Neural Networks,” IEEE Access 6, 35915–35925 (2018). [CrossRef]  

26. Z. Q. Guo, H. L. Lu, T. Shih, Y. Lin, Y. J. Lu, and Z. Chen, “Spectral Optimization of Candle-Like White Light-Emitting Diodes with High Color Rendering Index and Luminous Efficacy,” J. Display Technol. 12(11), 1393–1397 (2016). [CrossRef]  

27. H. Daicho, K. Enomoto, H. Sawa, S. Matsuishi, and H. Hosono, “Improved color uniformity in white light-emitting diodes using newly developed phosphors,” Opt. Express 26(19), 24784–24791 (2018). [CrossRef]  

28. M. Zhao, H. X. Liao, M. S. Molokeev, Y. Y. Zhou, Q. Y. Zhang, Q. L. Liu, and Z. G. Xia, “Emerging ultra-narrow-band cyan-emitting phosphor for white LEDs with enhanced colorrendition,” Light Sci Appl 8(1), 1–5 (2019). [CrossRef]  

29. S. Fumagalli, C. Bonanomi, and A. Rizzi, “An experiment on the color rendering of different light sources,” in Proc. SPIE 8652, Color Imaging XVIII: Displaying, Processing, Hardcopy, and Applications, Burlingame, California, United States (Academic, 2013).

30. G. X. He and H. F. Yan, “Optimal spectra of the phosphor-coated white LEDs with excellent color rendering property and high luminous efficacy of radiation,” Opt. Express 19(3), 2519–2529 (2011). [CrossRef]  

31. G. Z. Zhang, K. Ding, G. X. He, and P. Zhong, “Spectral optimization of color temperature tunable white LEDs with red LEDs instead of phosphor for an excellent IES color fidelity index,” OSA Continuum 2(4), 1056–1064 (2019). [CrossRef]  

32. P. J. Pardo, E. M. Cordero, M. I. Suero, and Á. L. Pérez, “Influence of the correlated color temperature of a light source on the color discrimination capacity of the observer,” J. Opt. Soc. Am. A 29, A209–A215 (2012). [CrossRef]  

33. A. Pedro, Garcaí. R. Huertas, M. Melgosa, and G. H Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24(7), 1823–1829 (2007). [CrossRef]  

34. S. Kim, M. Ouyang, and X. Zhang, “Compute spearman correlation coefficient with Matlab/CUDA,” in IEEE International Symposium on Signal Processing and Information Technology, Ho Chi Minh City, (2013, IEEE), pp. 55-60.

35. M. Royer, K. Houser, D. Durmus, T. Esposito, and M. Wei, “Recommended methods for conducting human factors experiments on the subjective evaluation of colour rendition,” Lighting Research & Technology 1, 14771535211019864 (2021). [CrossRef]  

36. P. Sedgwick, “Spearman's rank correlation coefficient,” Br. Med. J. 28, 1756–1833 (2014). [CrossRef]  

37. K. Smet and P. Hanselaer, “Geographical effects on memory colors and their impact on color rendition evaluation[C]//28th CIE session,” CIE, 2015.

38. F. L. Schmidt and J. E. Hunter, Methods of Meta-analysis: Correcting Error and Bias in Research Findings (Sage Publications, 2014), Chap. 2.