Open Access
Add to BibSonomy
Abstract
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 ${{26}}\sim{{45}}$ 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.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. INTRODUCTION
Three-dimensional (3D) printing, also known as additive manufacturing, allows objects to be built directly from digitally rendered models. 3D printing can reduce the amount of materials required for production, compared to traditional manufacturing techniques, and facilitate the prototyping and manufacturing of complex objects [1]. The technology has made the manufacturing industry more personalized and convenient. In recent years, with the application of new materials and technologies, the limitation of a single material and color in 3D printing technology no longer exists, and multiple materials and colors can now be used to build 3D objects simultaneously. 3D full color printing technology has also become a possibility and can be applied in many fields, such as graphic art, rapid prototyping, medicine, education, and so on [2–5]. Therefore, the color measurement and color difference evaluation of 3D sample pairs are becoming more important in the process of color control and color reproduction [6].
Conventionally, color difference evaluation and prediction are based on flat color samples, such as the CIELAB [7] and CIEDE2000 [8] formulas recommended by Commission Internationale de l’Éclairage (CIE) for industrial color difference evaluation. Similarly, color appearance models CIECAM02- (LCD/SCD/UCS) [9] and CAM16-(LCD/SCD/UCS) [10] are used to predict the color difference of 2D color samples. The development and validation of these formulas are usually based on visual data sets from 2D colors, such as printed matter, textiles, and self-illuminated color samples.
Compared with 2D samples, the visual color perception of 3D samples is more complicated, and it may be affected by factors including the shape [11], the geometrical structure of the light field [12], translucency [5], gloss [13,14], and shadow. When the surface of a 3D sample is illuminated, the uneven shape of the surface will reflect the light in different directions, resulting in different color perceptions when viewed in different directions. The use of existing color difference evaluation and prediction formulas to 3D sample pairs is therefore an important area of research that needs to be studied.
Table 1. Detailed Information of the Four Groups of Experiments
With the abovementioned issues in mind, CIE Technical committee TC 8-17 was established to study “Methods for Evaluating Color Difference between 3D Color Objects” [15]. Jiang et al. [16] conducted a study to evaluate the color difference of 3D objects. Seventy-five pairs of 3D sphere samples and 75 pairs of 2D flat samples were prepared, and their color differences were evaluated by 10 observers using the gray-scale method. Ten color difference formulas, including CIELAB, CMC, CIEDE2000, CIECAM02, DIN99, OSA, and so on, were evaluated. The results indicated that the color difference magnitude, light source, and 3D shape had more or less influence on the perceived color differences, which will affect the performance of existing color difference formulas. Most of data collected in this study relate to objects with large color differences but with the same level of gloss, size, and shape. There is therefore a need to collect a comprehensive color difference data set for 3D objects that cover different parameters, including shape, size, and gloss.
In this study, we prepared 440 pairs of 3D printed color samples with three shapes (spheres, cones, and cylinders), two sizes (4 cm and 2 cm), and two gloss level (matte and gloss). The color difference experiments were conducted by 26–45 color normal observers, and 20,710 color difference data were collected. The influence of parametric effects on the perceived color difference of 3D objects was analyzed comprehensively.
2. EXPERIMENT
A. Information of the Experiments
According to different experimental samples and observation conditions, our experiment is divided into four phases, henceforth named EXP. I, EXP. II, EXP. III, and EXP. IV. Table 1 summarizes the experimental information of the four data sets studied; the 3D sample pairs were prepared with different shapes, gloss, and sizes, and they were also illuminated by different light sources. The four groups of experimental data sets were divided into eight phases according to the shape of the samples, named Sp-4-m, Sp-4-g, Sp-2-m, Co-4-m, Cy-4-m, Sp-2-g, Co-4-g, Cy-4-g as shown in the column “Abbr.” in Table 1. The combination of two letters in front of the short line represents the shape of the sample (Sp, Co, Cy are sphere, cone, cylinder, respectively), and the numeral 4 or 2 represents whether the size of the sample is 4 cm or 2 cm, respectively, and ${\rm m}$ or ${\rm g}$ represent whether the sample surface is matte or glossy.
B. Light Sources
The visual experiments were carried out in a dark room with a viewing cabinet. In EXP. I and EXP. III, the matte samples were illuminated by the directional light, which was equipped with a GretagMacbeth The Judge II viewing cabinet and named L1, L3, respectively. The samples were directly illuminated by light sources in the cabinet and light diffusely reflected in the walls of the cabinet. In EXP. II and EXP. IV, the gloss samples were illuminated by the diffused light, which was equipped with a spectrally tunable LED lighting system, provided by Thouslite Inc., China, named L2. The size of the GretagMacbeth The Judge II viewing cabinet is ${{67}}\;{\rm{cm}}\;({\rm{length}}) \times {{51}}\;{\rm{cm}}\;({\rm{width}}) \,\times {{55}}\;{\rm{cm}}\;({\rm{height}})$, and the size of the spectrally tunable LED lighting system is ${{50}}\;{\rm{cm}}\;({\rm{length}}) \times {{50}}\;{\rm{cm}}\;({\rm{width}}) \times {{60}}\;{\rm{cm}}\;({\rm{height}})$. The samples were placed in the middle of the cabinet. The colorimetric values of the background of GretagMacbeth The Judge II and LED lighting system measured by the X-Rite Ci64 spectrophotometer with the condition of D65/10° were ${{L}}_{10}^* = {64.18},{{a}}_{10}^* = {0.15},{{b}}_{10}^* = {2.12}$ and ${{L}}_{10}^* = {71.69},{{a}}_{10}^*= - {0.74},{{b}}_{10}^* = {1.50}$, respectively. The relative spectral power distributions (SPDs) of L1, L2, and L3 were measured at the position of the samples using the Photo-Research PR655 spectroradiometer, and the results are shown in Fig. 1.The illuminance at the position of the samples for the three light sources of ${{L1}}\sim{{L3}}$ were 878 lx, 1052 lx, and 890 lx; the correlated color temperatures (CCT) were 6253 K, 6492 K, 6344 K; and the CIE color rendering indices (CRI) [17] were 93.3, 96.9, and 92.1, respectively, which were measured by handheld illuminance meter UPRtek MK350N.
C. Sample Preparation
In this study, the 3D samples were printed by Sailner J400 and J501 3D color printers provided by Sailner 3D Technology Co., Ltd., Zhuhai, China, with the optical properties of matte and gloss. The principle of the 3D printers in this study is similar to that of a 2D inkjet printer, which contains four primary colors, such as cyan, magenta, yellow, black, and an additional white color was added to adjust the lightness of the printed samples. The print head prints a thin layer of photosensitive resin each time, and then it is quickly cured with ultraviolet light. When the printer finishes printing one layer, the forming tray of the machine descends to print the next layer. All the printed samples are matte, and in the post-processing, some samples were selected and varnished for polishing as glossy samples. Considering the operability of gloss measurement, the flat samples that had the same gloss as the 3D samples were selected. The values were 3.6 GU and 96.6 GU for matte and glossy samples measured by GLOSS METER TC-108DPA provided by TOKYO DENSHOKU Co. Ltd., Japan, with the angle of 60°. Specifically, three different shapes (sphere, cone, and cylinder) were prepared with the sizes of 4 cm and 2 cm. The dimensional definition of the samples are as follows: the diameter of the sphere were 4 cm, and the bottom diameter and height of the cone and cylinder were both 4 cm. For the 2 cm sized samples, the diameter of the sphere was 2 cm. Figure 2 shows the view of the samples. All the samples were prepared surrounding the CIE five color centers [18] (gray, red, yellow, green, and blue), which were recommended by the CIE for evaluating the uniformity of color space and the performance of color difference formulas. In the experiments, the samples were prepared carefully, and the 440 samples were selected from thousands of samples with different $\Delta E_{ ab}^*$ color difference magnitudes.
D. Color Measurement
Due to the limited uniformity of 3D samples in the production process, the surface of the samples with uniform color were carefully selected and used as the observation region in the psychophysical experiment. In color measurement, five points on the observation region were randomly selected and measured by the X-Rite Ci64 spectrophotometer, and then the averaged values were used to represent the final values of the 3D samples. The uniformity of the samples was characterized using the Mean Color Difference from the Mean (MCDM) [19] values in the CIE 1976 ${{{L}}^*}{{{a}}^*}{{{b}}^*}$ color space with the condition of D65/10° as shown in Eq. (1):
where $N = {{5}}$ indicates the number of the measurements, ${C_i}$ represents the ${{{L}}^*}{{{a}}^*}{{{b}}^*}$ values of the $i$th ($i = {{1}}\sim{{5}}$) measurement, ${C_{\rm{ave}}}$ represents the average ${{{L}}^*}{{{a}}^*}{{{b}}^*}$ values of the $N$ measurements, and ${f_{\Delta E}}$ is a function to calculate color differences such as $\Delta {{E}}_{{ab}}^*$. The mean MCDM values of the samples in EXP. I to EXP. IV were 1.4, 1.5, 1.5, and 1.3 $\Delta {{E}}_{\textit{ab}}^*$ units, respectively, and the maximum MCDM values of the samples in EXP. I to EXP. IV were 3.8, 2.9, 3.8, 4.6 $\Delta {{E}}_{ab,10}^*$ units, respectively. This means that the uniformity of the sample meets the experimental requirements.The spectral reflectances of all 3D samples were measured by the X-Rite Ci64 spectrophotometer with the mode of SPIN, and the colorimetric values were calculated based on different light sources and CIE 1964 10° color matching functions in the following work. As mentioned in Table 1, the CIELAB color differences of the 440 sample pairs in EXP. I to EXP. IV ranged from ${0.46}\sim{16.86}$, which included threshold color difference (TCD), small color difference (SCD), and large color difference (LCD). Further, we divided these color differences into different magnitudes; Fig. 3 shows the number of samples belonging to different CIELAB color difference ($\Delta {{E}}_{ab,10}^*$) magnitudes. There are 26.8%, 27.5%, 25.2%, and 13.9% sample pairs in ${0.0}\sim{3.0},\;{3.0}\sim{5.0},\;{5.0}\sim{8.0}$, and ${8.0}\sim{10.0}$ color difference magnitudes, respectively. In the preparation of the 3D samples, it is very difficult to make sure that the color difference was only or mainly from $\Delta {{L}}_{10}^*,$ $\Delta {{C}}_{10}^*$, and $\Delta {{H}}_{10}^*$. The weight effects of different parameters are similar in most samples. For example, the distributions of color differences in $\Delta {{a}}_{10\:}^*\Delta {{b}}_{10}^*$ and $\Delta {{L}}_{10}^*$ $\Delta {{C}}_{ab,10}^*$ for yellow center in EXP. I are shown in Fig. 4.
Fig. 4. Distributions of color differences in CIELAB: (a) $\Delta\;{{a}}_{10\:}^*\Delta\;{{b}}_{10}^*$ and (b) $\Delta{{L}}_{10}^*\;\Delta{{C}}_{ab,10}^*$ for yellow center in EXP. I.
E. Gray Scale
The gray-scale method [20] was used to evaluate the color difference of the sample pairs as shown in Fig. 5. Our gray scales had color difference grades from 1 to 14 and were printed by an Epson Stylus PRO 7908 inkjet printer on the substrate of semigloss paper (with the gloss of 36.1). The printed gray scales were attached to a black matte card with the ${{L}}_{10}^*{{a}}_{10}^*{{b}}_{10}^*$ values of 33.31, ${-}{0.6},\;{{- 0}.{64}}$. Considering the accuracy of the gray scale, we used four gray scales numbered No.1–No.4 (used in EXP. I–IV) in different time periods, and the linear relationship between their grades (GS) and color difference value $\Delta {{E}}_{ab,10}^*$, as well as the goodness of fit ${{{R}}^2}$, are shown in Eqs. (2 )–(5), which represent the gray-scale fitting results of EXP. I–IV, respectively:
F. Visual Experiment
During the visual evaluation experiment, each sample pair was placed with no gap and in the front of the gray scale in the viewing cabinet (see Fig. 6). The circular face of the cone was placed downward, and the cylinders were horizontally placed as shown in Fig. 2. The observers viewed the sample pairs with a distance of 40 cm, the field of view formed by a pair of sphere (4 cm) or cone (4 cm) or cylinder (4 cm) was ${11.4}^\circ \times {5.7}^\circ$, and the field of view formed by a pair of spheres (2 cm) was ${5.7}^\circ \times {2.9}^\circ$. The observers were trained on the gray scale method of color difference evaluation before the formal experiment. The observer refers to the color difference between the gray scales to judge the color differences of the 3D samples (it is recommended that the visual color difference given by the observer is kept to one decimal place). Before the beginning of the visual experiments, the light sources were warmed up for at least 15 min. Each observer viewed the viewing cabinet for 1 min for fully chromatic adaptation.
In EXP. I–EXP. IV, 26–45 human observers (16 males and 29 females) aged from 19 to 26 (${\rm{mean}} = {20.5}\;{{\pm}}\;{1.44}$) were organized to participate in the visual experiments. All the observers had normal color vision, passing the Ishihara Color Vision Test, and they had participated in similar color difference experiments before. In order to evaluate the repeatability of the observers, 4–24 observers carried out 2–3 repeated assessments. In total, 20,710 ($= {{43}} \times {{150}}\;{ + }\;{{50}} \times {{50}}\;{ + }\;{{49}} \times {{40}} \times {{3}}\;{ + }\;{{49}} \times {{40}} \times {{3}}$) color difference data were collected in this study. It should be mentioned that the printed samples were composed of a broadband primary color spectrum, and the CRIs of the three light sources were all above 92.1; some supplementary visual experiments on some matte samples in the L2 light source were conducted, and the results indicated that the three light sources have little effect on the experimental results.
Fig. 7. Visual results ($\Delta {{V}}$) plotted against $\Delta {{E}}_{ab,10}^*$ in each phase: (a) Sp-4-m; (b) Sp-4-g; (c) Sp-2-m; (d) Co-4-m; (e) Cy-4-m; (f) Sp-2-g; (g) Co-4-g; and (h) Cy-4-g.
Table 2. Intra-Observer and Inter-Observer Variability in Terms of STRESS in EXP. I ∼ EXP. IV
3. RESULTS AND ANALYSIS
A. Observer Variability
Observer variability includes intra-observer and inter-observer variations, which are evaluated by the Standardized Residual Sum of Squares (STRESS) index [21,22]. Intra-observer refers to the difference between each judgment and the average judgments of the observer, and inter-observer refers to the difference between each observer’s average judgment and the average of all observers. The STRESS values for intra-observer and inter-observer variability in each experiment are listed in Table 2.
In different phases, the main differences are light source and gloss difference. The STRESS of intra-observer as well as the inter-observer in different experiments is very similar. The results indicate that the parametric effect on observer variability of the color difference experiment was relatively small. Compared with similar previous studies [23,24], the observer viability results are within a reasonable range, indicating that the experimental data collected in this study is reasonable.
B. Color Difference Data
For each pair of color samples, the color differences assessed by different observers under different repetitions were averaged to represent overall visual results. The gray-scale grade (GS) was then used to covert mean observer results to visual color difference value ($\Delta {{V}}$) using the linear transform [Eqs. (2 )–(5)]. Figures 7(a)–7(h) shows the scatter distributions of observer visual color differences ($\Delta {{V}}$) and device measured CIELAB color differences ($\Delta {{E}}_{ab,10}^*$) of eight phases (Sp-4-m, Sp-4-g, Sp-2-m, Co-4-m, Cy-4-m, Sp-2-g, Co-4-g, Cy-4-g) in Exp. I–Exp. IV. The linear relationship between $\Delta {{V}}$ and $\Delta {{E}}_{ab,10}^*$ for each phase is further fitted.
Table 3. Average $\overline {\Delta {{V}}} ,\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$ and $\overline {\Delta {{V}}} /\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$ for Each Phase
The average visual values ($\overline {\Delta {{V}}}$) and average CIELAB values ($\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$) for each part were calculated. The results are divided into two categories according to matte and glossy samples and given in Table 3. $\overline {\Delta {{V}}} /\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$ is also displayed in the last column of Table 3. The difference in visual color difference of different sample sets, that is, the parameters, can be characterized by comparing the value of $\overline {\Delta {{V}}} /\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$.
It can be seen that the $\overline {\Delta {{V}}} /\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$ of the matte samples (with the value of 1.12) is larger than that of the gloss samples (with the value of 1.02), that is, the visual color differences from the matte samples are larger than those of the gloss samples when they had the same color difference. The samples used in the four parts in each column have different shapes or sizes, and the $\overline {\Delta {{V}}} /\overline {\Delta {{E}}} _{{{ab}},10}^{{\;*}}$ values of Sp-4-m and Sp-4-g are larger those of than other phases. We can preliminarily conclude that the sphere has a larger visual color difference than the values from cone and cylinder sample pairs, and the visual color differences of a 4 cm sphere (Sp-4-m and Sp-4-g) are larger than those of a 2 cm sphere (Sp-2-m and Sp-2-g).
In the following work, the visual color differences and the chromaticity ellipses are used to further investigate the parametric effects on perceived color difference.
C. Parametric Effect
1. Effect of Gloss
The data sets in the four experiments were divided into two types based on their optical properties, such as matte and gloss. The matte data sets in EXP. I and EXP. III and the gloss data sets in EXP. II and EXP. IV were analyzed.
In Fig. 8, it can be concluded that the visual color differences of 3D matte sample pairs are always greater than those of gloss sample pairs when they have similar calculated color differences $\Delta {{E}}_{ab,10}^*$. In order to quantify the difference in visual color difference of two data sets, the percentage of difference between two data sets is analyzed using Eq. (6):
where ${k_1}$ and ${k_2}$ mean the slopes of the fitting lines by the two data sets.Fig. 8. Comparisons of visual color differences $\Delta V$ and computed color differences $\Delta {{E}}_{ab,10}^*$ from sample pairs with different gloss.
It can be calculated from Eq. (6) that the visual color difference of the matte samples increased by 10.9% compared to gloss samples. The results indicate that human perception is more sensitive to the color difference of matte sample pairs and that 3D gloss sample pairs will bring less color difference perception. Higher lightness and saturation of the gloss objects may have impacted the human perception of their color difference more than that of matte objects, with human perception being more sensitive to sample pairs with low lightness and saturation.
2. Effect of Shape and Size
The data sets from the sample pairs with different shapes but the same size are summarized in Fig. 9. In order to exclude the effect of gloss, Fig. 9 is divided into matte and gloss sample sets as shown in Figs. 9(a) and 9(b). Similarly, the data sets of samples with the same shape but different sizes are summarized in Fig. 10, according to the properties of matte and gloss; see Figs. 10(a) and 10(b).
Fig. 9. Comparisons of visual color differences $\Delta {{V}}$ and computed color differences $\Delta {{E}}_{ab,10}^*$ from sample pairs with different shapes: (a) matte and (b) gloss.
Fig. 10. Comparisons of visual color differences $\Delta {{V}}$ and computed color differences $\Delta {{E}}_{ab,10}^*$ from sample pairs with different size: (a) matte and (b) gloss.
We can conclude that the sphere samples will arouse larger visual color difference compared with cone and cylinder samples with the same gloss, and the visual color difference of a 4 cm sphere is greater than that of a 2 cm sphere. In the matte and glossy sample sets, the visual color differences for spheres increased 2.7% and 13.6% with respect to the values found for cone and increased to 5.5% and 6.9% with respect to values found for cylinder. In addition, in the matte and glossy sample sets the visual color differences for spheres of 4 cm increased 9.3% and 31.8% with respect to values found for spheres of 2 cm. These results were obtained using Eq. (6) and may be due to the surface of the sphere being more regular than that of the cone and cylinder. When the observers evaluated the color difference of the sphere sample pair, their attention was more focused, leading to obvious color difference perception on the surface of sphere samples. In addition, when the observers were looking at a pair of spheres of 4 cm and 2 cm, the fields of view for each sample were ${11.4}^\circ \times {5.7}^\circ$ and ${5.7}^\circ \times {2.9}^\circ$, respectively. In general, large visual fields allow better color discrimination than fields covering only the foveal region [25]. Moreover, as reported in a previous work using random-dot simulated textures [26], visual color differences decreased with increasing density of textures. From the point of view of color differences, nonuniform colors produced by lighting of 3D samples may lead to a similar visual effect to the one produced by mentioned random dots.
3. Effect of Color Difference Magnitudes
At the same time, the sample pairs were divided into two parts according to their CIELAB color difference magnitudes, such as SCD and LCD. Figure 11 shows the results of different color difference magnitudes where SCD means sample pairs have small color differences ($\Delta {{E}}_{ab,10}^*\; \lt \;{5.0}$) and LCD means samples pairs have large color differences ($\Delta {{E}}_{ab,10}^*\; \gt \;{5.0}$) in this paper. Two mathematical regression relations, including linear and power exponential regressions, were used to study the relationship between the computed color differences $\Delta {{E}}_{ab,10}^*$ and visual color differences $\Delta {{V}}$.
Fig. 11. Comparisons of visual color differences $\Delta {{V}}$ and computed color differences $\Delta {{E}}_{ab,10}^*$ from sample pairs with different color difference magnitudes: (a) linear relationship and (b) power function relationship.
With the increase of $\Delta {{E}}_{ab,10}^*$, especially when $\Delta {{E}}_{ab,10}^*$ was larger than 5.0, the $\Delta {{V}}$ reported by observers tended to decrease gradually. The regression results are quite similar to those from the 2D sample pairs [27,28]. In the visual experiments involving small color differences, observers had difficulty in scaling color differences, and they tended to avoid $\Delta {{V}}$ values that were close to zero, reporting overestimated $\Delta {{V}}$ values [29]. On the other hand, it is also known that the visual estimations in the range from moderate to large color differences tend to be slightly asymptotic [30].
D. Chromaticity Discrimination Ellipses
1. Chromaticity Ellipses in This Study
The degree of the influences of different parameters on the visual color difference can be quantified by the chromaticity ellipsoids and ellipses, which can be calculated in CIELAB color space for visualization of experimental data. The ellipsoid equation in Eq. (7) was used to fit experimental results for each color center.
Fig. 12. Chromaticity ellipses are grouped and compared according to different parameters: (a) spheres with different gloss; (b) matte samples with different size; (c) gloss samples with different size; (d) matte samples with different shapes; and (e) gloss samples with different shapes.
The properties of the ellipses from different parts can reveal the influences of different parameters on the visual color difference, and especially the size of the ellipses can reflect the color difference tolerance in each color region. The eight sets of experimental data mentioned in Table 1 are drawn into the chromaticity ellipses according to different parameters of the experimental results as shown in Fig. 12. The parameter variables of the data series in Fig. 12(a) are gloss and matte, in Fig. 12(b) and Fig. 12(c) are different sizes, and those in Figs. 12(d) and 12(e) are different shapes.
The parameters for each ellipse in different phases, in terms of semi-major axis (A), semi-minor axis (B), orientation angle ($\theta$), and the size of ellipse (S) calculated from ellipse area ($\pi {{AB}}$), are summarized in Table 4.
Table 4. Chromaticity Ellipses Parameters for Different Phases
Table 5. Comparison of the Present Results with Different Phases in Terms of STRESS Using the Ellipse Equation
The estimation accuracy was evaluated by the STRESS value between the calculated $\Delta {{E}}_{ab,10}^*$ values from Eq. (7) and the visual color differences from the visual experiments. The valuesranged from 5.67 to 40.61, with the mean of 22.16. Compared with the previous studies, the ellipses for 2D samples, such as the RIT–DuPont data from glossy paint samples reported in reference [24,32]; the BFD data set, relating to small to medium color differences of the surface colors including textile, paint, ink samples; and the BIGC data sets from matte and gloss printed samples reported in reference [24,33], were quite similar with those for 3D samples in each color center, considering the shape, the orientation, and the size. From Fig. 12 and Table 4, the ellipses for each color region in different phases have different shapes, sizes, and orientations, which may be aroused by different parameters in the experiments. In total, the average size ${{\bar S}}$ of the five ellipses in each part was used to investigate the influences of the parameters, such as gloss, size, and shape on the visual color difference perception, with the values ranging from 3.88 to 5.11. In Sp-4-m and Sp-4-g, the values were both 3.88, and the values were 4.04 and 5.11 in Cy-4-m and Cy-4-g, which indicated that human perception is more sensitive to the color difference from the sphere sample pairs and more tolerant to the glossy cylinder sample pairs. Meanwhile, in Sp-2-m, the average size of the five ellipses is 4.37, larger than that from Sp-4-m, indicating that the 2 cm size of the sphere sample pairs will arouse less visual color difference than that of 4 cm size. Similarly, Sp-4-g and Sp-2-g also support this conclusion. In summary, the results in Table 4 support the conclusions from Section 3, indicating that the matte sphere sample pairs with 4 cm size will arouse larger visual color differences.
Moreover, a quantitative comparison between the ellipses of the present four phases was carried out using the Monte Carlo method developed by Strocka et al. [34], where the $\Delta {{E}}_{ab,10}^*$ values from two ellipses’ equations using 1000 pairs of randomly generated color samples were compared using the STRESS index. The results are given in Table 5 for different phases. The average variation using this method was 19.3 STRESS units for the five color centers, where the blue center has the best consistency, and the gray center has the worst consistency.
Table 6. Main Information of Jiang Lan’s Experiment
Table 7. STRESS Values between the Results from the Present Study and Those from Jiang Lan’s
The last column in Table 5 shows the variables of the two data sets. The STRESS value of the difference between the chromaticity ellipses of each data set in the CIELAB space is used to quantify the effect of different variables. The largest difference is 25.9 between the spherical glossy samples (Sp-4-g) and the cylindrical glossy samples (Cy-4-g), only with shape difference in the two groups. Meanwhile, the smallest difference is 10.9 for Co-4-m and Cy-4-m, with shape difference in the conical matte samples and the cylindrical matte samples. The results indicate that glossy shapes will greatly affect the visual results; see the results from Fig. 12(e).
2. Comparing with Jiang Lan’s Study
The current experimental results for each color center were compared with those found in previous experiments from Jiang et al. [16]. The main information about Jiang Lan’s experiment is summarized in Table 6.
The light source and visual experiment method in our experiment Sp-4-m are similar to the DS and DF data sets obtained in their work. The difference between the two studies is that in Sp-4-m, the color difference belongs to the small and medium color difference magnitudes, with the mean value of 5.0, while in Jiang Lan’s DS sample pairs, the color difference is larger than that of the present study, with the mean value of 10.3. The Monte Carlo method proposed by Strocka et al. [34] was also used to analyze the relationships between the ellipses from Sp-4-m and DS, DF in Jiang Lan’s study. The STRESS values found from ellipse’s equations are shown in Table 7. The best for each phase is indicated in bold, and the worst is underlined.
In the comparison of the chromaticity ellipse differences between the Sp-4-m and the DS, DF data sets from Jiang Lan’s study, the shape had a greater influence than color difference magnitudes on the visual color difference computed by different chromaticity ellipses. It can also be seen that the difference between the plane and the sphere on the chromaticity ellipse is larger than the difference between other shapes in Table 5, which had the maximum STRESS value of 25.9 among different shapes.
4. DISCUSSION AND CONCLUSION
In this study, 440 pairs of 3D samples with different shapes (spheres, cones, and cylinders), different sizes (4 cm and 2 cm), and different optical properties (matte and glossy) were prepared by Sailner 3D color printers, surrounding the CIE five color centers (gray, red, yellow, green, and blue). These samples were divided into four experiments with a total of eight phases. The average CIELAB color difference of each phase sample is 4.74–6.16, belonging to the magnitudes of small and medium color difference; 26–45 observers performed the visual experiments with the gray scale method, and finally 191 sets of visual data sets were collected.
The parametric effects (gloss, 3D shape, and size) on the perceived color difference were compared by the visual color differences and chromaticity ellipses. The results showed that:
- a) The visual color difference of the matte sample pairs increased by 10.9% compared to the glossy sample pairs. As the $\Delta {{V}}/\Delta {{E}}_{\textit{ab}}^*$ values of the matte samples were larger than those of the glossy samples, and the sizes of the matte and glossy samples had little differences, it can be concluded that the major visual differences between the matte and glossy samples were lightness differences, since the mean differences of the chromaticity ellipse size are very small.
- b) Comparing different 3D shapes, it was found that the spheres possessed larger visual color differences compared with those with the shapes of cone and cylinder when they have similar $\Delta {{E}}_{ab,10}^*$. In the matte and glossy sample sets, the visual color differences for spheres increased 2.7% and 13.6% with respect to the values found for the cones, and they increased 5.5% and 6.9% with respect to values found for the cylinders, respectively.
- c) The visual color differences of 4 cm spheres are greater than those of 2 cm spheres. In the matte and glossy sample sets, the visual color differences for spheres of 4 cm increased 9.3% and 31.8% with respect to values found for spheres of 2 cm, respectively.
The chromaticity ellipses were calculated to compare the color difference and the consistency of different parameters with the indices of the size of the ellipses and the STRESS value, respectively; the results indicated that the glossy samples with different shapes will arouse quite different visual perceptions, especially for sphere and cylinder samples. Beside the high number of visual assessments performed in the current work, following CIE recommendations on color difference evaluation [35], we feel that new reliable experimental data are necessary, in particular for 3D objects.
Funding
Beijing Municipal Youth Talent Support Program (2018); College’s Scientific Research Project (BIGC Ec202003, BIGC Ec202102); Discipline Construction of Light Industry Technology and Engineering (BIGC 21090122016).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
REFERENCES
1. T. Debroy, H. L. Wei, J. Zuback, T. Mukherjee, and W. Zhang, “Additive manufacturing of metallic components—process, structure and properties,” Prog. Mater. Sci. 92, 112–224 (2018). [CrossRef]
2. Y. L. Cheng and K. C. Huang, “Preparation and characterization of color photocurable resins for full-color material jetting additive manufacturing,” Polymers 12, 650 (2020). [CrossRef]
3. A. Sohaib, K. Amano, K. Xiao, J. M. Yates, C. Whitford, and S. Wuerger, “Colour quality of facial prostheses in additive manufacturing,” Int. J. Adv. Manuf. Tech. 96, 881–894 (2018). [CrossRef]
4. K. Xiao, F. Zardawi, R. Noort, and J. M. Yates, “Developing a 3D colour image reproduction system for additive manufacturing of facial prostheses,” Int. J. Adv. Manuf. Tech. 70, 2043–2049 (2014). [CrossRef]
5. A. Brunton, C. A. Arikan, and P. Urban, “Pushing the limits of 3D color printing: error diffusion with translucent materials,” ACM Trans. Graph. 35, 4 (2015). [CrossRef]
6. J. Yuan, G. Chen, H. Li, H. Prautzsch, and K. Xiao, “Accurate and computational: a review of color reproduction in full-color 3D printing,” Mater. Des. 209, 109943 (2021). [CrossRef]
7. P. D. Burns, “Accuracy of approximations for CIELAB chroma and hue difference computation,” Color Res. Appl. 22, 61–64 (1997). [CrossRef]
8. M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001). [CrossRef]
9. M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006). [CrossRef]
10. C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, M. H. Brill, and M. Pointer, “Comprehensive color solutions: CAM16, CAT16, and CAM16-UCS,” Color Res. Appl. 42, 703–718 (2017). [CrossRef]
11. M. Giesel and K. R. Gegenfurtner, “Color appearance of real objects varying in material, hue, and shape,” J. Vis. 10(9):10 (2010). [CrossRef]
12. M. Olkkonen and D. H. Brainard, “Perceived glossiness and lightness under real-world illumination,” J. Vis. 10(9):5 (2010). [CrossRef]
13. R. J. Lee and H. E. Smithson, “Low levels of specularity support operational color constancy, particularly when surface and illumination geometry can be inferred,” J. Opt. Soc. Am. A 33, A306–A318 (2016). [CrossRef]
14. B. E. I. Xiao and D. H. Brainard, “Surface gloss and color perception of 3D objects,” Visual Neurosci. 25, 371–385 (2008). [CrossRef]
15. CIE, “CIE 8-17 methods for evaluating colour difference between 3D colour objects,” 2017, http://cie.co.at/technicalcommittees/methods-evaluating-colour-difference-between-3d-colour-objects.
16. L. Jiang, G. Cui, M. Melgosa, K. Xiao, and S. Sueeprasan, “Color-difference evaluation for 3D printed objects,” Opt. Express 29, 24237–24254 (2021). [CrossRef]
17. CIE, “Colour fidelity index for accurate scientific use,” CIE 224:2017 (CIE, 2017).
18. CIE, “CIE guidelines for coordinated research on colour-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).
19. R. S. Berns, Billmeyer and Saltzman’s Principles of Color Technology, 3rd ed. (Wiley, 2000).
20. M. Melgosa, J. Martínez-García, L. Gómez-Robledo, E. Perales, F. Martínez-Verdú, and T. Dauser, “Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula,” Opt. Express 22, 3458–3467 (2014). [CrossRef]
21. P. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007). [CrossRef]
22. M. Melgosa, P. A. García, L. Gómez-Robledo, R. Shamey, D. Hinks, G. Cui, and M. R. Luo, “Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability in color-difference experiments,” J. Opt. Soc. Am. A 28, 949–953 (2011). [CrossRef]
23. CIE, “Validity of formulae for predicting small colour differences,” CIE 230:2019 (CIE, 2019).
24. M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and colour-difference formulae using printed samples,” Color Res. Appl. 37, 326–335 (2012). [CrossRef]
25. W. R. J. Brown, “The effect of field size and chromatic surroundings on color discrimination*,” J. Opt. Soc. Am. 42, 837–844 (1952). [CrossRef]
26. R. Huertas, M. Melgosa, and E. Hita, “Influence of random-dot textures on perception of suprathreshold color differences,” J. Opt. Soc. Am. A 23, 2067–2076 (2006). [CrossRef]
27. M. Huang, G. Cui, M. Melgosa, M. Sánchez-Marañón, C. Li, M. R. Luo, and H. Liu, “Power functions improving the performance of color-difference formulas,” Opt. Express 23, 597–610 (2015). [CrossRef]
28. M. Huang, Y. Xi, J. Pan, Y. Li, Y. Wang, and X. Li, “Optimization of the method for color measurement and color-difference calculation of holographic prints with light pillars,” Appl. Opt. 60, 6989–6999 (2021). [CrossRef]
29. E. Kirchner and N. Dekker, “Performance measures of color-difference equations: correlation coefficient versus standardized residual sum of squares,” J. Opt. Soc. Am. A 28, 1841–1848 (2011). [CrossRef]
30. G. G. Attridge and M. R. Pointer, “Some aspects of the visual scaling of large colour differences—II,” Color Res. Appl. 25, 116–122 (2000). [CrossRef]
31. M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986). [CrossRef]
32. M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997). [CrossRef]
33. M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29, 883–891 (2012). [CrossRef]
34. D. Strocka, A. Brockes, and W. Paffhausen, “Influence of experimental parameters on the evaluation of color-difference ellipsoids,” Color Res. Appl. 8, 169–175 (2010). [CrossRef]
35. M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007). [CrossRef]
