Color difference thresholds in dental ceramics

journal of dentistry 38s (2010) e57–e64 available at www.sciencedirect.com journal homepage: www.intl.elsevierhealth.com/journals/jden Color difference thresholds in dental ceramics Razvan Ghinea a, Marı́a M. Pérez a,*, Luis J. Herrera b, Marı́a José Rivas a, Ana Yebra a, Rade D. Paravina c a Department of Optics, Faculty of Science, University of Granada, Campus Fuentenueva s/n 18071, Granada, Spain Department of Computer Architecture and Computer Technology, E.T.S.I.I.T. University of Granada, s/n 18071, Granada, Spain c Department of Restorative Dentistry and Biomaterials, The University of Texas Dental Branch at Houston, 6516 M.D, Anderson Boulevard, Ste. 493, Houston, TX, USA b article info abstract Article history: Objectives: The objective of the study was to determine the perceptibility and acceptability Received 22 April 2010 thresholds for dental ceramics using CIEDE2000 (DE00) and CIELAB ðDEab Þ color difference Received in revised form formulas and a novel TSK Fuzzy Approximation. 17 July 2010 Methods: A 13-observer panel performed independent observations of perceptibility and Accepted 19 July 2010 acceptability judgments on 105 pairs of ceramic discs (14 mm in diameter and 3 mm thick). Color differences of the disc pairs were calculated using both color difference formulas (DE00 ranged from 0.10 to 9.91). Two fitting procedures were used: S-shaped curve and TSK Fuzzy Keywords: Approximation. For both procedures, from the resultant fitting curves, the 95% confidence CIEDE2000 intervals were estimated and the 50:50% thresholds were calculated (50% positive and 50% CIELAB negative answers). Acceptability thresholds Results: With the S-shaped fitting procedure, a 50:50% acceptability threshold was found to Perceptibility thresholds be DE00 = 2.25 (r2 = 0.88) and DEab ¼ 3:46 (r2 = 0.85). Corresponding values with a TSK Fuzzy Fuzzy Approximation Approximation were DE00 = 2.23 (r2 = 0.89) and DEab ¼ 3:48 (r2 = 0.86). The perceptibility Dental ceramics thresholds for fitted S-shape curves were DE00 = 1.30 (r2 = 0.74) and DEab ¼ 1:80 (r2 = 0.70) and DE00 = 1.25 (r2 = 0.75), and DEab ¼ 1:74 (r2 = 0.71) for the TSK Fuzzy Approximation. The DL0 , DC0 , DH0 values corresponding to a 50% acceptability threshold were DL0 = 2.44, DC0 = 3.15 and DH0 = 3.24 respectively. Conclusions: The CIEDE2000 color difference formula provided a better fit than CIELAB formula in the evaluation of color difference thresholds of dental ceramics. There was a statistically significant difference between perceptibility and acceptability thresholds for dental ceramics. The TSK Fuzzy Approximation has been proved to be a reliable alternative approach for the color threshold calculation procedure. # 2010 Elsevier Ltd. All rights reserved. 1. Introduction Color difference formulas are designed to provide a quantitative representation (DE) of the perceived color difference (DV) between a pair of colored samples under a given set of experimental conditions. Color difference has been used extensively in dental research and applications, including the quantification of color change caused by processing dental materials1,2, descriptions of coverage error of dental shade guides3,4, color accuracy and precision5,6, color perceptibility and acceptability7,8 and translucency parameter.9 * Corresponding author at: Office 137, Department of Optics, Faculty of Science, University of Granada, Campus Fuentenueva s/n 18071, Granada, Spain. Tel.: +34 958246164; fax: +34 958248533. E-mail address: mmperez@ugr.es (M.M. Pérez). 0300-5712/$ – see front matter # 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jdent.2010.07.008 e58 journal of dentistry 38s (2010) e57–e64 [(Fig._1)TD$IG] In majority of dental color studies, color and color difference are quantified using the CIELAB color space and the associated DEab respectively.10 With the aim of improving the correction between computed and perceived color differences of CIELAB formula, three advanced color difference formulas have been developed: CMC11, CIE9412 and CIEDE2000.10,13,14 CIE10 presently recommends the use of the CIEDE2000 formula whenever in the past the CIE94 or CMC formulas were used. The CIEDE2000 utilises the concepts of chroma and hue, reinforcing the importance of the conceptual developments of Munsell. Comparisons of CIELAB and CIEDE2000 color difference formulas are available in dental literature.15,16 Recent reports showed significant correlations between DEab and DE00 values after polymerisation or thermocycling.16–18 The majority of reported correlations showed only that the values obtained from these formulas were proportional, but not that the two color differences formulas could be used interchangeably to evaluate the color differences of resin composites. Just perceptible color difference refers to smallest color difference that can be detected by human observer. Color difference that can be noticed by 50% of observers corresponds to 50:50% perceptibility threshold. Analogously, the difference in color that is acceptable for 50% of observers corresponds to 50:50% acceptability threshold. The color difference formula is important to allow better correlation between visual judgments (perceptibility and acceptability) and instrumental color difference values. Improved correlation might provide a more accurate clinical interpretation of the color differences in dentistry. A sizeable literature exists on perceptibility and acceptability thresholds in dentistry.7,8,19,20 However, these references predominantly used CIELAB color difference formula, while the number of studies that used CIEDE2000 formula is limited. Mentioned studies are diverse in methodologies employed and results obtained. The objective of the present study was to determine the perceptibility and acceptability thresholds for dental ceramics using the CIEDE2000 and CIELAB color difference formulas. In addition to standard adjustment procedures,7,8,21 a novel Fuzzy Approximation of the perceptible/acceptable percentage curves using a Takagi–Sugeno–Kang (TSK) fuzzy model was performed.22,23 Null hypothesis was that there was no difference between perceptibility and acceptability thresholds for dental ceramics. 2. Materials and methods 2.1. Samples and color measurements A total of 15 ceramic discs, 14 mm in diameter by 3 mm thick, were fabricated8 using mixtures of Vita Omega 900, Vitapan 3D-Master opaque powders, and pink, white, and mauve color opaque powders (VITA Zahnfabrik, Bad Säckingen, Germany). The range of the color coordinates of the ceramic discs were L* = 53.95–76.05, a* = 0.33–9.94 and b* = 4.59–29.75. All discs were within the color range of central and lateral incisor and canine teeth from a published study.24 The 15 ceramic discs were combined to create a total of 105 disc pairs, with Fig. 1 – Relative distribution of CIEDE2000 color differences among pairs of ceramic discs. CIEDE2000 color differences ranging from 0.10 to 9.91. The distribution of color differences is shown in Fig. 1. A non-contact SpectraScan PR-704 spectroradiometer (Photo Research, Chatsworth, USA) was used to measure the spectral reflectance of the ceramic discs. This device can measure color in a way that matches the geometry of the visual assessments, and it has been previously used in dental research.25,26 The discs were positioned 40 cm away from the spectroradiometer and measured at 458. A VeriVide CAC60 viewing cabinet (VeriVide Limited, Leicester, United Kingdom), with a light source simulating the spectral relative irradiance of CIE D65 standard illuminant was employed to provide consistent viewing conditions. The ceramic discs were placed in the centre of the viewing cabinet on a 458 tilted base (which corresponds to diffuse/08 illuminating/measuring geometry). The CIE 1931 28 Standard Colorimetric Observer was used to calculate color. Since teeth are translucent and the oral cavity is dark, a Munsell black background (L* = 2.8, a* = 0.7, b* = 1.9) was used for measurements in this study. Similar to another study,26 a triangular stand was built to hold samples to avoid the specular reflection from the glossy surface. CIELAB color difference ðDEab Þ is calculated as follows:10 h i 2 1=2 DEab ¼ ðDL Þ2 þ ðDa Þ2 þ ðDb Þ (1) where DL*, Da*, and Db* are the differences in lightness, greenred coordinate and blue-yellow coordinate, respectively. CIEDE2000 color difference (DE00) is calculated as follows:10,13,14 DE0 ¼ " DL0 KL SL 2 þ DC0 KC SC  2 þ DH0 KH SH  2 þ RT DC0 KC SC   DH0 KH SH #1=2 (2) where DL0 , DC0 , and DH0 are the differences in lightness, chroma, and hue for a pair of samples in CIEDE2000, and RT is a function (the so-called rotation function) that accounts for the interaction between chroma and hue differences in the blue journal of dentistry 38s (2010) e57–e64 region. Weighting functions, SL, SC, SH adjust the total color difference for variation in the location of the color difference pair in L0 , a0 , b0 coordinates and the parametric factors, KL, KC, KH, are correction terms for experimental conditions. In the present study, the parametric factors of the CIEDE2000 color difference formula were set to 1. To calculate using the CIEDE2000 color difference formula, discontinues due to mean hue computation and hue-difference computation were taken into account, whereby both were pointed out and characterised by Sharma et al.27 2.2. Psychophysical experiments 2.2.1. Acceptability The 105 ceramic disc pairs were judged by a panel of 13 observers (7 females and 6 males aged between 20 and 48). All observers have been screened for normal color vision using the Ishihara charts (Ishihara Color Vision Test, Kamehara Trading Inc., Tokio, Japan 2004) and all have previous experience in color discrimination experiments. During the visual comparisons, the observers were approximately 40 cm away from the ceramic discs pair, which was the same distance used for instrumental color measurements. Each observer was instructed to focus their attention on the centre of the ceramic discs and answer the following question: ‘‘Would you accept the color difference between the two ceramic discs under clinical conditions?’’ The responses for each pair of ceramic discs and each observer (DV – visual color difference) were processed. 2.2.2. defined as the color difference at which an observer had a 50% probability of making dichotomous judgment. The 50% DE point was the level of perceptibility and acceptability, respectively, for each of these judgment types. 2.3.1. S-shaped curve Procedures described in previous studies21,28 were employed to explore the correlation between the visually perceived and instrumentally measured color differences. Thus, for each pair, the percentage of DV answers (% unacceptable or % imperceptible) has been plotted against the instrumentally measured color differences DE00 and DEab . Then, a S-shaped curve given by the equation y = A/[1 + exp(B + Cx)] was fitted using an iterative algorithm (Matlab 7.1 Optimization Toolbox, MathWorks Inc., Natick, MA) of successive approximations to the function and its derivatives, until maximising the value of r. 2.3.2. TSK Fuzzy Approximation A TSK Fuzzy Approximation is generally a method to approximate the unknown function that generates the set of observed data. This approach is used as an alternative method to obtain a smooth curve without a pre-designed formulation that likewise fits the data. A TSK Fuzzy Approximation with Gaussian membership functions and constant consequents was used to perform the approximation of the percentage of answers against the instrumentally measured CIEDE2000 and CIELAB color differences (Matlab 7.1 Fuzzy Logic Toolbox, MathWorks Inc., Natick, MA). Perceptibility For the calculation of the perceptibility threshold, the observers answered the following question: ‘‘Can you detect a color difference between the two ceramics discs?’’ Each observer made a total of 105 perceptibility judgments and these responses (DV – visual color difference) were processed. 2.2.3. Acceptability thresholds in the L0 , C0 and H0 directions (DL0 , DC0 and DH0 ) A preliminary study of acceptability thresholds for lightness, chroma and hue differences has also been conducted in this research. To calculate the acceptability threshold for DL0 , 15 ceramic disc pairs, with the absolute DC0 and DH0 values smaller than 0.5 units, were selected from the initial 105 ceramic discs pairs. Therefore, it was considered that the color differences among these pairs originated basically from the lightness differences, which ranged from DL0 = 0.12–3.11. Similarly, to evaluate the DC0 acceptability threshold, only samples with DL0 and DH0 smaller than 0.5 units were selected (18 pairs, DC’ = 0.15–7.44), while only ceramic pairs with DL0 and DC0 below 0.5 units were used in evaluation of the DH0 threshold (16 pairs, DH0 = 0.13–4.07). 2.3. e59 Fitting procedures Two fitting methods were used, S-shaped curve and TSK Fuzzy Approximation. For both procedures, from the resultant fitting curves obtained, the 95% confidence intervals were estimated and the 50:50 (50% of positive answers and 50% negative answers) threshold was calculated. The 50% DE point was 3. Results 3.1. Acceptability threshold The values of percent ‘‘unacceptable’’ by the observers against the CIEDE2000 color difference (DE00) and 95% confidence curves are plotted in Fig. 2. The fitted curve-percent had the optimal Sshaped curve parameters: A = 97.40, B = 4.53, C = 2.03 and r2 = 0.88 (Fig. 2a). The color difference for 50% acceptability was DE00 = 2.25 (95% confidence interval 1.52–3.03). Corresponding value with a TSK Fuzzy Approximation was DE00 = 2.23 (95% confidence interval 1.55–3.00), with r2 = 0.89 (Fig. 2b). For CIELAB color difference formula, the fitted curvepercent parameters were: A = 98.12, B = 4.29, C = 1.25 and r2 = 0.85. The color difference for 50% acceptability was DEab ¼ 3:46 (95% confidence interval 2.48–4.48) (Fig. 3a). Using a TSK Fuzzy Approximation, the corresponding value was DEab ¼ 3:48 (95% confidence interval 2.49–4.44), with r2 = 0.86 (Fig. 3b). 3.2. Perceptibility threshold Figs. 4 and 5 show the values of percent ‘‘imperceptible’’ and the 95% confidence curves plotted against DE00 and DEab , respectively. For CIEDE2000 color difference formula, the fitted curve-percent was 97.91/[1 + exp(2.75  2.16x)], with r2 = 0.74. The DE00 value corresponding to 50% perceptibility for fitted Sshape curves and TSK Fuzzy Approximation was 1.30 (95% confidence interval 0.50–2.13) (Fig. 4a) and 1.25 (95% confidence interval 0.69–2.22) with r2 = 0.75 (Fig. 4b), respectively. e60 [(Fig._2)TD$IG] journal of dentistry 38s (2010) e57–e64 Fig. 2 – Unacceptable percentages versus color differences (DE00) between pairs of ceramic discs: (a) fitted S-shape curve y = A/[1 + exp(B + Cx)] (b) TSK Fuzzy Approximation with 4 equally distributed rules along the x-axis and constant consequents. For CIELAB color difference formula, the fitted curvepercent was 97.56/[1 + exp(2.59  1.47x)], with r2 = 0.70 (Fig. 5a). The DEab value corresponding to 50% perceptibility for fitted S-shape curve and TSK Fuzzy Approximation was 1.80 (95% confidence interval 0.74–2.92) and 1.74 (95% confidence interval 0.94–2.94) with r2 = 0.71 (Fig. 5b), respectively. 3.3. Acceptability thresholds in the L0 , C0 and H0 directions (DL0 , DC0 and DH0 ) Table 1 shows the optimal parameters determined for the Sshaped curve and the optimal number of rules used for the TSK Fuzzy Approximation for CIEDE2000 acceptability thresholds in the L0 , C0 and H0 directions (DL0 , DC0 and DH0 ). The values for DL0 , DC0 , DH0 corresponding to a 50% acceptability threshold are presented in Table 2. 4. Discussion The 50:50% CIEDE2000 acceptability threshold calculated using the S-shape adjustment curve and the TSK Fuzzy Approximation were similar, but the TSK Fuzzy Approximation has a slightly better adjustment (r2 = 0.89). Recent report8 showed lower values for the CIEDE2000 acceptability threshold. There are a number of important differences between that study and the current one, including range of color differences and different experimental conditions (surround, use of a shutter, etc.) which might have caused discrepancy of [(Fig._3)TD$IG] Fig. 3 – Unacceptable percentages versus color differences ðDEab Þ between pairs of ceramic discs: (a) fitted S-shape curve y = A/[1 + exp(B + Cx)] (b) TSK Fuzzy Approximation with 4 equally distributed rules along the x-axis and constant consequents. [(Fig._4)TD$IG] journal of dentistry 38s (2010) e57–e64 e61 Fig. 4 – Imperceptible percentages versus color differences (DE00) between pairs of ceramic discs: (a) fitted S-shape curve y = A/[1 + exp(B + Cx)] (b) TSK Fuzzy Approximation with 5 equally distributed rules along the x-axis and constant consequents. the obtained thresholds. As for the acceptability threshold, the DE00 corresponding to a 50:50% perceptibility threshold was similar when the S-shaped adjustment curve or the TSK Fuzzy Approximation were used, with better fit obtained with the latter method. The values obtained in this study for the CIEDE2000 acceptability/perceptibility thresholds corresponded approximately to 70% of the values obtained using the CIELAB formula. These results are in agreement with previous studies that pointed a linear correlation between DE00 and DEab , with DE00 values representing a 70–80% of the values of DEab .15,18 Although this behaviour may be valid for specific points in color space (the region of the color space of the studied ceramic discs) it should be noted that it is not necessarily generally valid. The null hypothesis was rejected for both color difference formulas using both fitting procedures. Assuming the 50:50% values as normal distributions with variance estimated [(Fig._5)TD$IG] according to the confidence intervals of the respective curves, a t-test confirmed the difference between the perceptibility and acceptability thresholds, obtaining in all cases a pvalue < 0.001. The mean 50:50% acceptability and perceptibility thresholds obtained with the best fit were DE00 = 2.23 and DE00 = 1.25, respectively. The results showed that the 50:50% perceptibility thresholds were lower than the corresponding acceptability thresholds. Recent study, using computer-simulated teeth, found that the acceptability and perceptibility thresholds were nearly identical.29 Another study, on ceramic fused to metal crowns, found that the DEab acceptability threshold was significantly greater than the perceptibility threshold.30 This comparison among perceptibility and acceptability judgments were not performed independently (only the subjects who previously identified a perceptible color difference were allowed to judge whether the difference was acceptable). Fig. 5 – Imperceptible percentages versus color differences ðDEab Þ between pairs of ceramic discs: (a) fitted S-shape curve y = A/[1 + exp(B + Cx)] (b) TSK Fuzzy Approximation with 5 equally distributed rules along the x-axis and constant consequents. e62 journal of dentistry 38s (2010) e57–e64 Table 1 – Optimal parameters of the S-shaped fitting curves and optimal number of rules used for the TSK Fuzzy Approximation. S-shaped curve y = A/[1 + exp(B + Cx)] optimal parameters 0 DL DC0 DH0 A B C 758.44 93.69 68.90 5.13 3.32 3.11 0.95 1.10 1.26 In our study, the sensorial experiments were independent, so the results could not be affected by the method used in the visual judgments. The use of an adequate color difference formula is important to obtain a better correlation of perceptibility and acceptability to instrumental color difference values. Improved correlation might provide a more accurate clinical interpretation of color differences which can result in research targeted at improving the color replication process in dentistry. We found that CIEDE2000 color difference formula provided higher degree of fit than the CIELAB formula for both acceptability and perceptibility judgments. It is well established that the CIEDE2000 formula that adjusts for the so-called hue-super importance leads to statistically significantly improved performance of the formula against visual data when compared to CIELAB, as does CMC and CIE94. Nevertheless, it seems appropriate to continue studying the CIEDE2000 weighting functions (SL, SC, and SH), which may result in an even better fit with the visual judgments. It is also beneficial the use of an efficient research design to determine the optimum adjustment functions for color of human teeth. Using a valid and applicable formula will improve the modelling of tooth colored aesthetic materials and, ultimately, patient satisfaction. As noted, the number of pairs used to calculate the thresholds for L0 , C0 and H0 differences is markedly lower than the one used for acceptability and perceptibility thresholds, but nevertheless is similar to those reported in literature.8 The results of our study revealled slight differences in tolerance for thresholds in lightness, chroma and hue, especially for the later two. It is well documented in the literature that in the Euclidean metric of CIELAB there is an increase of the tolerance when the color difference is due essentially to the difference in chroma or hue, or the difference in chroma is very large.31 In CIELAB-based color difference formulas, such as CIEDE2000, the tolerance of chroma difference is corrected with a specific weighting function (SC). Some authors have shown that chroma correction is sufficient to eliminate tolerance differences in lightness, chroma and hue and that the hue correction, although significant, is less important than the DC0 correction.32 The slight difference between the tolerance in lightness compared TSK Fuzzy Approximation optimal number of rules 3 3 3 to tolerances in chroma and hue could be due to the specific weighting function defined for lightness in CIEDE2000, or to the fact that the parametric factor KL should have different value. In addition, the rotation function (RT) introduced in CIEDE2000 to weight the interaction between chroma and hue differences in the blue region, was found to be close to zero (for the region of the color space of the studied ceramic discs), which means that this term might have not influenced the values of the DE00. Future work for the development of a new term that includes the interaction between lightness and chroma and hue differences should be undertaken. The calculated acceptability thresholds in each of these directions were higher than the recorded acceptability threshold. This result could be justified by the weighting functions (SL, SC, SH). In our study, the tolerances in chroma, hue and lightness were determined from the differences between the values of chroma, hue and lightness of each sample of the pair (according to: DL0 ¼ L02  L01 ; DC0 ¼ C02  C01 pffiffiffiffiffiffiffiffiffiffiffi and DH0 ¼ 2 C01 C02 sinðDh0 =2Þ), while when calculating the acceptability threshold, the differences in chroma, hue and lightness are weighted by their corresponding functions (always greater than unity). Therefore, for proper comparison between the acceptability threshold and tolerances for each of the directions, the influence of the weighting function on the value of the color difference should be considered. In addition to the usual adjustment procedures, a novel Fuzzy Approximation of the perceptible/acceptable percentages curves using a Takagi–Sugeno–Kang (TSK)22,23 Fuzzy model with Gaussian membership functions and constant consequents was used in this study. As an alternative method to traditional statistics inference, data fuzzy modelling represents a flexible and effective method to model an unknown function from a set of observed data relative to that function or phenomenon.33 This method is receiving more and more attention in explaining and predicting clinical results in medical sciences34 and is being currently used in colorimetric studies in dentistry.23 In a one dimensional approximation problem, the optimisation of a TSK Fuzzy Approximation requires the determination of the number of rules, the position of their respective centres Table 2 – Value for DL’, DC’, DH’ corresponding to a 50:50% unacceptance percentage. r2 50:50% Acceptability threshold DL0 DC0 DH0 S-shaped curve TSK Fuzzy Approximation S-shaped curve 2.71 3.25 3.33 2.44 3.15 3.24 0.92 0.96 0.95 TSK Fuzzy Approximation 0.93 0.96 0.96 journal of dentistry 38s (2010) e57–e64 and the calculation of the optimal consequents.35 In this work, the rule centres were considered equally distributed along the input space, and the rule consequents were optimally obtained using their derivatives with respect to the model output in the minimisation of the value of r (Least Squares LSE approach).36 The number of rules in each case was selected using a 10-fold cross-validation procedure; the number of rules for which the model provided a lowest cross-validation error was chosen to perform the approximation using all data. The performance and generalisation capabilities of both fitting procedures were additionally assessed in each individual fitting using a combined repeated 10-fold cross-validation (10 times 10-fold cross-validation using different random reorderings) and t-test analysis. The t-test confirmed the better performance of the TSK Fuzzy Approximation in comparison to the S-shaped models, with an expected difference among them similar to that shown in the results for the overall In general, we can claim that the real shape of the curve representing the relationship between the instrumental color differences and human-eye perceptibility is unknown. TSK Fuzzy Approximation enable soft and accurate approximations, without limiting the expected shape of the objective function. It does not model a predefined function shape, allowing the adaptation to unknown shapes on the available data, opposite to the S-shaped function. The results of this study showed that TSK Fuzzy Approximation led to a slightly better accuracy in the approximation of the curves than the S-shaped fit, being therefore a reliable alternative for this problem and a recommendable methodology for approximating color data in dentistry. 5. Conclusions Within the limitations of this study, it was found that:  The CIEDE2000 color difference formula provided a better fit than CIELAB formula in the evaluation of color difference thresholds of dental ceramics, which recommends its use in dental research and in-vivo instrumental color analysis.  There was a statistically significant difference between perceptibility and acceptability thresholds for dental ceramics.  TSK Fuzzy Approximation led to a slightly better accuracy than traditional S-shaped curve in the color threshold calculation procedure thus suggesting its use for this type of research and in general for approximating color data in dentistry. Conflict of interest None declared. 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