Dental Shade Matching Method Based on Hue, Saturation, Value Color Model with Machine Learning and Fuzzy Decision

Color information is an important indicator of color matching. It is recommended to use hue (H) and saturation (S) to improve the accuracy of color analysis. The proposed method for dental shade matching in this study is based on the hue, saturation, value (HSV) color model. To evaluate the performance of the proposed method in matching dental shades, peak signal-to-noise


Introduction
The techniques of big data analysis and machine learning are used widely in medicine [detecting pneumonia, (1) autism, (2) and risk of falling, (3) the classification of cancers, (4) and the analysis of cell pseudo-color images (5) ]. A method of dental image analysis is developed in this study. The classification of dental shade was previously reported in Refs. 6-8, and a further study on dental shade analysis is presented in this study.
Most well-known algorithms use machine learning for training and classification. Guo et al. (9) proposed adaptive mask training for vehicle detection with an assistive system for intelligent transportation. In the system, to improve traffic flow, it is easier to study traffic flow using trained data. Moreover, when a feature vector is compromised and used to store biometric information, through deep learning, a machine-learning-based biometric recognition system can ensure accurate results. Yang et al. (10) utilized edge devices that reduce latency and achieved real-time data services in Internet-of-Things (IoT) systems. In healthcare system development, the diagnosis of specific malignancies uses artificial intelligence (AI) techniques to classify symptoms and distinguish whether samples are clean or infected. (11) The results are classified on the basis of promise training and may enable the diagnosis of lymph node malignancy in clinical trials. On the other hand, a widely used application of recognition in biometrics is fingerprint detection. Hsia (12) used binary robustness as a feature of finger vein recognition as a new verification strategy. Finger veins were shown to be a much more stable feature than other biometrics that cannot be copied or stolen.
A small number of people were chosen to receive a new set of teeth, tooth filling, tooth whitening, and other dental surgeries. For teenagers and middle-aged people, a good set of teeth seems to be particularly important. As a result, helping dental patients find the right denture color has become important and necessary. The skill of dentists to accurately determine the right denture color for patients is one of the major factors for patients to consider during denture making. At present, most dentists still use artificial tooth samples as a way for patients to determine the denture ratio by comparing the color of the artificial tooth samples with that of native teeth. A dental plate is used as the standard reference to easily determine the color that matches the natural tooth color.
To determine the tooth color, dentists often compare tooth color labels. (13,14) However, color swatches do not completely cover the distribution range of the natural color shade of a human tooth. Most palettes lack a series of darker red and yellow colors. Moreover, because of the natural tooth color variability and continuous 3D space of the color distribution, a color block cannot contain all the colors in each color range. If the color difference between the real tooth color and the tooth color tab is within the same range, the difference cannot be distinguished by the human eye and the requirements for practical applications can be met. (14,15) The VITA classical color cards are currently being used as the standard in the dental market. Figure 1 shows the VITA classical color cards, Vita Zahnfabrik,(16) and its product-based Vitapan 3D-Master color guide. (17,18) However, the use of these color cards often causes disputes between dentists and patients because the process involved in producing the actual artificial tooth results in a difference between its final color and the color swatches used in color selection. Moreover, the eyes of a dentist may be fatigued after working long hours, thereby reducing the accuracy of color matching. Furthermore, factors such as light, age, mood, and fatigue can also cause discrepancy in the resulting actual color. (19) All of these factors will negatively affect the color matching results. As such, an effective color analysis method based on the HSV color model for color processing and a new fuzzy decision making method is proposed.
To avoid the above-mentioned problems caused by manual judgment, we propose an image processing technique for color matching. For standard dental colorimetric images, a digital camera is used to create a picture library of the VITA 3D-Master shadow tab, as shown in Fig.  1. Typical resulting images of the captured color chart are shown in Fig. 2. The color of the denture can be determined by comparing the real tooth sample with the color samples in the colorimeter to attain a more accurate match.

Literature Review
Algorithms for automatically matching the color of teeth using image processing have been proposed. (20,21) First, color correction is applied to different images. The system that decides on the color matching analyzes the image of the color card captured with a digital camera. (22) Because the tooth surface is measured with a different device, a color map or average color is necessary. Both the reproduction and verification of shade are needed in the analysis to carry out color matching in the dental clinic. (23) A camera calibration model that includes the Spatial CIELAB (S-CIELAB) method was proposed in Refs. 24 and 25. Using the big data to obtain the required accuracy is the key point to increase the accuracy of all the results. (26) The method of computer-aided image processing uses S-CIELAB (27) as a classification indicator and was proposed in Ref. 28. Furthermore, a structural similarity index (SSIM) comparison module (28) has been used to analyze hue, saturation, value (HSV) colors. Statistical issues in big data regarding values and attributes have been observed. The regression modelling with basic inference procedures, the aspects of model adequacy confirmation, and polynomial regression models and their variations have been investigated. (29) Attempts to establish or identify related dependent or independent values have been presented in Ref. 30. The mathematical expressions for modeling the behavior of random variables have been derived. Furthermore, one variable in the linear modeling of the regression results has been found to be used frequently. Lin et al. (31) proposed a new program for analyzing colorimetric tooth color matching using peak signal-to-noise ratio (PSNR) and a fuzzy decision method. The results indicated an improved accuracy of 92.31%, which is significantly higher than the accuracy of only 32.69% of previous methods. The fuzzy decision method has a higher accuracy and a higher score than the PSNR standard method. Furthermore, this matching method is consistently much better than the traditional method used by dentists. As such, the basis of the matching color method (31) techniques, specifically linear regression, have been widely used because of their simplicity and effectiveness. In machine learning, a classifier is trained using the defined features. In particular, the accuracy is always the key component of analysis. The improved accuracy in tooth color matching (32) confirmed the validity of the use of the color template with four measured values. Digital images of the samples were taken from digital cameras with color accuracy. Wee et al. (33) used various calibration models for the dental color matching of the 264 color patches and 65 shade tabs.
Labeling with a certain accuracy is necessary to calculate the required weighting coefficients, which are examined while training and testing the classifier. To attain the exactness of the classifier, appropriate features and sufficient data are chosen to train a specific set. In addition, the accuracy of the classifier is relative to the amount of data provided to the classifier and the number of selected attributes. The images of the tooth are first converted to the HSV color system representation. (34) Different color layers of the HSV have been analyzed using the matching criteria of the PSNR, composite peak signal-to-noise ratio (CPSNR), SSIM, and S-CIELAB. Y'CbCr can be used to optimize the transmission of color signals. Here, Y stands for brightness or luminosity, which is a grayscale value; Cb and Cr stand for blue and red density offset components, respectively. Therefore, this approach is backwardcompatible with monochrome television, which is entirely black and white. Furthermore, three independent video signals are transmitted simultaneously using the RGB color model. We provide the benefits of reduced transmission data and a smaller bandwidth used by the methods of saturating images and specified pixels in colors. Thus, the HSV color system is similar to visual judgment, but the combination of HSV and machine learning results in a huge improvement.

Image acquisition
A digital camera is used to obtain pictures of each VITA 3D-Master shade tab. (34) It is ensured that the environment while capturing photos of each tab simulates the actual conditions of the dentist assisting the patients during the matching of tooth color. Two photos are taken to generate two sets of images for the test datasets, namely, datasets A and B. A colorimetric analysis is then performed on these two datasets to label each photo, and the photos are arranged in the same order as those of the VITA 3D-Master shade tabs. Each dataset includes 26 tagged photos with depths of 24 bits per pixel and 8 bits for each of the R, G, and B color values. The average size of the images in the dataset is 360 × 520 pixels. Figure 3 shows the flowchart of the proposed tooth color matching algorithm. There are four main steps: color photo preprocessing, criteria evaluation, the addition of parameters for weighting coefficients, and fuzzy decision.

Step 1: Preprocessing of color photos
Normalization is applied to the raw images to adjust the pixel intensity range. The extension of the dynamic range is the main idea of standardization. This standardization brings the image into a range of normalized values to avoid diagnosis error. The image file should be normalized to a format that includes the whole dynamic range of the digital blocks specified. After the standardization, the photo is segmented to remove unnecessary items from the standardized features. Furthermore, the segmentation is fixed by changing one aspect ratio to another without stretching the image. After these preprocessing steps, the images must be evaluated while using the dataset to ensure the completeness of data. The S-CIELAB, CPSNR, and PSNR formulas are captured from an image obtained using a digital camera. As such, the original image is stored in an RGB format. Accordingly, the substep pertaining to the format is the conversion of the RGB image to the HSV format, which is advantageous since it simplifies the colorimetric analysis. Equations (1)-(3) show the conversion from the RGB format to the HSV format.
Each tooth photo is then scaled to a fixed size of 300 × 500 pixels, followed by the segmentation of the length and width of the photo to 50 to 250 pixels. As shown in Fig. 4, the scaled image is used for comparison with other data sets. The scaling and cutting process is part of the normalization of the size of the tooth images. Consequently, the accuracy of the colorimetric analysis is improved.

Step 2: Evaluation of criteria
The captured images in datasets A and B were obtained using the same VITA 3D-Master shade tabs. Therefore, these two datasets are compared by different tooth color matching methods to determine the matching accuracies of the methods. When the target photo in one  dataset is matched with the corresponding photo in the other dataset by the tooth color matching method, matching is considered correct. When the dental color matching method identifies a photo that does not correspond to the target, matching is considered incorrect. The two datasets are used to evaluate the performance characteristics of the different tooth color matching methods.
There are four evaluation criteria that are used in the proposed algorithm. The first criterion is the S-CIELAB of the HSV image, which is a measure of the color difference. A small S-CIELAB value indicates that the colors of the two images are highly similar. Therefore, the first evaluation criterion is to select the tooth image with the smallest S-CIELAB value. The second and third criteria respectively concern the H (hue) and S (saturation) values of the PSNR criterion of the tooth image. The higher the PSNR, the higher the color similarity. The fourth criterion is the SSIM standard, which is used to evaluate the similarity of the dental image structure. In terms of image measurement, it is consistent with the judgment of the image by the human eyes. As such, the higher the SSIM, the more similar are the images. Finally, the target image will be selected on the basis of the smallest S-CIELAB value, the highest SSIM, and the highest H and S PSNRs. Once determined, the module for the weighting coefficients of parameters is set.

Image evaluation criteria
S-CIELAB (35) In previous studies, (32,34) ΔE * ab in S-CIELAB was used, and the color difference was applied individually to a single uniform color patch. This is based on the concept of spatial distribution. A smaller S-CIELAB value implies that the images are more closely related and have smaller distortions. The S-CIELAB ΔE * ab can be calculated using Eqs. (4)- (8).
, where X, Y, and Z are the three color values of the object. X n , Y n , and Z n are the three color values of the reference white. Each halftone patch of high visibility is represented by the scanned values of X n , Y n , and Z n . After the prediction of S-CIELAB, the calculation of specifications, and the comparison of halftones, the average field and ΔE values are distributed at average levels. (34) Moreover, the values of the original halftone patch for both the pixel and the corresponding pixel are compared with the overall index. The parameter L is 100 times the Munsell brightness; when L is set to 0, the color becomes black, and when it is set to 100, the color becomes white. The parameters a * and b * indicate red-green and yellow-blue coordinates, respectively.
CPSNR (36) In the general method, the components of the R, G, and B color model are combined to form a colored image. The quality of the resulting image can be evaluated using the CPSNR criterion. In this work, the CPSNR is calculated by combining the components of H, S, and V to form an image, and then it is used for judgment. A larger CPSNR implies a smaller image distortion. The relevant definitions of CPSNR are shown in Eqs. (9)-(11).
PSNR (37) PSNR values are commonly measured in work on image quality. As shown in Eqs. (12)- (14), the maximum value and error terms in the images are considered for evaluation.  I n is the n-th pixel value of the original image and P n is the n-th pixel value of the processed image.
Structural similarity index (SSIM) (38) SSIM is an index used to measure the similarity of two digital images. As shown in Eqs. (15) and (16), the maximum value of the image and the error term are considered for evaluation. Because of its simplicity and effectiveness, SSIM has been popularly used in applications related to image and video processing in recent years.
Step 3: Add parameters for weighting coefficients Draper and Smith (30) described a method of obtaining the values and attributes of a problem through a statistical graph. In addition, the dependent and independent variables are identified and analyzed for establishing or identifying existing relationships between them. This procedure is described as linear regression in statistics and is commonly used since it is simple and efficient.
The steps are as follows. First, the analysis of the colorimetric modules of datasets A and B. Second, the appropriate interval weighting coefficients are integrated by linear regression. The coefficients are obtained from experimentally determined evaluation indices. Third, the control interval is adjusted throughout the experiment. The idea is to widen the interval of its judgment values by using the dichotomy, which compares the two adjacent values and marks the close one to simplify the procedure, to easily compare these indices. The dichotomy compares the two adjacent values and marks the close one to simplify the procedure.
Training the modules by applying the values of the colorimetric modules, i.e., SSIM, PSNR(H), and PSNR(S), is acceptable since the weighting factors are required and limited. The valid range of correct ratios is between 1 and 9%. Although the valid range is continuously increasing, the results will be less than expected. PSNR(Hw) and PSNR(Sw) represent the adjusted weights of PSNR(H) and PSNR(S), respectively. Figure 5 shows the scores obtained from the scoring formula of colorimetric modules for dentures with 1 to 9% weight training. Figure 6 shows the correct ratios of dentures obtained using the colorimetric module with 1 to 9% weight training.

Step 4: Fuzzy decision
The fuzzy decision is well known in many fields of studies such as power control (39) and prediction. (40) Gulzard et al. (41) provided a fuzzy mapping approach for usability qualities. For individual photos, the matching photo is deter mined by adaptive correspondence by the fuzzy decision. (42) Additionally, the fuzzy controller seeks highquality results automatically. The related factors are set to the correct results of the fuzzy processor and simplistically displayed. For example, the proposed method provided the brightness, contrast value, hue, saturation, and environmental parameters, which are found in each tooth detail and are therefore beneficial to controlling the fuzzy decision. The fuzzy decisions based on experimental evaluation (43) and fuzzy logic (44) are well suited for solving problem spaces with partial authenticity. Data mining, the concept of fuzzy logic with classification techniques, is used for processing the uncertainty in a dataset.
A new type of fuzzy decision making that obeys the fundamental rules of machine language was realized (44) and is applied here to the proposed algorithm to select S-CIELAB, SSIM, PSNR(H), and PSNR(S) for tooth color matching. In the proposed fuzzy decision method, one of the inputs is the brightness of tooth color. The brightness of the tab photo is b(n). The other input is the hue of the tooth color in the tab photo. The chroma of the tab photo is c(n). The lightness b(n) and chroma c(n) are indicated by tab numbers of the VITA 3D-Master color guide. For example, the tab number in Fig. 2(d) is 5M1, which means that b(n) is 5 and c(n) is 1.
On the basis of the expert system, the algorithm is designed to use datasets A and B to calculate each accuracy score induction. Table 1 shows the tooth color matching accomplished using the initial fuzzy adjusted rules. Moreover, the values given in the experimental result section are used for training the adjustment rules for a different fuzzy dataset. On acquiring accuracy and score results, the datasets are used to train the different machine learning datasets listed in the following tables. The scoring results obtained using datasets A and B to train the fuzzy adjustment rules are listed in Table 1. To obtain the results in Table 1, datasets C and D are used as test datasets. With the input fuzzy sets of b(n) and c(n), the fuzzy adjustment rule maps the two features to the output fuzzy set of o(n).
With the use of datasets C and D as test datasets, the accuracy and score results listed in Tables 10-14 were obtained. The fuzzy adjustment rule of the two features, namely, the input

Experimental Results
The VITA 3D-Master color guide (15) has 26 dental shadow tabs that can be classified on the basis of brightness and chroma information. As shown in Table 1, the classifications of XM1, XM2, XM3, XL1.5, XL2.5, XR1.5, and XR2.5 are based on brightness. On the other hand, the classifications of 1MX, 2MX, 3MX, 4MX, and 5MX are based on chroma. To develop an index to evaluate the accuracy of tooth shadow matching, a scoring formula [Eq. (17)] with values between 0 and 100 is developed to determine the accuracy of tooth shadow matching. The scoring formula considers the effects of brightness and chroma and uses a linear decrement for matching. On the basis of the results in the above processing, the base image in the comparison database and the reference image in the reference dataset have the most relevant chroma values. As such, the comparison score of the reference image is determined as 100. The second-highest correlation can yield the score of the reference image reduced by one by comparing the chroma value of the real image in the dataset. The total number of teeth defined as having the highest score of 100 is divided by 26 (the number of dental shadow tabs) to obtain a gap unit of about 3.8462. Therefore, the score can be calculated as where N is the ground truth image in the comparison of the dataset, and its chroma value is the most relevant to the Nth reference image in the reference dataset. It shows that even if the score is not accurate, it is close to 100. It also represents the different color spaces of each dental shadow tab. For example, if the colorimetric result is correct, the score is 100 points. If the Table 1 Fuzzy adjustment rules for brightness b(n) and chroma c(n).
colorimetric value is the second most relevant, the given score is 100 -3.8462 = 96.15 points. If a value is the third smallest, the score is 100 -(3.8462 × 2) = 92.31 points and so on. The method discussed in this section is compared with the existing S-CIELAB method for tooth shadow matching. (32) Table 2 shows the results of S-CIELAB (H, S, V) and S-CIELAB (Y, Cb, Cr) (34) with the average score of each reference image in two modes of comparison. The results of CPSNR (H, S, V) and CPSNR (Y, Cb, Cr) (30) are given in Table 3. From Tables 2 and  3, it is evident that the accuracy rates of the evaluation, analysis, and screening using the HSV approach of the VITA 3D-Master color guide (7) are higher than those obtained using Ycbcr.
To determine the clinical application of this method, this study was carried out in collaboration with Dr. Nung-Hsiang Lin and Dr. Yufang Guo of the Department of General Dentistry of Chang Gang Memorial Hospital. Figure 7 shows a sample of original images of a tooth in datasets A, B, C, and D. Through the use of tooth colorimetric plates and related clinical resources provided by Chang Gang Memorial Hospital, the relevant clinical environment has been restored and constructed, including the tooth ratio in the swatch photographing environment and the ease of capturing the target tooth color and using the color comparison technology proposed in this article. The aim of this study is to develop a technology that can be easily used by dentists to automatically compare tooth colors using the proposed program. This will reduce the time taken for tooth color comparison and finding the appropriate denture color. The two proposed methods are S-CIELAB and CPSNR. SSIM, PSNR(H), PSNR(S), and fuzzy methods are also used. The values used for training were from datasets A and B. The performance of color matching is evaluated using different criteria. Each dataset has 26 tooth shadow images taken under different conditions. The S-CIELAB (24) method was used with the first shadow image in dataset A as a reference. Twenty-six (26) S-CIELAB values were calculated using the 26 tooth shadow images in database B. The S-CIELAB value of the tooth Table 3 Scores obtained using CPSNR(H, S, V) and (Y, Cb, Cr) (23)   shadow image in dataset B with the highest correlation (the lowest S-CIELAB value or the highest CPSNR, SSIM or PSNR value) to one tooth shadow image in dataset A is displayed and specified as the correct result. This is done for all 26 tooth shadow images in dataset A. This process is repeated continuously and considered to produce the reference datasets. The number of correct results after comparing dataset A with dataset B is listed in Table 2. Equation (18) is used to compute the accuracy by dividing the number of correctly matched images with the total number of pictures (26 tooth shadow images per dataset). .

No of correct shade matching pictures Accuracy
Total no of pictures = × (18) In Table 3, the comparison accuracies of datasets B and A are listed. The test is repeatedly applied with all the comparison methods described above using the same set of steps with dataset B as the reference for comparing the images in dataset A. Table 4 shows the values of PSNR(V). Tables 5-7 show the values of SSIM, PSNR(H), and PSNR(S) after machine learning was used to select the best weighting coefficients. The weights (H), (S), and (V) are labeled (Hw), (Sw), and (Vw), respectively.
The results of the fuzzy method show that the accuracy of analysis and screening when using HSV is higher than that when using YcbCr. In addition, the whiter areas of the VITA 3D-Master color guide (15) have a higher accuracy, as listed in Table 8.      Table 9 (H, S, V) vs (Y, Cb, Cr). (23) Numbers of exact shadow matching pictures obtained by different methods. SCIELAB (Y,Cb,Cr) (27) CPSNR (Y Cb,Cr) (27) Fuzzy decision (Y,Cb,Cr) (27) Tables 9 and 10 show the corresponding results obtained using dataset B as the reference for comparing dataset A. Furthermore, a statistical method was developed on the basis of the submechanism to standardize the results. Consequently, the results of comparison could be examined in greater detail. Another comparison is performed and the results obtained are listed as scores of machine learning of SSIM and numbers of accurate shade matching pictures. The colorimetric is decided by the purposed algorithm to find out the most closed color of the original tooth color. The goal for this current comparison is to simplify this binary result and show any intermediate trend of inaccuracy.
At the beginning of the experiment, the weight of PSNR(Hw) had a markedly wide color range. To optimize the comparison accuracy, the trial-and-error method may provide a smaller color range. In the following methods, weights in the range from W = 1.0 to 1.1 were used for the dataset images. On the other hand, integrating machine learning enabled the determination Applying the same steps as with PSNR(Hw) to PSNR(Sw), the best weight was found to be W = 1.04. The scores shown in Table 11 were obtained with W = 1.03 and 1.05, which are different from those used to obtain the results in Table 10 (W = 1.07 and 0.9). The weight of PSNR(Sw) is lower than that of PSNR(Hw). The best resulting average can reach up to 100 when using W = 1.02 and 1.04. The results obtained with W = 1.03 and 1.05 are too close to that obtained with W = 1.04. Therefore, the averages of the results obtained with W = 1.02 and 1.06 were used to determine the difference; the accuracies are up to 99.26 and 97.93%, respectively. Table 12 shows the best results for PSNR(Hw) for comparing dataset A with dataset B. Here, it is clearly evident that the optimal accuracy is different from that in Table 10. In contrast to the case of the original PSNR(H) value, the result is significantly improved. When using the original PSNR(H), the average score can only reach 57.4% at the highest. In contrast, with W = 1.08, the average accuracy score can reach as high as 98.52%.   Table 13 shows the best results for PSNR(Sw) for comparing dataset A with dataset B. Here, it is clearly evident that the optimal accuracy from Table 12 is different. As seen in Table 9, when using the original PSNR(S), the score can only reach 98.22%. When W = 1.04 is used, the accuracy can reach 100%.
By applying the same steps as with PSNR(Hw) and PSNR(Sw), we found the best weight using the SSIM(Hw, Sw, V) method to be W = 1.02. Referring back to Table 13 above, adding a weight when comparing the images results in an accuracy higher than that obtained without weight. Furthermore, the comparison accuracy does not continue to improve as the weight increases. After the accuracy reaches a certain value, it decreases as the weight increases further. Therefore, each method has its own optimal weight that gives the highest comparison accuracy. There is no single weight value that can result in the highest comparison accuracy for all the different methods.
The average accuracies obtained using the four different criteria are listed in Table 15. The proposed method (41) had an accuracy of 32.69%. Considering the CPSNR(HSV), SSIM, and PSNR(V) methods, the average accuracy rate increased to 93.72, 91.94, and 83.58%, respectively. The use of the PSNR measurements of H and S layers resulted in improved accuracies of 56.59 and 98.00%, respectively. Compared with existing methods, the method proposed in this study yields a significant improvement. In addition, the results with machine  learning in each colorimetric calculation also improved the scores for PSNR(H) and PSNR(S) to 97.64 and 99.93%, respectively. As for the fuzzy decision method, the proposed method showed the best performance with 100% accuracy.
In Tables 12-15, the differences in scores are due to adding the different weighting coefficients after adding PSNR(H) and PSNR(S). Moreover, Table 15 shows the results of the comparison of dataset B with dataset A. Testing is repeated with all the methods and the results are listed accordingly. Here, dataset B is used as the reference for comparing dataset A, and Table 16 shows the results when dataset A was used as the reference. The results of the two comparison modes are averaged, as shown in Table 17.

Conclusions
The S-CIELAB index combines luminance, red-green positions, and yellow-blue positions into one index. In addition to using a mixed index (including luminance and color information), 26 dental shadow tabs were classified into the two dimensions of luminance and chroma for selecting a color space. Therefore, using the indexes PSNR(H), PSNR(S), and PSNR(V) increased the accuracy of shadow matching because the focus of the proposed method is on one color space of the image without affecting the information in the other color spaces. Table 15 (H, S, V) vs (Y, Cb, Cr) (31) . Accuracy results for four different criteria for shade matching. SCIELAB (Y,Cb,Cr) (27) CPSNR (Y,Cb,Cr) (27) Fuzzy Decision (Y,Cb,Cr) (  As shown in Table 13, the average score of S-CIELAB (H, S, V) was 94.53%. For CPSNR (H, S, V), the average score increased to 93.72%, as shown in Table 3. The average scores were significantly improved to 97.64 and 99.93% by using PSNR(Hw) and PSNR(Sw), respectively, as shown in Tables 7 and 8.
Finally, the proposed fuzzy decision was found to show the best performance, with an average score of 99.26%, as shown in Table 8. The use of the H and S image layers for tooth color matching together with the proposed fuzzy decision making method yielded excellent results compared with the other methods.