An efficient image processing methodology based on fuzzy decision for dental shade matching

Abstract

For dentists, it is very important to determine the color of the denture. Shade selection in dental practice is an important and difficult task. In the dental shade matching process, the shade selection will be affected by the observer’s physiological conditions such as age, mood, fatigue, and so on. These will make a difference on the judgement between the matching shade and the actual teeth color. In the past, dentists use shade tabs as a reference basis to match the teeth in the intra-oral environment. In this paper, an efficient color analysis methodology based on image processing and fuzzy decision techniques is proposed for dental shade matching. Since the color information is a very important index for the shade matching, the proposed methodology used the chrominance values Cb and Cr to increase the accuracy of color analysis. In order to improve the performance of the proposed methodology, three formulas, such as PSNR value of Cb, PSNR value of Cr, and S-CIELAB value, were selected by a fuzzy decision model. As shown in the results, the proposed efficient methodology based on fuzzy decision techniques improved at least 1.92 % in average accuracy and 0.59 in average score from the PSNR (Cb) and PSNR (Cr) in this work. In addition, the average values of the accuracies and scores in this work are 92.31% and 98.74, respectively, which are much better than the previous studies. To summarized, this work is the first study that applied fuzzy decision with the PSNR (Cb), PSNR (Cr) and S-CLIELAB information for dental shade matching. The results showed that the proposed methodology performs better than the previous work and other methods.

Keywords

Dental shade matching fuzzy decision chrominance Cb Cr PSNR (Peak Signal-to-Noise Ratio)S-CLIELAB

1 Introduction

For dental color determination, the method of comparison of teeth color and shade tabs is frequently applied [1, 2]. There are many kinds of shade guides commonly used in dental market. For example, Vita Zahnfabrik [3] and its product evidence-based Vitapan 3D-Master shade guide [4, 5] is shown in Fig. 1. However, it is not accurate enough to determine shade matching by using human eyes only to compare the colors of the shade guides and the real teeth. Since the comparison results will be affected by the ambient light source or the observer’s physiological conditions, the matching results are not accurate or obvious enough. Moreover, the eyes of dentists will be tired for a long working time, which will decrease the accuracy of the shade matching. This will lead to a negative impact to influence the shade matching results.

Fig.1

(a) VITA classical [3] and (b) VITA 3D-Master [4].

In order to avoid the above-mentioned problems, an image processing technique is proposed for the shade matching. For a standard dental shade image, a digital camera was used to create shading picture library of the shade tabs VITA 3D-Master as shown in Fig. 1(b). Typical results of shading tabs are shown in Fig. 2. The shade of the denture can be determined by comparing the real teeth with shade tabs to get an accurate matching result.

Fig.2

Four shade tabs photos in VITA 3D-Master (a) 1M1, (b) 2M2, (c) 3M3, and (d) 5M3.

Several efficient image-processing-based computer algorithms to automatically match the dental shades were proposed in [6]. The color correction is first applied for different images. The color spectrum captured by digital camera [7] was analysed and clustered for the decision system to perform shade matching with good performance. A computer-aided image processing methodology by using S-CIELAB [8] as the classification indication was presented in [9]. A CIELAB methodology included camera-calibration models had been proposed in [10]. In order to improve the accuracy of dental shading matching of tooth color, a methodology by using four measurements on shade tabs was proposed in [11]. In this paper, a dental image is first decomposed into YCbCr color representation. An analysis on different color layers of YCbCr is performed with matching criterion based on PSNR, CPSNR, and S-CIELAB. The analysis of PSNR(Y) was not used in this work because the shade tabs of VITA 3D-Master were divided into five groups based on their luminance.

A shade matching algorithm is proposed using the chroma elements Cb and Cr with better classification performances. In addition, a fuzzy decision method for dental shade matching is developed, so that each different color of the shade tabs has its own corresponding image evaluation criteria. This improves the accuracy of the dental shade matching. The average accuracy can be as high as 92.31% by using the fuzzy decision method. The organization of this paper is as follows: In Section 2, the proposed novel image processing and fuzzy decision methods are presented. Section 3 discusses the experimental results and compares with other methods. Finally, conclusions are summarized in Section 4.

2 The proposed methodology

2.1 Image evaluation criteria

S-CIELAB, CPSNR, and PSNR are the three image evaluation criteria adopted in the proposed methodology to evaluate the quality of images. These criteria were widely used in image processing.

1. S-CIELAB: Since the S-CIELAB $Δ E_{ab}^{*}$ [12, 13] color difference is only applicable to a single uniform color block, it is derived from the concept of spatial distribution. A smaller S-CIELAB value corresponds to a smaller distortion. The value of S-CIELAB $Δ E_{ab}^{*}$ can be calculated using Equations (1– 5): $Δ E_{ab}^{*} = \sqrt{(Δ L^{*})^{2} + (Δ a^{*})^{2} + (Δ b^{*})^{2}}$ (1) $Δ L^{*} = {\begin{matrix} 116 {(\frac{Y}{Y_{n}})}^{\frac{1}{3}} - 16 & if \frac{Y}{Y_{n}} > 0.008856 \\ 903.3 (\frac{Y}{Y_{n}}) & if \frac{Y}{Y_{n}} \leq 0.008856 \end{matrix}$ (2) $a^{*} = 500 \times (f (\frac{X}{X_{n}}) - f (\frac{Y}{Y_{n}}))$ (3) $b^{*} = 200 \times (f (\frac{Y}{Y_{n}}) - f (\frac{Z}{Z_{n}}))$ (4) $f (t) = {\begin{matrix} t^{\frac{1}{3}} & if t > 0.008856 \\ 7.787 \times t + \frac{16}{116} & if t \leq 0.008856 \end{matrix}$ (5) where $= \frac{X}{X_{n}} = \frac{Y}{Y_{n}} = \frac{Z}{Z_{n}}$ . X, Y, and Z are the three stimulus values of the object. The X_n, Y_n, and Z_n are three stimulus values of the reference white. Each halftone patch in high visibility is represented by the scanned values of X_n, Y_n, and Z_n. By using the specification of SCIELAB predictions and calculations with halftone compared, uniform field with mean equivalent and ΔE values are in average [12]. Furthermore, the pixel values of original halftone patch and corresponding are compared with overall indicators. The L is 100 times of the Munsell brightness value. When L is 0, the color is black and when the value of L is 100, the color is white. The a^* refers to red-green coordinates, and the b^* refers to yellow-blue coordinates.

2. CPSNR (Color Peak Signal to Noise Ratio) [14]: This combines the components of R, G and B to form a color image and then the quality of the resulting image can be evaluated by this criterion. In this paper, the values of CPSNR were calculated by combining the components of Y, Cb and Cr to form an image and then obtained the CPSNR values for judgement. A larger CPSNR value corresponds to a smaller distortion. The relevant definition of the CPSNR is shown in Equations (6– 8). $CPSNR = 10 \times {log}_{10} (\frac{255^{2}}{CMSE})$ (6) $CMSE = \frac{\sum_{n = 1}^{FrameSize} (I_{n} - P_{n})}{FrameSize}$ (7) $\begin{matrix} FrameSize = Image lenth \times Image width \\ \times Number of channels (Gray scale is 1, color is 3) \end{matrix}$ (8) where I_n refers to the nth pixel value in the original image and P_n refers to the nth pixel value in the processed image.

3. PSNR (Peak Signal to Noise Ratio): The PSNR value is widely used in the area of image quality measurement. The maximum value of the image and the error term are considered for evaluation, as shown in Equations (9– 11). $PSNR = 10 \times {log}_{10} \frac{255^{2}}{MSE}$ (9) $MSE = \frac{\sum_{n = 1}^{FrameSize} (I_{n} - P_{n})^{2}}{FrameSize}$ (10) $\begin{matrix} FrameSize = Image lenth \times Image width \\ \times Number of channels (Gray scale is 1, color is 3) \end{matrix}$ (11) where I_n refers to the nth pixel value of the original image and P_n refers to the nth pixel value of the processed image.

2.2 Image collection

In order to evaluate the performance of different methodologies for dental shade matching, a digital camera was used to take pictures of each tab in the VITA 3D-Master shade tabs [7]. In advance, the shooting environment was simulated as the actually environment when the dentist help patients to do the dental shade matching. Second, taking two shots and two sets of images used to create two testing datasets. These two datasets are called Dataset A and Dataset B in this study. Third, these two datasets were subjected to colorimetric analysis. The name of each photo in the datasets is also arranged in the same way of VITA 3D-Master shade tabs. Each dataset includes 26 tab photos and the pixel depth is 24 bits, in which R, G, and B are 8 bits each. The average size of images in the datasets is 360×520 pixels.

2.3 The proposed dental shade matching algorithm

Figure 3 shows the flowchart of the proposed dental shade matching algorithm, in which there are three main steps in the algorithm. The first step is pre-processing, the second step is criteria evaluation, and the third step is fuzzy decision. The details of each step will be described as follows:

Fig.3

Flowchart of the proposed dental shade matching algorithm.

Step 1. Pre-Processing

Normalization is a process used to change the range of pixel intensity values. The dynamic range expansion is the main idea of normalization. It brings the image into a range that is normal to the sense and to avoid false evaluation. The motivation is to normalize the full dynamic range of the number blocks specified in the image file format. After normalization the next step is cutting. It removes unnecessary details from the normalized ones. The cutting-fixed is to change it from one aspect ratio to another, without stretching the image. In order to complete the data, the evaluation of image with the datasets is required. It is the prerequisite of S-CIELAB, CPSNR, and PSNR formulas.

After capturing the image on the digital camera, the original images are stored in RGB format. Hence, the first sub-step in pre-processing is to convert the images in RGB format to YCbCr format, which is helpful for facilitating the colorimetric analysis. Equations (12– 14) illustrate the transform of RGB to YCbCr formats. In addition, each tooth photo is scaled to the fixed size of 300×500 pixels, and then the length and width of the photo are cut within a range of 50 to 250 pixels as shown in Fig. 4. The scaled image is used for comparing with the other dataset. The scaling and cutting processes are used to normalize the size of the teeth images for comparison to improve the accuracy of colorimetric analysis. $Y = 0.299 R + 0.578 G + 0.114 B$ (12) $Cb = 0.564 (B - Y)$ (13) $Cr = 0.713 (R - Y)$ (14)

Fig.4

(a) Original image and (b) the normalized and cut region of the image.

Step 2. Criteria Evaluation

The photos in the Dataset A and Dataset B were taken by the same VITA 3D-Master’s shade tabs. Hence, we can use these two datasets as comparison with the different dental shade matching methods to determine the matching accuracy of the proposed method. If a dental shade matching method finds the target of the tab photo in the other dataset, the matching result is correct. Otherwise, if the dental shade matching method finds the tab photo which is not the target, the matching result is incorrect. By using these two datasets, we can judge the performance of different dental shade matching methods.

There are three evaluation criteria used in the proposed algorithm. The first criteria is S-CIELAB of YCbCr images which is used to find the difference of colors and smaller S-CIELAB values represent more similar colors between two images. Hence, the first evaluation criteria is used to select the teeth images which have the smallest S-CIELAB values. The second criteria used PSNR criterion to evaluate the chrominance values Cb of teeth images. In the same way, the third criteria used PSNR criterion to evaluate the chrominance values Cr of teeth images. A higher PSNR value corresponds to higher similarity. Hence, the second and third evaluation criteria are used to select one of the teeth images which has the smallest PSNR value. Finally, the tab images which have the smallest S-CIELAB, and highest PSNR value of Cb and Cr images will be selected. It will then send to the fuzzy decision module.

Step 3. Fuzzy Decision

Fuzzy decision is widely applied in many fields, for example, power control [15], prediction [16], and so on. The fuzzy decision methods based on experimental evaluation [17] and fuzzy logic techniques [18, 19] are suitable to solve the problem spaces with partial truth. In the proposed algorithm, a fuzzy decision method based on if ⋯ then ⋯ rules was created to select one of the three evaluation criteria, S-CIELAB, PSNR (Cb), and PSNR (Cr), for the dental shade matching. In the proposed fuzzy decision method, one of the inputs is brightness of the shade tabs. The intensity of brightness of the tab photos is defined as b(n). The other input is chrominance of the shade tab photos. The value of chrominance of the tab photos is defined as c(n). The brightness b(n) and chrominance c(n) are defined by the number of VITA 3D-Master’s shade tabs. For example, the tab number in Fig. 2(d) is 5M3, which means that the b(n) is 5 and c(n) is 3.

Table 1 shows the fuzzy adjustment rules for the proposed dental shade matching algorithm, which is designed based on an expert system. The datasets used to obtain the results of accuracies and scores in Tables 3 and 9 are different datasets to train the fuzzy adjustment rules. The Dataset C and Dataset D were used to train the fuzzy adjustment rules tabulated in Table 1. The results of accuracies and scores in Tables 3 and 9 were obtained by using Dataset A and Dataset B as testing datasets.

Table 1

Fuzzy adjustment rules for the brightness b(n) and chrominance c(n)

b(n)/c(n)	XM1	XM2	XM3	XL1.5	XL2.5	XR1.5	XR2.5
1MX	S-CIE	S-CIE	x	x	x	x	x
	LAB	LAB
2MX	PSNR	PSNR	PSNR	S-CIE	S-CIE	PSNR	S-CIE
	(Cb)	(Cb)	(Cb)	LAB	LAB	(Cr)	LAB
3MX	PSNR	PSNR	PSNR	PSNR	PSNR	PSNR	PSNR
	(Cr)	(Cr)	(Cr)	(Cr)	(Cr)	(Cr)	(Cr)
4MX	PSNR	PSNR	PSNR	PSNR	PSNR	PSNR	PSNR
	(Cb)	(Cb)	(Cb)	(Cb)	(Cb)	(Cb)	(Cb)
5MX	PSNR	PSNR	PSNR	x	x	x	x
	(Cr)	(Cr)	(Cr)

Table 2

Numbers of accurate shade matching picture for different methods

	S-CIE LAB [9]	CPSNR	PSNR	PSNR	PSNR	Fuzzy
	(Y, Cb, Cr)	(Y, Cb, Cr)	(Y)	(Cb)	(Cr)	Decision
Dataset A compared to Dataset B	7	8	7	23	23	24
Dataset B compared to Dataset A	10	14	15	24	21	24

Table 3

Accuracy results of four different criteria for the shade matching

Test image	S-CIE LAB [9]	This Work
	(Y, Cb, Cr)	CPSNR (Y, Cb, Cr)	PSNR (Y)	PSNR (Cb)	PSNR (Cr)	Fuzzy Decision
Dataset A compared to Dataset B	26.92%	30.77%	26.92%	88.46%	88.46%	92.31%
Dataset B compared to Dataset A	38.46 %	53.85%	57.69%	92.31%	80.77%	92.31%
Average	32.69%	42.31%	42.31%	90.39%	84.62%	92.31%

Table 4

Score results of S-CIELAB (Y, Cb, Cr) criterion

Reference Tab	S-CIELAB
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100
1M2	100	100	100
2M1	69.23	11.54	40.39
2M2	96.15	96.15	96.15
2M3	100	92.31	96.16
2L1.5	100	100	100
2L2.5	92.31	80.77	86.54
2R1.5	92.31	53.85	73.08
2R2.5	100	100	100
3M1	53.85	53.85	53.85
3M2	88.46	42.31	65.39
3M3	80.77	65.38	73.08
3L1.5	92.31	100	96.16
3L2.5	61.54	76.92	69.23
3R1.5	73.08	100	86.54
3R2.5	69.23	50	59.62
4M1	61.54	96.15	78.85
4M2	61.54	100	80.77
4M3	84.62	65.38	75
4L1.5	100	100	100
4L2.5	69.23	80.77	75
4R1.5	38.46	80.77	59.62
4R2.5	42.31	76.92	59.62
5M1	15.38	100	57.7
5M2	65.38	96.15	80.77
5M3	100	100	100
Average	77.22	81.51	79.36

Table 5

Score results of CPSNR (Y, Cb, Cr) criterion

Reference	CPSNR
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100
1M2	100	100	100
2M1	69.23	26.92	48.08
2M2	100	100	100
2M3	100	100	100
2L1.5	100	100	100
2L2.5	80.77	46.15	63.46
2R1.5	96.15	84.62	90.39
2R2.5	100	100	100
3M1	65.38	61.54	63.46
3M2	96.15	42.31	69.23
3M3	88.46	80.77	84.62
3L1.5	69.23	100	84.62
3L2.5	80.7	92.31	86.51
3R1.5	80.77	100	90.39
3R2.5	69.23	57.69	63.46
4M1	84.62	100	92.31
4M2	88.46	100	94.23
4M3	96.15	88.46	92.31
4L1.5	100	100	100
4L2.5	84.62	96.15	90.39
4R1.5	46.15	80.77	63.46
4R2.5	50.00	76.92	63.46
5M1	19.23	100	59.62
5M2	73.08	100	86.54
5M3	100	100	100
Average	82.25	85.95	84.10

Table 6

Score results of PSNR (Y) criteria

Reference	PSNR (Y)
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100.00
1M2	100	100	100.00
2M1	69.23	19.23	44.23
2M2	96.15	100	98.08
2M3	100	100	100
2L1.5	100	100	100
2L2.5	76.92	34.61	55.77
2R1.5	96.15	65.38	80.77
2R2.5	100	100	100
3M1	57.69	50	53.85
3M2	96.15	30.77	63.46
3M3	76.92	76.92	76.92
3L1.5	65.38	100	82.69
3L2.5	57.69	80.77	69.23
3R1.5	76.92	100	88.46
3R2.5	53.85	53.85	53.85
4M1	80.77	100	90.39
4M2	80.77	100	90.39
4M3	53.85	65.38	59.62
4L1.5	100	100	100
4L2.5	61.54	100	80.77
4R1.5	38.46	76.92	57.69
4R2.5	53.85	76.92	65.39
5M1	15.38	100	57.69
5M2	53.85	100	76.93
5M3	100	100	100
Average	75.44	81.95	78.70

Table 7

Score results of PSNR (Cb) criteria

Reference	PSNR (Cb)
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100
1M2	100	100	100
2M1	100	100	100
2M2	100	100	100
2M3	100	100	100
2L1.5	100	100	100
2L2.5	69.23	73.08	71.16
2R1.5	100	100	100
2R2.5	100	100	100
3M1	100	100	100
3M2	96.15	76.92	86.54
3M3	100	100	100
3L1.5	88.46	100	94.23
3L2.5	100	100	100
3R1.5	100	100	100
3R2.5	100	100	100
4M1	100	100	100
4M2	100	100	100
4M3	100	100	100
4L1.5	100	100	100
4L2.5	100	100	100
4R1.5	100	100	100
4R2.5	100	100	100
5M1	100	100	100
5M2	100	100	100
5M3	100	100	100
Average	98.22	98.08	98.15

Table 8

Score results of PSNR (Cr) criteria

Reference	PSNR (Cr)
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100
1M2	100	100	100
2M1	100	100	100
2M2	100	100	100
2M3	100	96.15	98.08
2L1.5	100	96.15	98.08
2L2.5	80.77	76.92	78.85
2R1.5	100	100	100
2R2.5	100	96.15	98.08
3M1	100	100	100
3M2	100	76.92	88.46
3M3	100	100	100
3L1.5	84.62	100	92.31
3L2.5	100	100	100
3R1.5	100	100	100
3R2.5	100	100	100
4M1	100	100	100
4M2	100	100	100
4M3	100	100	100
4L1.5	100	100	100
4L2.5	100	100	100
4R1.5	92.31	100	96.16
4R2.5	100	100	100
5M1	100	100	100
5M2	100	100	100
5M3	100	100	100
Average	98.37	97.78	98.07

Table 9

Score results of the proposed fuzzy decision method

Reference	Fuzzy Decision
Image	Dataset A compared to Dataset B	Dataset B compared to Dataset A	Average
1M1	100	100	100
1M2	100	100	100
2M1	100	100	100
2M2	100	100	100
2M3	100	100	100
2L1.5	100	100	100
2L2.5	92.31	80.77	86.54
2R1.5	100	100	100
2R2.5	100	100	100
3M1	100	100	100
3M2	100	76.92	88.46
3M3	100	100	100
3L1.5	84.62	100	92.31
3L2.5	100	100	100
3R1.5	100	100	100
3R2.5	100	100	100
4M1	100	100	100
4M2	100	100	100
4M3	100	100	100
4L1.5	100	100	100
4L2.5	100	100	100
4R1.5	100	100	100
4R2.5	100	100	100
5M1	100	100	100
5M2	100	100	100
5M3	100	100	100
Average	99.11	98.37	98.74

The fuzzy adjustment rules map the two characteristics of input fuzzy sets, b(n) and c(n) to an output fuzzy set o(n). By using the results of the evaluated criteria of Dataset A and Dataset B, each tooth image can be matched to the shade tab with the highest accuracy by selecting the best one of the three criteria. By the proposed fuzzy logic decision method, the accuracy of dental shade matching can be improved efficiently.

3 Experimental results

In this section, the proposed methods are compared with the existing method S-CIELAB for dental shade matching [9]. The proposed methods are CPSNR (Y, Cb, Cr), PSNR (Cb), PSNR (Cr) and Fuzzy Decision. In order to compare the performance of using different criteria for shade matching, we tested on two datasets, Dataset A and Dataset B. Each of the dataset contains the same 26 dental shade images taken at different time. For example, the method S-CIELAB [9] takes the 1st dental shade image from Database A as reference to compute the 26 S-CIELAB values with 26 dental shade image from Database B, respectively. If the S-CIELAB value corresponding to the 1st dental shade image in Dataset B shows the highest correlation (lowest S-CIELAB value, or highest CPSNR or PSNR values), the result is recorded as correct. The above procedure is repeated for all 26 dental shade images in dataset A as references, and the number of correct cases is recorded, as in the Dataset A compared to Dataset B Table 2. If the number of correct cases is divided by the total number 26, the accuracy can be obtained:

$\begin{matrix} Accuracy = \\ \frac{no . of correct shade matching pictures}{total no . of pictures} \times 100 \end{matrix}$ (15) The accuracy is recorded for the Dataset A compared to Dataset B in Table 3. The above procedure is repeated for all compared methods and the results are tabulated correspondingly. The reverse experiment can be done for another direction of comparison which use Dataset B as reference to compare with images in Dataset A; all the corresponding results are recorded in the row of Dataset B compared to Dataset A in Tables 2 and 3. The accuracies of the methods in both comparison directions are averaged, and the results are shown in Table 3. As tabulated in Table 3, on average, the existing method [9] does not perform well, with 32.69% accuracy. For the proposed CPSNR (YCbCr) and PSNR(Y) methods, both the average accuracies were improved to 42.31%. For the proposed use of Cb and Cr layer with PSNR measurement, the performances are improved to 90.39% and 84.62%, respectively. This has a significant improvement from the existing method. Furthermore, for the proposed Fuzzy Decision method, the performance can be up to 92.31%, showing the best results among the proposed methods. In addition, a statistical method through the sub-mechanism is developed to standardize the results. It is more detailed to see the comparison results. We perform another comparison procedure on the results obtained in Table 2. Previously, the comparison of the images of one dataset which shows the most correlated colorimetric in another dataset use the result as correct, otherwise not correct. We aim to ease this binary result and show the intermediate trends of the accuracy. There are 26 shade tabs in VITA 3D-Master [4] and it can be classified according to luminance and chrominance information. For, example, the classification of XM1, XM2, XM3, XL1.5, XL2.5, XR1.5 and XR2.5, as shown in Table 1, is based on luminance. The classification of 1MX, 2MX, 3MX, 4MX and 5MX is based on chrominance. Hence, it is necessary to develop an index to judge the accuracy of the dental shade matching. We developed a score between 0 to 100 degrees to judge the accuracy of the dental shade matching as shown in Equation (16). The concepts of this scores are fair to consider the effect of luminance and chrominance and used linear decrease for miss matching. The idea is as follows. If the result in the above procedure is perfect matching, that is, the ground-truth image in compared database has the most correlated colorimetric value with the reference image in the reference dataset, the comparison score of this reference image is defined as 100. If the ground-truth image in compared dataset has the second most correlated colorimetric value with the reference image in the reference dataset, the score of this reference image is decreased by a decrement, and so on. The decrement is defined as the highest score 100 divided by the total number of shade tabs 26, which is roughly to be 3.8462. Therefore the computation of the score can be calculated as: $score = 100 - (3.8462 * (N - 1))$ (16) where N is the ground-truth image in the compared dataset which has the Nth most correlated colorimetric value with the reference image in the reference dataset. It means that if the score is close to 100, even though it is not entirely correct, it represents only a small color difference. For example, if the colorimetric results are correct, the score is 100 points. If the colorimetric value is the second most correlated, the given score is 100-3.8462 = 96.15 points. If it is the third small, the score is 100- (3.8462 * 2) = 92.31 points, and so on. For the results of S-CIELAB (Y, Cb, Cr), the scores of each reference images for two comparison directions are shown and averaged in Table 4. The results of CPSNR (Y, Cb, Cr), PSNR(Y), PSNR (Cb), PSNR (Cr) and fuzzy decision are shown in Tables 5– 9, respectively. The S-CIELAB is a color difference index and it is derived from the concept of spatial distribution. The color space used in S-CIELAB describes the colors in three dimensions: (1) L^* represents the lightness of the color (2) a^* represents the position between red/magenta and green and (3) b^* represents the position between yellow and blue. It is efficient for the visual representation of the color space. However, the VITA 3D-Master is classified by using luminance and chrominance information. The S-CIELAB index mixes lightness, red/green position, and yellow/blue position into one index and uses the mixed index, including brightness and color information, to select 1 of 26 dental shade tabs classified into the luminance and chrominance two-dimension spaces. Hence, the indexes of PSNR(Y), PSNR(Cb) and PSNR(Cr) can match the shade matching more accurately because they can focus on one space of image without affecting information of other spaces. As shown in Table 4, the average score of S-CIELAB (Y, Cb, Cr) [9] is 79.36. For CPSNR (Y, Cb, Cr), the average score is increased to 84.10, as shown in Table 5. The average scores of the method PSNR (Cb) and PSNR (Cr) are significantly improved to 98.15 and 98.07, as shown in Tables 6 and 7, respectively. Finally, the proposed fuzzy decision has the best performance with an average score of 98.74, as listed in Table 8. Using the Cb and Cr image layers for dental shade matching and the proposed design of fuzzy decision method showed an outstanding results compared with the other methods.

4 Conclusion

In this paper, a novel methodology using PSNR and Fuzzy Decision Method for colorimetric analysis for dental shade matching was proposed. The results showed that the proposed methodology has 92.31% accuracy which is higher than the existing method that has an accuracy of only 32.69%. Through the fuzzy decision method, the accuracy and scores are higher than the PSNR criteria, and this matching method is more objective and consistent than traditional (dentist) judgement. This research results are beneficial for dentists in terms of saving the dental shade matching time and also improving the matching accuracy.

References

Alomari

and Chadwick

R.G.

, Factors influencing the shade matching performance of dentists and dental technicians when using two different shade guides, Br Dent J 211 (2011), 23.

Lee

Y.K.

, Yu

, Lim

J.I.

and Lim

H.N.

, Perceived color shift of a shade guide according to the change of illuminant, J Prosthet Dent 105 (2011), 9–91.

VITA, VITA classical A1-D4 shade guide. [Online]. Available: https://www.vita-zahnfabrik.com/en/VITA-classical-A1-D4-shade-guide-39699,27568.htm.

VITA, VITA Toothguide 3D-MASTER. [Online]. Available: https://www.vita-zahnfabrik.com/en/VITA-Toothguide-3D-MASTER-26230,27568.html.

Paravina

R.D.

, Performance assessment of dental shade guides, J Dent 37 (2009), e15–20.

Chu

S.J.

, Trushkowsky

R.D.

and Paravina

R.D.

, matching instruments and systems, Reviewer of Clinical and Research Aspects, Journal of Dentistry 38 (2010), e2–e16.

Tam

W.K.

and Lee

H.J.

, Dental shade matching using a digital camera, Journal of Dentistry 40 (2012), e3–e10.

Pecho

O.E.

, Ghinea

, Alessandretti

, Pérez

M.M.

and Della

A.B.

, Visual and instrumental shade matching using CIELAB and CIEDEcolor difference formulas, Dent Mater 32 (2016), 82–92.

Wang

S.L.

, Wang

W.T.

, Wu

A computer-aided analysis on dental prosthesis shade matching, International Biomedical Engineering and Informatics Conf BMEI, Shanghai, China, vol. 4, 2011, pp. 1950–1954.

10.

Wee

A.G.

, Lindsey

D.T.

, Kuo

and Johnston

W.M.

, Color accuracy of commercial digital cameras for use in dentistry, Dent Mater 22 (2006), 553–559.

11.

Ishikawa-Nagai

, Ishibashi

, Tsuruta

and Weber

H.-P.

, Reproducibility of tooth color gradation using a computer color-matching technique applied to ceramic restorations, Journal of Prosthetic Dentistry 93 (2005), 129–137.

12.

Zhang

and Wandell

B.A.

, A spatial extension of CIELAB for digital color-image reproduction, J Soc Inf Display 5(1) (1997), 61–63.

13.

, Anisetti

, Wu

, Damiani

and Jeon

, Bayer demosaicking with polynomial interpolation, IEEE Trans Image Process 25(11) (2016), 5369–5382.

14.

Chung

K.L.

, Hsu

T.C.

and Huang

C.C.

, Joint chroma subsampling and distortion-miminization-based luma modification for RGB color images with application, IEEE Trans Image Process 26(10) (2017), 4626–4638.

15.

Wan

S.P.

and Yi

Z.H.

, Power average of trapezoidal intuitionistic fuzzy numbers using strict t-norms and t-conorms, IEEE Trans Fuzzy Systems 24(5) (2016), 1035–1047.

16.

Kavousi-Fard

, Khosravi

and Nahavandi

, A new fuzzy-based combined prediction interval for wind power forecasting, IEEE Trans Power Systems 31(1) (2016), 18–26.

17.

Gulzard

, Sang

, Ramzan

and Kashif

, Fuzzy approach to prioritize usability requrements conflicts: An experimental evaluation, IEEE Access 5 (2017), 13570–13577.

18.

Chen

S.L.

, A power-efficient adaptive fuzzy resolution control system for wireless body sensor networks, IEEE Access 3 (2015), 743–751.

19.

K.L.

, Lin

Y.J.

and Siew

W.H.

, Fuzzy control of nonlinear systems using rule adjustment, IEE Proceedings 146 (1999), 276–282.