The determination of age and gender by implementing new image processing methods and measurements to dental X-ray images

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The determination of age and gender by implementing new image

processing methods and measurements to dental X-ray images

Emre Avuçlu

a,⇑

_{, Fatih Bas}

_ßçiftçi

b

a

Department of Computer Technology, Aksaray University, Aksaray, Turkey

b

Department of Computer Engineering, Technology Faculty, Selçuk University, 42003, Selçuklu, Konya, Turkey

a r t i c l e i n f o

Article history:

Received 2 November 2017

Received in revised form 14 June 2019 Accepted 23 August 2019

Available online 28 August 2019 Keywords:

Age and gender estimation from teeth Morphological measurements Panoramic radyografi Image processing techniques

a b s t r a c t

All of the features used to identify and distinguish people from others constitute that person’s identity. For any reason, a person’s identity may need to be identified and distinguished from other people. Authorities provided the credentials of a living or dead person in such cases from the forensic institutions. The identification process must be done correctly. In this study, specific measurement calculations were made on dental x-ray images to determine age and gender. Age and gender information of the persons were systematically determined by working with panoramic dental ray images. Panoramic dental x-ray images were taken out of bounds, and a total of 1315 tooth images and 162 different tooth groups were used. These images have been subjected to 3 different preprocess operations. Each preprocessed image is recorded in different (M1, M2, M3) folders. Then, image processing techniques applied for the first time to the tooth images (Area, Perimeter, Center of gravity, Similarity ratio, Radius calculation) were applied. This information of the teeth is also kept in separate XML (XMLlist-1, 2, 3) files. The application was developed in C # programming language. The user loads the tooth image into the application. This image can be predicted by comparing it with the comparison group (area, etc.) after the desired prepro-cessing. The highest estimated age and gender estimates are 100% and 95%, respectively.

1. Introduction

Identification is one of the most important aspects of forensic medicine. All the features that are active in recognizing, identifying and distinguishing a person are called ‘‘identity”. For many reasons (earthquake, flood, fire etc.), it may be necessary to define the iden-tity of a living or lifeless body[1]. The concept of identity is not only an individual or a social phenomenon but also an interna-tional character[2]. One of the most important elements in the concept of identity is to determine the age of the person. Age; is one of the physical characteristics that make up the individual’s medical identity, such as gender, height, body weight, hair, skin, eye color, fingerprints, bones and teeth[3].

The person’s body may have undergone a significant change due to any cause, or the external characteristics may not give any infor-mation to that person. In this case, the only structure that can be used for identification is the teeth. They are not affected much by physical factors and external factors. They can stay together

for long periods of time and stay on the lifeless body. For this rea-son, it has been stated that using teeth for identification has a more positive result than other organs. Atlases depicting the stages of development and the emergence of teeth, dental applications and is used for age estimation in forensic science. This method is used in x-ray images taken from teeth found both in living individuals and in inanimate bodies. Especially in mass disaster where there are many lifeless bodies, it is a method used in identification stud-ies[4–8]. It has also been suggested that teeth have more accurate results than other organisms in the organism due to their hardness and low metabolism[9–11].

Determination of age in forensic medicine, is a very important issue in terms of criminal and civil law. Therefore, identifications made by looking at anatomical features and lifetime changes on the organism should be made with the least amount of error and objective evidence[10–12]. Studies carried out in judicial events to date show that identification will remain a favorite field of foren-sic sciences. In terms of forenforen-sics, operations for individuals or inanimate bodies begin with identification. Race, gender, age, phys-ical characteristics (height, weight, skin, hair, eye color, etc.) are the identification parameters given priority by forensics[4–11,13–15]. Many studies have been done on dental x-ray images. They per-formed different segmentation and identification processes on

https://doi.org/10.1016/j.measurement.2019.106985

⇑ Corresponding author at: Department of Computer Technology, Aksaray University, Aksaray, Turkey.

E-mail addresses:emreavuclu@aksaray.edu.tr(E. Avuçlu),basciftci@selcuk.edu. tr(F. Basßçiftçi).

Contents lists available atScienceDirect

Measurement

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dental x-ray images[16–24]. They performed age estimation using dental X-ray images using different methods[25–28]. Age estima-tion was performed by measuring the different areas on the ground [29]. Estimates of age were made by measuring in young and child teeth [30–34]. Age estimation was performed depending on the skeletal size in the area[35–37]. Different applications and mea-surements were made about teeth[38]. Emre et al. to determine the age and gender from dental images, they performed different studies using image processing and artificial intelligence tech-niques[39,40].

In this study, the database was prepared manually with tooth images obtained from panoramic dental X-ray images. Pre-processing techniques are applied to these images first. Then, image processing methods that have not been applied to dental X-ray images have been applied. These methods were developed by calculating the area, perimeter, center of gravity, similarity ratio, and radius of teeth. Image processing techniques applied in the image are explained in detail in the following sections. With these image processing techniques used, the age and gender of the tooth images were estimated.

2. General Methodology

In this study, age and gender were estimated by applying image processing techniques to dental x-ray images. The dental images are kept in the source folder in the main index. Then this folder is applied Method-1, Method-2, Method-3 respectively. Images created from these methods are stored in folders M1, M2, M3. Each method is a separate image processing technique for preprocess-ing. The methods are described in detail in the following sections. XML lists are created for each of the M1, M2, M3 folders. For each tooth, these XML files contain numerical information obtained by area, perimeter, center of gravity, similarity ratio, and radius. This numerical information is compared to the knowledge of the tooth image loaded into the application. Comparison can be performed according to a desired method. As shown in Fig. 1 below, the methods are applied to the tooth images as preprocessing first. Then, according to preference (with otsu or classic threshold) the tooth images are converted into binary form. In the application, if Method-1 and by area comparison are selected, the area

information of all the teeth in XMLlist-1 is compared. In the same way, the comparison process can be performed according to the perimeter, center of gravity, similarity rate, radius. The general structure of the program is as shown in Fig. 1 below. Each process is independent of each other. Preprocessing methods and techniques can be combined as desired.

2.1. Dataset creation

The result of official correspondence with panoramic dental x-ray images was obtained from different oral and dental health cen-ters and private hospitals. These images are in the form of a panoramic dental X-ray image. Panoramic dental X-ray images were first recorded with age and gender information. Each image was examined one by one on these recorded images and robust teeth were selected.

In the universal numbering system, the numbering of the teeth begins with the number 1 on the right upper and back teeth (3rd molar). The entire chin is wandered and the upper left most rear tooth (3rd molar) becomes 16. The universal teeth numbering sys-tem shown inFig. 2below.

2.2. Zoom and free drawing operations

Zooming is the software increment of the pixel size of a low pixel size imager. With this application, zooming, size changing and zooming operations can be performed on the dental images.

Fig. 1. General Methodology.

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For smooth transitions in image zoom, digital zooming is used as in Fig. 3.

The user can zoom on the desired tooth image (6x zoom (a)) according to the value of the trackbar, as shown inFig. 4. Zooming is shown to the user by cloning (b) the test picture on a different PictureBox. Once the image boundaries (c) have been drawn, the user clicks on the OK button to learn the age and gender of this image.

The tooth area is selected by the user. The click zones are marked with green circles (a) as shown inFig. 4. These sections can be corrected later if desired. The image zooming technique is used to accurately extract the image of the tooth. Selected teeth are separated from border regions. With this selection, the data-base is created. Each tooth is registered to the datadata-base with age, gender, number and Count (AGE_GENDER_ TOOTHNUMBER_-COUNT. jpg). As a result, 23 years old male, tooth number 18, 2nd tooth is recorded as follows: 23_M_18_2.jpeg. If the gender of the tooth is female, the tooth name is kept as F instead of M. These operations were applied to 1315 images obtained by scan-ning a total of 2000 images. A portion of this dataset created in Fig. 5appears.

InTable 1shows how many teeth are used from the 4–21 age group.

InTable 2shows how many teeth were used from the 21–63 age group.

2.3. Pre-Process operations

Many different image processing techniques have been tried during pre-processing. However, the best estimation results are obtained by applying the recommended methods.

2.3.1. Method

The input image is first contrast stretched. Then, the LevelsLin-ear filter is applied. The image is then grayscale converted to grayscaleThresholding is performed in the last step to convert to binary form.

2.3.1.1. Contrast-stretching. Poorly contrasted images (images that are spread over a narrow area of the histogram) are a general way to improve their contrast. The process here is spreading the histogram over a large area. To improve their contrast, we can spread the gray level values out of the original range, applying a piecewise linear function. It is possible to enrich the contrast in the image by using the histogram.

InFig. 6shows the tooth image before and after the contrast stretching process. In the first picture, the histogram value is stacked around 149, while in the second picture it is distributed between 0 and 255. The aim here is to increase the brightness of the gray areas and to make binary regions of the teeth.

2.3.2. Method

The input image is first converted to grayscale. Then the Fore-groundEnhance method is used. The Median softening filter is used to remove the noises that occur after the ForegroundEnhance method. Finally, the image is converted to binary.

Fig. 3. Zooming.

Fig. 4. Zooming and freehand drawing.

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Table 1 4–21 Age DataSet.

Age Gender Count Age Gender Count Age Gender Count

4 F 2 9.5 M 5 15.5 F 7 4 M 4 10 F 11 15.5 M 4 4.5 F 3 10 M 7 16 F 5 4.5 M 6 10.5 F 7 16 M 6 5 F 8 10.5 M 10 16.5 F 10 5 M 9 11 F 5 16.5 M 5 5.5 F 12 11 M 11 17 F 5 5.5 M 11 11.5 F 8 17 M 4 6 F 15 11.5 M 4 17.5 F 9 6 M 18 12 F 4 17.5 M 6 6.5 F 17 12 M 2 18 F 9 6.5 M 13 12.5 F 2 18 M 5 7 F 19 12.5 M 4 18.5 F 12 7 M 16 13 F 4 18.5 M 2 7.5 F 14 13 M 5 19 F 10 7.5 M 16 13.5 F 5 19 M 8 8 F 17 13.5 M 6 19.5 F 16 8 M 16 14 F 7 19.5 M 9 8.5 F 9 14 M 4 20 F 3 8.5 M 8 14.5 F 4 20 M 4 9 F 15 14.5 M 5 20.5 F 7 9 M 8 15 F 4 20.5 M 7 9.5 F 6 15 M 4 21 F 9 Table 2 21–63 Age DataSet.

Age Gender Count Age Gender Count Age Gender Count Age Gender Count

21 M 8 28 M 12 35 M 7 42 M 2 21.5 F 13 28.5 F 11 35.5 F 5 42.5 F 9 21.5 M 7 28.5 M 7 35.5 M 3 42.5 M 10 22 F 7 29 F 5 36 F 12 43 F 2 22 M 8 29 M 11 36 M 5 43 M 3 22.5 F 12 29.5 F 15 36.5 F 10 43.5 F 8 22.5 M 13 29.5 M 7 36.5 M 9 43.5 M 8 23 F 6 30 F 5 37 F 7 44 F 2 23 M 5 30 M 3 37 M 2 44 M 3 23.5 F 10 30.5 F 7 37.5 F 11 44.5 F 5 23.5 M 5 30.5 M 11 37.5 M 6 44.5 M 5 24 F 11 31 F 6 38 F 6 45 M 3 24 M 7 31 M 6 38 M 7 45.5 F 8 24.5 F 8 31.5 F 6 38.5 F 7 45.5 M 4 24.5 M 7 31.5 M 10 38.5 M 9 46 F 10 25 F 5 32 F 5 39 F 4 46 M 5 25 M 7 32 M 6 39 M 3 47 F 9 25.5 F 11 32.5 F 9 39.5 F 6 47 M 7 25.5 M 8 32.5 M 10 39.5 M 9 48 F 9 26 F 6 33 F 6 40 F 6 49 M 5 26 M 8 33 M 4 40 M 6 50 M 5 26.5 F 7 33.5 F 5 40.5 F 4 51 M 7 26.5 M 11 33.5 M 9 40.5 M 3 52 F 5 27 F 13 34 F 3 41 F 7 52 M 7 27 M 4 34 M 6 41 M 4 57 M 5 27.5 F 7 34.5 F 4 41.5 F 5 60 M 5 27.5 M 6 34.5 M 10 41.5 M 7 63 M 5 28 F 8 35 F 5 42 F 3 – – –

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2.3.2.1. Foreground enhance. In order to achieve a higher success rate, a frontal reinforcement method has been developed to ensure that the teeth with the lowest density appear optimally. In this method, the process sequence is as follows;

a) The average color (avg) is calculated from 0 to 255 according to the image histogram (HiÞ.

a

v

g¼X 255 i¼0 Hii= X255 i¼0 Hi ð1Þ

b) The average color (T) between avg-255 is calculated again according to the image histogram.

T¼X 255 i¼avg Hii= X255 i¼avg Hi ð2Þ

c) For each pixel in the image, the comparison is made accord-ing to the T threshold value. Thus, the teeth become more distinctive.

F x; y½ ¼ 0 if F x; y½ > T F x; y½ otherwise

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2.3.2.2. Median fitler. As a result of the color reduction process, an unwanted noise may appear on the new image. To remove this, use the formula in Eq.(4);

F x; y½ ¼ median g p; qf ½ g ð4Þ

where g[p,q] refers to the convolution kernel. In this study, a 3 3 convolution matrix was chosen for performance. The Median filter example is shown inFig. 7.

In the next step in Eq.(5);

T x; y½ ¼ 255 if F x; y½ t

0 otherwise

ð5Þ

the image is transformed into binary by applying Otsu thresh-olding process.

2.3.3. Method

The input image is first made to GrayScale. Then the Fore-groundEnhance method and Median Filter is used. Canny edge detection is applied in the final process.

2.4. Comparing by area

Conected-Components Labeling is applied to binary image obtained from Method-1, Method-2 and Method-3Accordingly, the total number of white pixels in the object obtained gives the area information. The area finding process starts at the (0,0) point and continues until the last white spot on the picture. The area of the image shown in the example image inFig. 8below is 22 pixels.

2.4.1. Connected-Components Labeling

It is used to determine the composition of each object in an image based on neighborhood relations. It is usually preferred in jobs with automatic supervision[41].

The imaged component is measured according to the proximity or colors of neighboring pixels at a certain level and is labeled with a number in the unique structure. Given their proximity, there are 4 and 8-linked types commonly used. In this study, the use of the 4-linked model was preferred because it gave satisfactory results.. The image is represented by an R [x, y] array containing m columns and n rows. Where,8x2 0; :::; m 1f g and8y2 0; :::; n 1f g repre-sent column and row indices. If we think each pixel in the image is a potential disjoint region, we need to define an L [x, y] array of the same size as the R [x, y] array to hold the bound component tags. If we think that the segmented image comes from the discrete region,8S2 R;

Rf¼ Rcb¼

[S x¼1;x–1

Ri ð6Þ

In Eq.(6), Rf represents the objects in the image, Rcis the

com-plement of the cluster, Rb represents the background of the

clus-ters. Two-pass algorithm is used in this study. In the first pass; By scanning the R image line by line, it makes an L value (label) assignment that is non-zero for each non-zero R [x, y] pixel. The L value in this is determined by looking at the pixel neighborhood type as shown inFig. 9.

The 4 connected component labeling methods are shown on a sample image Fig. (10-a). The result obtained after the 1st and 2nd pass is likeFig. 10-b.

2.5. Comparing by perimeter

A binary image obtained from 1, 2 or Method-3 is applied to the Conected-Components Labeling method. Accordingly, Canny edge extraction filter is applied to the obtained object, and the sum of the edge points is found. This gives us the perimeter. Canny edge detection algorithm is applied in the exam-ple image inFig. 11below and an enlarged corner of the tooth is shown. Red arrows are used to calculate the perimeter of each tooth by gathering the edges shown as examples.

In order not to find the wrong edge, the edge detection algo-rithm is applied as inFig. 12.

Fig. 7. Median Filter.

Fig. 8. Area calculation.

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The freely drawn part is the pulp area of the tooth. For this rea-son, this area should be included in the tooth. The number of dots that form the edges of a tooth is the perimeter.

2.6. Comparing by gravity

A binary image obtained from 1, 2 or Method-3 is applied to the Conected-Components Labeling method. Accordingly, the center of gravity of the object is obtained. The

result is a point P (x, y). If there is more than one center of gravity, the Polygon center of gravity is applied.

2.6.1. Polygon center of gravity

For each object in image (Conected-Components), the center of gravity is calculated separately. Since the coordinate values of all the objects in this image are known, the center of gravity of the image can be calculated by the function shown as M1 in the fol-lowing Eqs.(7-a),(7-b).

The resulting binary images may contain two or more different numbers of areas. For this reason, the connected component label-ing method is applied. If a slabel-ingle label value is assigned in the acquired image, one gravity center is calculated. If there is more than one object occurrence, different objects are calculated one by one. After this process, the center of gravity of each object is cal-culated again with the coordinates of its own center of gravity. This gives to us more accurate results. Such teeth are more common in children. The calculation is formulated as the calculation of the center of gravity of a polygon object. The center of gravity calculate is easy for a one-piece binary tooth image shown inFig. 13a below. However, Polygon Center of gravity is used to calculate the center of gravity of a tooth image as inFig. 13b, c.

Fig. 10. 4-connectivity component labeling process.

Fig. 11. Edge detection.

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According to the coordinate values of all the objects in this image; can be calculated by the function shown as M1 in the fol-lowing Eqs.(7-a) and (7-b).

For example, the classical threshold is applied inFig. 14below (such an image is undesirable for accurate estimates). As a result, 11 different object centers were formed in the tooth image. First, the center of gravity of all of them is found one by one. Coordinate data of this center of gravity (x, y) is obtained. By applying the fol-lowing formula 7a and 7b to these coordinates, the general gravity center of the object is found.Fig. 14shows general the center of gravity and polygon with 11 corner points.

Where G inFig. 14is the final gravity center. In the polygons, the formula shown in the following Eqs.(7-a) and (7-b)is used in the calculation of the center of gravity of an 11-point object (y> = 0 and the center number of n objects):

M1x¼

Xn1

i¼1 xiþ1yi xiyiþ1

ðxiþ xiþ1Þ=11A ð7-aÞ

M1y¼

Xn1

i¼1 xiþ1yi xiyiþ1

ðyiþ yiþ1Þ=11A ð7-bÞ

where A is the number of objects and (x, y) is the coordinates of the center of gravity of the object i.

2.7. Comparing by similarity

The tanimoto similarity function (Ts), is used to compare the

similarity between two pictures in an environment where the pic-tures have bits that can be 1 or 0. In the two picpic-tures, each bit in the same coordinate is processed with the logical ‘‘and” and ‘‘or” operators to be compared to each other. Ai shows the i. bit of the A picture and Bi shows the i. bit of the B picture. Accordingly, the tanimoto similarity can be written as the following Eqs.(8-a)and in other words(8-b):

TsðA; BÞ ¼ cmpANDsumiðAi¼ Biand Ai¼ 255Þ;

cmpORsumiðAi¼ 255ior Bi¼ 255Þ;

ThenTsðA; BÞ ¼ cmpAND=cmpOR ð8-aÞ

TsðA; BÞ ¼ X i Ai^ Bi= X i Ai_ Bi ð8-bÞ 2.8. Comparing by knuckle

A binary image obtained from 1, 2 or Method-3 is applied to the Conected-Components Labeling method. The perimeter of the object obtained is drawn with a rectangle. Then the center of gravity method is applied to the center of gravity. By drawing a line from the center of gravity to the Xmin region of the rectangle, the radius of the region near the mid-distance is obtained. InFig. 15radius calculation process is shown.

2.9. Finding mirror teeth

Theoretically, a tooth is morphologically identical to its mirror (area, perimeter, etc.). When the tooth finding process is per-formed, the form as shown in Fig. 16below is opened. Fig. 16 below shows the image of the teeth in the lower left dent (number

Fig. 13. Polygon Center of gravity.

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19) and the mirror (number 30). These forms are two separate forms.

Fig. 17below shows the picture for children (K named) and the same tooth number mirrored (T named) teeth.

The images shown inFig. 16andFig. 17above are displayed as information to the user after recognizing and finding the teeth. 2.10. Flow diagram

In the flow diagram shown inFig. 18below, it is necessary to first create the datasets for the pre-process operations. The neces-sary calculations are made for all the numerical operations per-formed on these databases (area, perimeter etc.). This information is written to the XML file for quick comparison. The user loads the panoramic dental x-ray image he wants to test into the interface. The user draws the boundaries of this tooth. This tooth image is designated as the input image. The user can add this image to the database if he wants. If Mirror option is selected, mir-ror teeth are processed. Comparisons are made according to the method and comparison option. The tooth closest to the tooth information after comparison is found in the data base. The close-ness of all teeth with the nearest tooth is listed and shown in the graphic. After these operations, the age and gender of the tooth image uploaded by the user is estimated.

3. Results

Fig. 19shows the estimation and comparison of all teeth in the graph. The black lines show the distance of each tooth from the tooth being tested. The graph inFig. 19shows comparisons by area for all the teeth. The blue line represents the teeth to be predicted. The nearest tooth to this line is identified by the red rounded region and the label is displayed on the graph with the name.

The following Fig. 20 is the result graph according to the perimeter.

The distance graph according to the center of gravity inFig. 21 is shown below.

Fig. 22below shows a distance chart based on the similarity ratio of a different tooth image.

InFig. 23shows the calculation graph of the radius of a different tooth image.

As can be seen from the pictures, the most definite result is obtained by comparing the similarity rate.Fig. 24shows how the tooth to be predicted is different from the other teeth. So a good separation operation was carried out. Looking atTable 3 below, the best results were obtained as a result of the operations per-formed according to Method-2. Results based on the similarity rate provided a 100% success rate in all three methods.

4. Dıscussıon

Determination of age in forensic medicine is a very important process. In this study, new methods and techniques originally developed on tooth images were used to determine age and gen-der. The database used in the study was created manually. The database is the largest in the literature and contains gender and age knowledge from almost every age. In literature, it is very diffi-cult to find dental X-ray images arranged in any online system and there is very few image. In this study, not a single method for age determination, but many image processing methods are used. In the previous studies on dental X-ray images, tool or ready program was used in general. The application has a dynamic structure. The database can be reconstructed from different images. In applica-tion, a tooth image can be tested in different methods and tech-niques (area, etc.) for more precise identification. The most accurate estimate can be reached in the end according to the age and gender. This process provides more precise information.

Fig. 16. Mirror tooth finding in adults.

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In 37.5_F_18_1 and 37.5_F_18_2 the same age and gender group in the dental group, the dental images may be different as shown in Fig. 24. This situation can happen in any group of teeth. If the data-base is prepared this way, the error rate may be higher in some test methods. Since the center of gravity of such teeth is calculated incorrectly, the results are adversely affected.

The information (area etc.) of the teeth of two different ages may be the same. This event is a low possibility. Because the tooth images are processed with pixel calculations.

The application gives more accurate results if the teeth to be added to the database have a steep appearance. Creating a data-base is very difficult. Because it is difficult to find a panoramic den-tal X-ray image at the desired age when desired. In this study, 1300 (2630 teeth with mirrors) images were obtained from 1600

images. In practice and theory, the tooth dimensions of people are different from each other. For this reason, this study tried to remove this effect by using different methods and different bench-marks. Studies done in the literature only make age estimates. For any reason (inheritance, etc.), gender discrimination may also be required, whether live or not. With the application made, it is pos-sible not only to estimate the age but also to make the gender estimate.

5. Conclusion

In this study, age and gender determination was performed using image processing methods on dental x-ray images. Firstly,

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dental panoramic X-ray images are provided. From these images 1315 (2630 teeth with mirrors) were assigned a border image and added to the database. The morphological properties of the teeth were utilized in the age determination process. Preprocess opera-tions were first applied to the images and databases were created according to each method. When estimating the age, the areas of the teeth, the perimeter calculate, Center of gravity, the similarity

rate, and the radius are calculated separately. Age and gender esti-mates are compared separately with each of these characteristics. The results obtained are compared with the other age estimation studies in the literature and are shown inTable 4below.

In the implementation, the best estimates were obtained by comparing Method 2 and the similarity ratio. Comparisons based on area information have been high because the teeth of the white

Fig. 19. Result graph by area.

Fig. 20. Result graph by perimeter.

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region pixels were collected. Radius calculate has more accurate results than center of gravity. Since the perimeter values of the teeth in the database are very close to each other, the farthest esti-mates have been compared by the perimeter.

The highest estimation rates of the methods according to age and gender groups are as shown inTable 5. These ratios may be higher by changing the tooth images in the database.

Fig. 22. Result graph by similarity rate.

Fig. 23. Result graph according to radius.

Fig. 24. Teeth of the same age.

Table 3

Accurate estimation results by age and gender (%).

4–9 AGE 9–14 AGE 14–22 AGE 22–63 AGE

(M) (F) (M) (F) (M) (F) (M) (F)

Methot_1- Area %90 %90 %90 %90 %90 %90 %80 %80

Methot_1-Perimeter %70 %70 %70 %70 %70 %70 %60 %60 Methot_1-Center of Gravity %80 %80 %80 %80 %80 %80 %80 %80 Methot_1- Similarity Rate %100 %100 %100 %100 %100 %100 %100 %100 Methot_1-Radius %85 %85 %85 %85 %85 %85 %85 %85

Methot_2- Area %95 %95 %95 %95 %95 %95 %95 %95

Methot_3- Area %85 %85 %85 %85 %85 %85 %85 %80

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Declaration of Competing Interest

The authors declare that they have no known competing finan-cial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work is supported by the Selçuk University Scientific Research Projects Coordinatorship/Konya, Turkey.

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Table 4

Comparison with the other method.

Method Error (Standard Error = SE, Year = Y)

Number of teeth used Kvaal Method[42] ±9.8 SE, ± 0.5–2.5 Y 100 Cameriere Method[43] ± 5 SE 100 Yang and et al. Method[44] ± 8.3 SE 28 Star and et al. Method[45] ± 8.44 SE 111 Proposed Method -2, Area ±0.5 Y 1315 Proposed Method -2, Perimeter ±2 Y 1315 Proposed Method -2, Center of Gravity ±1.5 Y 1315 Proposed Method -2, Similarity Rate ±0 Y 1315 Proposed Method -2, Radius ±1 Y 1315

Table 5 Best results.

Area Perimeter Center of Gravity Similarity Rate Radius Method -1 %90 %70 %80 %100 %85 Method -2 %95 %80 %85 %100 %85 Method -3 %85 %70 %80 %100 %85