THE PEER ASSESSMENT RATING CALCULATION ON 2 DIMENSIONAL TEETH MODEL IMAGE FOR THE CENTERLINE COMPONENT AND TEETH SEGMENTATION ON THE OCCLUSAL SURFACE TEETH MODEL IMAGE

The PAR (Peer Assessment Rating) Index is used by orthodontists around the world to calculate the severeness of a malocclusion. A malocclusion is a dental disease where the teeth are not properly aligned. In Indonesia, the number of malocclusion is relatively high. The occurrence of orthodontics who can treat malocclusion is also low in Indonesia. In 2013, a research is done to create the tele-health monitoring system to provide better treatment of malocclusion in Indonesia. The research is further improved by using different Adaptive Multiple Thresholding methods to segmentate the image. The result will be used to calculate the Centerline component of the PAR Index. The result is a system that could calculate the PAR Index automatically and is compared to the results using manual method.


Introduction
Malocclusion is a type of dental disease where the teeth of a person are not aligned properly.This could cause the jaw to misalign [1].The complication of this disease could cause discomfort, difficulty of breathing, difficulty of swallowing, difficulty of talking and aesthetics issues of the patient's face.The disease could be caused by family genetics, daily diets and trauma caused by accedent.This disease could be treated by orthodontists by applying dental braces to re-align the patient's teeth.
The Peer Assessment Rating (PAR) Index is a method for evaluating the severeness of malocclusion [2].This index was developed by Richmo-nd and friends in 1987.It is one of the most popular malocclusion calculation method used by orthodontists.The calculations of the PAR index are done by measuring the misaligned parts of the teeth as guided in the instructions.A normal dentist will need a special training and guidance from an orthodontist to perform this calculation.
Studies have shown that many Indonesians are suffering from this disease therefore, treatments are needed [3].According to the Indonesian Medical Council (KKI), there are 25,198 dentists in Indonesia [4].This number is not enough according to OEDC countries guidelines.They stated that there needs to be 50 to 80 dentists for every 10,000 people [5] If those numbers are scaled to the Indonesian population, around 118,000 den-68 Jurnal Ilmu Komputer dan Informasi (Journal of Computer Science and Information), Volume 7  If the centerline difference between the lower and upper jaw is less than a quarter of the width of the first incisor of the bottom jaw. 1 If the centerline difference between the lower and upper jaw is between a quarter and a half of the width of the first incisor of the bottom jaw. 2 If the centerline difference between the lower and upper jaw is more than a half of the width of the first incisor of the bottom jaw.Upper right segment 2.
Lower right segment 5.
Lower right segment 6.
Lower left segment 7.
Left buccal occlusion Figure 1.An example of an ellipse with its variables.
tists are needed.The fact that we are short of dentists could hinder the people who really needs to get treatment for their malocclusion.
To solve that problem, in 2013, a research was proposed to create a telehealth monitoring system.This system will calculate the PAR Index remotely via the internet.To use the telehealth monitoring system, the dentist will need to create a model of the patient's teeth and scan it.The dentist will then send the scanned result to the website of the telehealth and the system will automatically calculate the result of the PAR Index using image processing techniques.
The introduction of the telehealth monitoring system is expected lower the case of malpractice in Indonesia.It is also expected that the system will help reduce the number of Indonesian citizens with malocclusion, so the nation could live healthier.
This research will be focused on improving the segmentation results of the occlusal surface done by the M. Febrian Rachmadi.The research has successfully calculate the Openbite and Overjet components bust lacking quality in the segmentation of the occlussal surface side of the teeth dental model image.This research will also calculate the Centerline component of the PAR index.

The PAR (Peer Assessment Rating) Index
As stated before, the Peer Assessment Rating (PAR) Index is used to calculate the severeness of a malocclusion.The index consists of 11 components that will be totaled by the end.Table 1 contains the list of components of the PAR Index.
On this research, we will focus on calculating the Centerline component.The Centerline component is calculated by measuring the differrence of the contact points of the first incisors for the upper and lower jaw.The difference will then be converted to the PAR Index score relative to the lower jaw incisor's width.If the difference is less than a quarter of the width then it is categorized as normal and given the score 0. If it is between a quarter and half of the width, then it is categorized as a malocclusion and will be given the score of 1.If the difference is larger than a half of the width, then it is severe and will be given the score 2.

Ellipse
The ellipse is a shape that is going to be used to eliminate some noise after the thresholding process.Equation (1) show the equation that is needed to draw the ellipse [7].
The variable x and y is a random variable on the edge of the ellipse a is the width of the ellipse and b is the height is the ellipse.The variable x 0 and y 0 is the center of the ellipse as shown in Figure 1.

Confusion Matrix
The confusion matrix is an evaluation that is used to analyze the accuracy of the segmentation done The result of the segmentation done by the system is classified as positive when the result of the segmentation done manually is positive.FP (False Positive) The result of the segmentation done by the system is classified as positive when the result of the segmentation done manually is negative.

TN (True Negative)
The result of the segmentation done by the system is classified as negative when the result of the segmentation done manually is negative.

FN (False Negative)
The result of the segmentation done by the system is classified as negative when the result of the segmentation done manually is positive.automatically compared to the segmentation done manually [8].The classification is divided into 4 classification.
The classification information could then be used to rate the accuracy from several parameters.The True Positive Rate (TPR) and True Negative Rate (TNR) calculates the rate that the program classify positives and negatives correctly.The False Positive Rate (FPR) and False Negative Rate (FNR) calculates the rate that the program classify positives and negatives incorrectly.The Accuracy calculates the correctness of the program based on TP, TN, FP and FN.The Precision calculates the percentage of the true positives from all the positives classified by the system.The Geometrical Mean (GM) calculates the accuracy when the positive data is significantlly lower than the negative data.For example.when the positive data is only is only 1 pixel, and the negative are 100 pixels, if we classify the all the data into negative, it will have a 99% ACC.But, if we use GM, the accuracy is 0%.In this research, the percentage of the teeth is smaller than the background, therefore to calculate the accuracy, it is more accurate to use geometrical mean.

Pre-Processing
Every image that is processed goes through the pre-processing stage.According to the previous research done by Rachmadi, after an image is minimized by 5 times, a milimeter is equal to 2 pixels in the image [6].The pre-processing is done by cropping the image.This is done to reduce the area of the image which doesn't contain any teeth.It will also make the image more uniformed so it is easier to segmentize the image later on.Figure 1 will show the result of the cropped image.
The next process is to calculate the amount of teeth relative to the image.This is done by creating a ground truth of the image and calculating the percentage of the teeth in the image.After this process is done, the results averaged at 23.3587%.

Adaptive Multiple Thresholding
In this research, Adaptive Multiple Thresholding (AMT) is used to segmentate the image.As men-     tioned previously, The AMT has already been used by Febrian in the previous research.This research still uses the AMT because other segmentation techniques like SLIC Superpixels [9] or any edge-based segmentation could not segmentate the image well.This is due to the fact that the image of the teeth model does not have a well pronounced edges between the teeth and the gum.
The AMT uses the value of the saturation channel of the image as a threshold.To get the saturation value, the image is converted into HSV color model.The image is then segmented according to the the threshold for each levels and all of the levels are going to be combined.
The first type of AMT used is the 15% with 4 levels.This type of Adaptive Multiple Thresholding has 4 stages of process.Each stages creates a different image.The first stage will start with the threshold value of 250 and will take the 5% of the image with the highest saturation value.It will then threshold the image.If the thresholded image is less than 5% of the total image, it will reduce the threshold value by 5 and redo the thresholding process until the thresholded image exceeded 5%.If it has exceeded 5%, then it will pass on the threshold value to the next stage and do the threshold process until it exceeded 10%.If it has exceeded 10% then the threshold value is passed on to the next stage, where it also gets the 10% of the image.
The last stage will get the background of the image with the saturation value between 0 and 120.Finally, the image from the first, second and third level is combined into a single image.
Another AMT method used to segmentate the image is an AMT that takes the same 15% of the image but with 6 levels.The stages are split into 2% each.The first stage will segmentate an area of 2%.The next stage will segmentate an area of 4%.The third and fourth stage will segmentate an area of 6% and 8%.The fifth stage will    segmentate 10% of the image.The last stage will also get the background of the image.
The last AMT method used in this program is AMT 20% with 5 levels.20% is chosen because as stated before, the average teeth to image ratio is around 23%.Therefore, it is expected to segmentate the image better than the previous AMTs.This AMT method have 5 stages, with the first stage segmenting 5% of the image.The next stage segmentate 10% of the image.The third and fourth stage segmentates 15% and 20% of the image.Same as the previous AMTs, the last stage segmentates the background of the image.
After the image is segmented using the Adaptive Multiple Thresholding, there will still be many residues left in the middle of the image.These residues comes from the gum area of the jaw.To eliminate these residues, approximation of an ellipse is going to be applied to the middle area of the image.An ellipse is chosen due to the shape that follows the shape of a human jaw.Each jaw 2, June 2014    has a different size of ellipse, so that it varies according to that jaw's size.
To determine the width and height of each ellipse, the width and length of the jaw needs to be calculated.This is done by calculating the distance of the top-most pixel and bottom most pixel in the jaw to calculate the height of the ellipse.To calculate the width, we calculate the distance of the left most pixel of the jaw and the right most pixel of the jaw.The ellipse is the drawn on to the image and used as a mask to eliminate the residues.
To further eliminate the gum residue near the teeth, the next process will threshold the image with the help of laplacian filter.The laplacian filter is used to define the edges of the image.This is useful in the thresholding, as we need to differrentiate the residue with the teeth.The teeth usually has a brighter area, so the threshold value is slightly lower than the pixel value of the teeth.This varies in each side of the image (bottom, left, top, right) as each side has different intensity.
After the image has been thresholded, there will be some noise left by the laplacian filter.To eliminate this the next process is going to use the hole filling algorithm.The hole filling algorithm will eliminate small noises and it will also fill out small holes between the teeth.
The final process in segmenting the image will use floodfill to fill out large holes between the teeth.The four corners and the center of the image will be the starting point of the floodfill.This is done to make sure that all the areas are filled by the floodfill.
After the image has been floodfilled, the image is then copied, inverted and used as a mask for the original image.When the process is finished, to eliminate gaps between the molars, the process will fill it with lines by using normal iterations.

Implementation of Centerline Component
The implementation of Centerline component takes the image result of the segmentation after the ellipse approximation has been applied (Figure 9).The segmented image will be transformed using morphological dilation and erosion.This is done to smoothen edges of the images, so it will be easier to locate the contact point of the firs incisors.
The next step is to find the center width of each jaw.This is done by calculating the width of the jaw and dividing it in half.After the center width of the jaw has been found, it will then iterate from the center width of the jaw to find the contact point of the first incisors.A contact point is defined by the shape of an arrow head.After the contact point has been discovered for each jaw, it is then subtracted to find the margin.The center width of the jaw is also subtracted with the other    jaw to find the margin.If the margin of the meeting point of the first incisors is 2,5 millimeters more than the margin of the two center width, then the two center width margin will be used as the Centerline calculation.If it is less than 2,5 millimeters, then the margin of the first incisors contact points will be used as the Centerline calculations.This is done so that incase the program falsely pinpoint the contact point of the first incisor, it can still calculate more accurately.

Results and Analysis
As mentioned previously to analyze the result of the segmentation, Confusion Matrix is going to be used [8].The accuracy of the segmentation will be indicated by the geometrical mean of the segmented image.The average result of the segmentation is divided by the three types of AMT used.The dataset of the segmentation consists of 30 occlusal view of the dental model images.Table 4 shows the increasing geometrical mean as each process is done.Process number 1 represents the Adaptive Multiple Thresholding 15% using 4 Level.Process number 2 represents the ellipse approximation.Process number 3 represents the thresholding with the help of laplacian filter.The increasing geometrical mean within each process show that each method used in the segmentation process is effective.
The result of the segmentation using the AMT 15% with 6 levels produce better result than the previous method.This is due to the fact that the AMT 15% with 6 levels has more data than the previous method, thus, increasing the true positive rate of the Confusion Matrix.The Precision also increases because the positive data increases.
The result of the segmentation using the AMT 20% with 5 levels produces the best segmentation overall.The AMT alone produce the worst result among the three due the fact that it also segmented many gum area, therefore decreasing the true positive rate.As the process goes on the geometrical mean increases.This shows that the ellipse approximation and the thresholding is best used with this AMT method.
According to the segmentation results, the color of the dental model also affect the segmentation result.The results shows that the model with the color white produces the best segmentation result.This is consistent with all AMT seg-  mentation.The white dental model manage to average 0.69 in AMT 15% using 4 levels.0.73 in AMT 15% using 6 levels and 0.73 in AMT 20% using 5 levels.
When tested with the same dataset, the Adaptive Multiple Thresholding 20% 5 levels with the ellipse approximation and thresholding with the help of laplacian filter, produces better results than the Adaptive Multiple Thresholding used by the previous research.The average Geometrical Mean of the image processed by the more recent method is 0.69.2 whereas the previous method only managed to average 0.62.
Table 7 shows the result of the Centerline calculation done by the system.It also shows the average difference between automatic calculations and manual calculations done by orthodontics.The average difference of calculation is 1.23 millimeters.With further analyzing the data, it is found that there are several factors that could make the calculations inaccurate.The first factor is if the dental model has a degree of rotation when scanned.This could make the calculations inaccurate as the midpoints are not calculated on a straight line.
The second factor that affects the calculation is the base of the dental model is not properly aligned.This causes the calculation to bias with the unleveled base.The misalignment is sometimes cause by the scanner shaking when scanning the image.The last factor that affects the calculation is the when the two first incisors are stacked together.This caused the system to miss-judge the point not as a contact point of the two incisors.

Conclusion
Of all the segmentation method used, the best segmentation method is the Adaptive Multiple Thresholding 20% 5 levels with ellipse approximation and thresholding with the help of laplacian filter.The result of the segmented image using that method has a Geometrical Mean average of 0.69.Also, the color white is the best dental model color for the segmentation.
The segmentation more recent method of segmentation is also better when compared with the previous method using the same dataset.It produces images with Geometrical Mean of 0.692 as supposed to 0.62 produced by the earlier method.
The Centerline component of the PAR Index is also successfully implemented in this research.But, the techniques used in the process needs to be further improved so that the results are closer to the manual calculations done by orthodontists.

Figure 2 .
Figure 2. The process of cropping an image in preprocessing.This is done to create a more uniformed image with another image.

Figure 3 .
Figure 3.An example of a ground truth of an image.

Figure 4 .
Figure 4.An example of the result of SLIC Super Pixels used on the occlusal surface of the teeth model image.The SLIC Super Pixels cannot segmentate the gum and the teeth.Set threshold_value to 250 for every level n do While level_n is true do for every pixels in image Theshold(threshold_value) Add the thresholded region into image Ln end for every pixels in Ln do Check the percentage of the region if region < 5, threshold_value -5 else if region > 5, level_n false end end end end Combine image L1, L2 and L3.

Figure 5 .
Figure 5. Pseudo code of a general AMT.

Figure 6 .
Figure 6.A flowchart of the AMT 15% with 4 levels process.

Figure 7 .
Figure 7.An example of the result of AMT 15% with 4 levels.

Figure 9 .
Figure 9.An example of the result of AMT 15% with 6 levels.

Figure 11 .
Figure 11.An example of the result of AMT 20% with 5 levels.

Figure 10 .
Figure 10.A flowchart of the AMT 20% with 5 levels process.

Figure 12 .
Figure 12.An example of the result of ellipse approximation.

Figure 13 .
Figure 13.An example of the laplacian filter applied on the image (left) and the result of thresholding (right)

Figure 13 .
Figure 13.An example of the laplacian filter applied on the image (left) and the result of thresholding (right)

Figure 16 .
Figure 16.The result of the morphological dilation and erosion on the image..

Figure 17 .
Figure 17.The final result of the Centerline calculation.The green line indicates where the Centerline of each jaw is located.

Figure 18
Figure 18.A sample of a dental model which has a degree of rotation

TABLE 2 CENTERLINE
COMPONENT OF THE PAR INDEX [2] Score Description 0