## 2 Method
### Image Segmentation
#### 2.2.3 Positioning Numbers
[6] referred to the permanent upper-left central incisor as tooth 21. The number records corresponding to each cut tooth are used to facilitate the comparison of results. According to the method described in [4], X-ray film can cause problems such as too large a tilt angle for teeth and inconspicuous tooth roots. Given that tangents will cross each other in advance, when this situation happens, it will cause cutting errors in the subsequent segmentation of the teeth. By looking for the edge as the tangent, the tangent will generally be too inclined. As a result, the cut tooth will be incomplete and will not fit the range of a single tooth. Figure 20: (**a**) Taking the center of the upper row of teeth and (**b**) the center of the bottom row of teeth. After using the proposed watershed algorithm, a new way of cutting teeth is required. [PERSON] et al. [23] proposed a two-step method for after the picture is converted, so that the picture of the teeth reaches a low pixel value due to the conversion. Otherwise, the tooth seam for the high pixel value is overlapped and not clear between the teeth. The pixel value is higher at the dental part, through which the gap, mouth, and long mouth can be connected by forming a continuous curve with a tooth cover. On the contrary, the tooth value is too low, similar to a basin, and the cut is located in conjunction with the last step of the tooth-seam point. This step involves dividing the upper- and lower-row teeth, primarily because the spacing of the upper-row teeth is larger and mostly vertical. The upper row of teeth can be cut using only a simple greedy algorithm [24] to find the gap point as the starting point, like the top or bottom, with which to move a small grid and find the two separated pixel values to the left and right. Five total grids are compared, and the highest value is selected to move. These steps are repeated until the boundary of the upper or lower jaws is reached. The lower teeth are cut with a vertical curve slope, using the gap point and the floral line of the cut slope to determine a vertical line of this slope, which can be used as the bottom row of the cut teeth. Figure 21: Missing teeth errors fixed. Figure 22: FDI World Dental Federation notation system. The cutting accuracy is based on whether the cut tooth area is at least 80% of its original area. We used a manual judgment method. All of the samples were compared to an area of real teeth in proportion. The correction of the tooth edge marking from using the method improved, the marking conditions created by [PERSON] et al. [14], resulting in the following completed marking diagram. As shown in Figure 26, the position of the missing teeth is detected smoothly so that the teeth can be cut more accurately. The growth in accuracy rate before and after manual positioning is recorded here. The cutting accuracy is shown in Figure 19. And Table 1 show the results of edge point detection. Table 2 provides the accuracy rates. In this paper, image contrast adjustment, flat-field correction, and adaptive histogram equalization were used to increase the accuracy of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tooth Position** & [14] & **Our Method** \\ \hline
18 & True & True \\
17 & True & True \\
16 & True & True \\
15 & False & True \\
14 & False & True \\
13 & True & True \\
12 & True & True \\
11 & True & True \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of edge point detection. Figure 26: (a) Edge-marking point before correction and (b) after correction. Figure 25: Completion of tooth cutting. tooth cutting gradually. The proposed method can be used to sequentially strengthen the contrast between teeth and interdental spaces, to improve the accuracy of the teeth cutting, thereby improving the accuracy of marking each tooth's position. According to the cutting results, 32 teeth could be obtained in one X-ray film. Each tooth is given a specific tooth position based on each cutting line.