## 2 Materials and Methods
### Ground Truth
#### 2.2.2 Extraction Difficulty Classification  
The extraction difficulty of mandibular third molars was determined to train the extraction difficulty classification model. The impaction pattern of the mandibular third molar is determined base on the [PERSON] and Gregory classification and the [PERSON]'s classification. The extraction difficulty was determined into four categories according to the surgical method for extraction. * Vertical eruption: Simple extraction without gum incision or bone fracture;
* Soft tissue impaction: Extraction after a gum incision;
* Partial bony impaction: Tooth segmentation is required for extraction;
* Complete bony impaction: Where more than two-thirds of the crown is impacted, this requires tooth segmentation and bone fracture. The surgical extraction method is determined by the combination of the impaction pattern of the mandibular third molar as determined by both [PERSON] and [PERSON]'s classification criteria [28]. Based on [PERSON] and [PERSON] classification, impacted mandibular third molars are classified as Classes A, B,and C according to the depth of the impacted mandibular third molar, and Classes I, II, and III according to the distance between the mandibular third molar and the ascending mandibular ramus. Figure 2 shows an example of each class. Depth of the impacted mandibular third molar:  
* Class A: The impacted mandibular third molar's highest point of occlusal surface is at the same height as the occlusal surface of the adjacent tooth. * Class B: The impacted mandibular third molar's highest point of occlusal surface is between the occlusal surface of the adjacent tooth and the cervical line. * Class C: The impacted mandibular third molars' highest point is below the cervical line of the adjacent tooth. Distance between the mandibular third molar and ascending mandibular ramus:  
* Class I: The distance between the distal surface of the mandible's second molar and the anterior edge of the mandible is wider than the width of the impacted mandibular third molar's occlusal surface. * Class II: The distance between the distal surface of the mandible's second molar and the anterior edge of the mandible is narrower than the width of the impacted mandibular third molars' occlusal surface and wider than 1/2. * Class III: The distance from the distal surface of the second molar of the mandible to the anterior edge of the mandible is narrower than the width of the impacted mandibular third molar's occlusal surface. Figure 3 shows the impaction patterns according to the depth of the impacted third molar and the distance between the third molar and the ascending mandibular ramus [36; 37; 38]. Based on [PERSON]'s classification, there are six types based on the angle of the impacted mandibular third molar: vertical (\(-10\) to \(10\)), mesoangular (\(11\) to \(79\)), horizontal (\(80\) to \(100\)), distoangular (\(-11\) to \(-79\)), transverse (buccolingual), and inverted (\(-80\) to \(111\)). Figure 3 shows the impaction pattern according to the angle of the impacted third molar, which is divided into six types based on the [PERSON]'s classification. Various studies have determined the extraction difficulty through a combination of impaction types [39; 40; 41; 42]. In addition, we determined the extraction difficulty of the mandibular third molar by the combination of the impacted pattern determined by Pell and Gregory classification and [PERSON]'s classification. According to Figure 4, the combination of impaction patterns determine the extraction difficulty of one of vertical eruption (VE), soft tissue impaction (STI), partial bony impaction (PBI) and complete bony impaction (CBI). Figure 2: [PERSON] and [PERSON] classification. The red teeth are the mandibular third molars. In the first row, there are figures regarding the depth of the impacted mandibular third molar, and classes A, B, and C from the left. In the second row, there are figures about the distance between the mandibular third molar and the ascending mandibular ramus, and classes I, II, and III from the left.