## 1 Introduction  
Cone Beam Computed Tomography (CBCT) has been widely used in the diagnosis of oral disease and treatment. This includes applications such as studying orthodontic plans, planning orthognathic surgery, determining the position of dental implants, and diagnosing maxillofacial diseases [1, 2, 3]. Compared to multi-slice CT, CBCT offers a higher spatial resolution and improved contrast-to-noise ratio, while significantly reducing radiation dose [4]. CBCT images offer high-quality diagnostic images of oral soft and hard tissues, allowing medical professionals to obtain more comprehensive information, such as precise 3D information about teeth and bones [5, 6]. This enhanced spatial characteristic allows for more accurate localization and evaluation, ultimately improving treatment plans. Correctly identifying and segmenting teeth from CBCT images plays an important role in supporting clinicians with diagnosis and treatment. The segmentation results can be further used for orthodontic treatment planning, 3D-guided implant surgery, or auto-transplantation of teeth in children, thereby improving the accuracy and success rate of the procedures. Nevertheless, achieving precise segmentation or extracting regions of interest (ROI) is a challenging task. In maxillofacial CBCT images, the pixel proportion of teeth is relatively low, especially in the apical regions, and challenges, such as noise, low contrast, and uneven exposure, are often encountered [7]. The roots also have similar densities as the surrounding alveolar bone, making it difficult to precisely distinguish their grayscale values in the images and capture the details of roots [8]. Moreover, there are some other reasons that cause the segmentation regions to overlap or have indistinct boundaries, including the occlusion between upper and lower dental arches, crowded teeth, impacted teeth, and artifacts resulting from dental restorative materials, such as fillings, crown restorations, and implants [9]. Long scan time also increases the possibility of image blurring due to patient movement. Hence, precise tooth detection and segmentation from CBCT images has become a significant research concern. Current tooth segmentation methods primarily rely on traditional manual segmentation with human-computer interaction, including threshold-based, region-based, and edge-based segmentation. The threshold-based segmentation is a traditional digital image processing algorithm that separates foreground from background by setting an appropriate grayscale level [10]. However, this segmentation method is highly influenced by the definition of foreground targets. When there are significant changes in the gray value of the target, it is challenging to accurately determine the segmentation results [11]. The region-based segmentation methods split the image into several regions based on discontinuities in intensity levels of pixels, and then merge the regions based on consistency [12]. However, the performance of this segmentation method is affected by similarity measurements and sensitivity to image noise [13]. It is also more computationally required due to the necessary continual region comparison and classification. Currently, the most widely used method for tooth segmentation is the Level Set Method (LSM) through geometric operations to detect topological changes in contours [14]. LSM offers more accurate localization and faster segmentation speed. [PERSON] et al. [15] initially applied the LSM globally to obtain high-density alveolar bone regions and then applied this locally to identify individual teeth within the alveolar bone. [PERSON] et al. used two different level sets in alternate evolution, further enhancing tooth segmentation accuracy [16]. Although LSM addresses some challenges in tooth segmentation, its accuracy remains limited for uneven regions and boundaries of missing teeth, and it lacks robustness for complex tooth occlusion relationships.