## 1 Introduction  
The connection between craniofacial anatomy and the upper respiratory tract continues to be a relevant subject in dentofacial anomaly research. The Functional Matrix Theory, proposed by [PERSON] in the 1960s, has been recognized as one of the fundamental mechanisms of craniofacial growth. According to this theory, skeletal structures are passive elements, and their growth and development are directed by the surrounding functional matrices. Unlike traditional perspectives, [PERSON] suggested that the growth of the craniofacial skeleton is influenced not primarily by genetic factors but rather by the demands of functional matrices, such as respiration, mastication, swallowing, and speech [1]. It has been concluded that obstructions in the airway or dysfunctions within the functional matrix, such as issues related to mastication and swallowing, may significantly impact craniofacial growth [1]. Studies have also reported that the volume and morphology of soft tissues may change due to craniofacial skeletal anomalies [2,3]. Vertical malocclusions are linked to the pharyngeal airway, with narrowed dimensions observed in hyperdivergent individuals [4, 5, 6]. This condition has been explained as the narrowing of the pharyngeal airway due to the downward and backward rotation of the mandible and the posterior displacement of the tongue [7]. These malocclusions may arise during adolescence due to factors like maxillary/mandibular development, tooth eruption, and tongue function [8]. [PERSON] [9] and [PERSON] et al. [10], noted that when condylar growth lags behind maxillary sutures, the mandible rotates backward, causing an open bite. This results in a high-angle or hyperdivergent growth pattern. Conversely, forward mandibular growth results in a hypodivergent pattern. This suggests that condylar volume may influence mandibular rotation and growth direction, thereby altering airway volume. Posteriorly positioned or small condyles may cause the mandible to rotate backward and downward. This condition, as seen in hyperdivergent individuals, may lead to a reduction in airway volume [11]. Research suggests that airway volumes vary with vertical and sagittal growth patterns. [PERSON] et al. [12] found that horizontal growth patterns correlate with larger airway volumes. [PERSON] et al. [13] reported that the condylar volumes of skeletal Class III patients are greater compared to Class II and Class I patients. Other studies have also shown that different skeletal and vertical patterns are associated with variations in the shape, size, and positions of the condyles [14, 15, 16]. [PERSON] et al. [11], through CBCT analysis, detected notable variations in the pharyngeal airway space among adult skeletal Class II patients based on different condylar positions, including anterior, posterior and central placements. Accurately identifying and segmenting teeth from CBCT images plays a significant role in assisting clinicians with diagnosis and treatment planning. However, achieving precise segmentation is a challenging process due to various anatomical and technical difficulties. The close proximity and occasional overlapping of anatomical structures to be segmented further complicate the segmentation process [17]. Additionally, the similar densities of these structures can make it difficult to distinguish different tissues in radiographic images [18]. Among the technical challenges, artifacts and low-contrast regions in CBCT images are significant factors that can affect segmentation accuracy. In particular, artifacts caused by metal restorations and orthodontic appliances can degrade image quality, making the segmentation process even more complex [17]. Current tooth segmentation approaches encompass techniques such as edge-based, region-based, and threshold-based segmentation methods [16]. These methods often face difficulties in accurately determining segmentation results [19,20].