# Semi-Supervised Deep Subspace Embedding for Binary Classification of Sella Turcica
orthodontic treatment planning, particularly in aligning the jaws [1] and facial bones [2]. Alterations in the shape or size of the ST often signify growth disturbances, which may lead to dentofacial deformities, such as malocclusions and jaw misalignments [3; 4; 5; 6]. According to the literature, the ST is divided into three segments: the anterior wall, floor, and posterior wall [7]. In addition, [PERSON] subdivided the standard sella shape into three types: oval, round or circular, and flat (Figure 1) [8; 9]. Among these, the oval shape is the most prevalent, while the flat shape is the least common. Another interesting morphological shape of the ST is the convergence of the anterior and posterior clinoid lobes, also known as bridging, illustrated in Figure 1. This morphology is strongly associated with certain syndromes and malformations involving skeletal and dental structures [10]. The accurate classification of ST morphology is essential, as specific variations such as bridging or flattening often correlate with dentofacial deformities, syndromes, and even endocrine disorders due to the proximity of the ST to the pituitary gland [11; 12; 13]. Currently, manual assessment tools, including visual inspection, linear measurements [7], and shape analysis of cephalometric X-rays [8], dominate clinical practice. However, these methods are time intensive, prone to variability, and heavily reliant on specialized expertise, underscoring the acute need for automated and objective assessment techniques [9]. Deep learning techniques have proven highly effective in various computer vision tasks. However, the effectiveness of these approaches heavily relies on the availability of labeled datasets. In unsupervised learning scenarios, evaluating the reliability of extracted features proves challenging due to the lack of prior information, making it difficult to assess their robustness [14]. Conversely, supervised learning methods are more commonly employed across diverse applications. Although supervised learning produces more reliable features, the process of annotating extensive datasets is often extremely time intensive and expensive. Consequently, there has been a growing interest in semi-supervised learning (SSL) methodologies that utilize deep learning models [15; 16]. Previous studies mainly used only unlabeled data during pre-training [17]. However, recent research efforts have focused on incorporating unlabeled data throughout training [18]. Semi-supervised learning (SSL) techniques are often used to improve model performance by extracting important features or insights from unlabeled data [19; 20; 21]. However, these approaches have two main limitations. First, many current methods do not effectively address contours in areas with high uncertainty and fail to explicitly model boundary distances. This can result in poor coverage of the targets or inaccurate boundary predictions, especially in medical images. Second, these approaches typically only apply semi-supervision at the final layer of the network, which can lead to the propagation of incorrect guidance throughout the network and undervalue the importance of labeled data compared to unlabeled data. This issue is particularly significant when training convolutional neural networks with a large number of parameters and complex architecture, especially when labeled data are scarce [22; 23; 24]. Furthermore, recent strategies that attempt  
Figure 1: Sample images of pre-defined Sella Turcica (ST) shapes: (**A**) Oval ST, (**B**) Circular ST, (**C**) Flat ST, and (**D**) Bridging ST. This study classified Circular ST as non-bridging, and Bridging ST was used for binary classification. to cluster inputs by incorporating noise and smoothing mapping functions locally are less effective when the raw data already contain significant noise. To address the challenges mentioned earlier, a novel four-step approach for the binary classification (bridging and non-bridging) of non-linear sella shapes using advanced deep SSL has been developed.