# DentalArch: AI-Based Arch Shape Detection in Orthodontics
## 1 Introduction  
Since the inception of the term \"computer-aided diagnosis\" over six decades ago by physician [PERSON] [1] in a chest radiography study, artificial intelligence (AI) has revolutionized information processing. AI has emerged as a permanent fixture, enhancing human deductive reasoning and observational skills [2; 3; 4]. This technological breakthrough is grounded in emulating our cognitive processes across various domains, such as image processing and pattern recognition, and led to the development of Artificial Neural Networks (ANNs) [5]. ANNs have found extensive applications in medicine [6; 7]. Significant advancements have been made in medical imaging [8; 9], given the vast amount of information, storage requirements, and creation of image databases that need rapid and efficient analyses, enabling physicians to make decisions based upon the experience coded in such large datasets. In orthodontics and dentistry, one key assessment is the identification of the arch shape, as it provides a basis to the expectations that can be set during treatment and a path to carry it out. Orthodontists and dentists utilize the arch shape as a tool to ascertain a patient's arch type. Preserving the arch shape or minimizing alterations during orthodontic treatments results in an improved stability during the retention phase. This was corroborated in 1995 by [PERSON] et al. [10], who conducted a long-term study on post-treatment dental arch shape changes, concluding that patients experiencing greater post-retention relapse have a direct correlation with an increased transversal magnitude [10]. Recent studies support this hypothesis, demonstrating higher relapse rates in arches that initially had a narrow shape and underwent increased transversal lengths [11; 12]. Arch shapes can be categorized into three primary forms: square, ovoid, and tapered. This classification generally relies on the expert's subjective evaluation through human vision and/or other tools, such as millimetric templates employed for diagnostic examinations in orthodontics. However, this approach is susceptible to human error and observer bias--which have been evidenced and measured--leading to inaccurate or observer-dependent results [13; 14]. Individual variations in arch configurations [15] pose challenges to the classification task. Several studies have tackled this problem using different approaches, including geometric analyses, mathematical shapes, and computerized methods to facilitate dental arch shape representation [16; 17; 18]. Various arch shapes have been proposed, such as the trifocal ellipse, catenary curve, parabola, U shape, modified sphere, and others [19; 20]. Generally speaking, the dental arch shape and size exhibit significant diversity among different human groups, leading to the introduction of morphometric templates by orthodontists and commercial companies [21; 22]. The accurate determination of the dental arch shape is important in orthodontics, greatly impacting the effectiveness and success of treatments [23]. This aspect is particularly significant in the context of utilizing memory wire arches, where the conformity of the wire to the patient's specific arch shape can dramatically affect the outcome of the treatment [24]. The compatibility between the arch shape and the applied corrective device is essential for achieving the desired dental alignment and occlusal harmony. Consequently, orthodontists rely on arch shape classification to tailor treatment plans that align with the unique dental structures of their patients. Innovations in diagnostic technologies, including the application of artificial intelligence for arch shape prediction, have markedly enhanced the accuracy and reliability of these classifications, promising improved treatment outcomes and patient satisfaction [25]. The intersection of artificial intelligence (AI) with orthodontic arch shape prediction has seen significant growth in interest and research [26].