An automatic teeth arrangement method based on an intelligent optimization algorithm and the Frenet–Serret formula - Li, Hong-an; Liu, Man (Biomedical signal processing and control, 2025)
Neat teeth can enhance an individual’s social confidence. To simulate the orthodontic process of teeth, this paper proposes an automatic tooth arrangement method based on an intelligent optimization algorithm and the Frenet–Serret formula to complete virtual orthodontic work, which consists of three main stages. The first stage mainly calculates the amount of translation required for teeth to reach the ideal position, including establishing the dental arch curve and central axis, taking the distance between teeth and dental arch curve and dentition symmetry as optimization objectives, and proposing an improved multi-objective particle swarm algorithm for solution. The second stage is determining the ideal pose of the teeth, including introducing the formula to establish an arrangement coordinate system for each tooth and selecting feature points to establish a local coordinate system. Determine the ideal rotation angle through two coordinate systems. The final stage is to detect and process the collision problem between adjacent teeth following spatial transformation. The experimental results show that our method is superior to existing methods regarding tooth arrangement effect. Through a series of processes such as precise fitting of dental arch curves, we can find the ideal position of teeth, significantly enhance the symmetry of the dentition and tooth arrangement efficiency, further improve the oral condition and facial aesthetics of patients, provide doctors with reliable technical references, and improve the predictability and success rate of treatment. Therefore, our method is a practical method for simulating orthodontic treatment and can be used as a reference for clinical practice [Display omitted] •The automatic alignment of 3D teeth is an important content of virtual orthodontics.•We propose the IMOPSO algorithm to solve the teeth translation to the ideal position.•We use the Frenet-Serret formula to create a coordinate system for teeth arrangement.•We solve the rotation amount used for teeth transformation through the euler angles.•We propose a novel detection and adjustment strategy to solve the collision problem.