[Deep learning algorithms for intelligent construction of a three-dimensional maxillofacial symmetry reference plane].

Objective: To develop an original-mirror alignment associated deep learning algorithm for intelligent registration of three-dimensional maxillofacial point cloud data, by utilizing a dynamic graph-based registration network model (maxillofacial dynamic graph registration network, MDGR-Net), and to provide a valuable reference for digital design and analysis in clinical dental applications.

Methods: Four hundred clinical patients without significant deformities were recruited from Peking University School of Stomatology from October 2018 to October 2022. Through data augmentation, a total of 2 000 three-dimensional maxillofacial datasets were generated for training and testing the MDGR-Net algorithm. These were divided into a training set (1 400 cases), a validation set (200 cases), and an internal test set (200 cases). The MDGR-Net model constructed feature vectors for key points in both original and mirror point clouds (X, Y), established correspondences between key points in the X and Y point clouds based on these feature vectors, and calculated rotation and translation matrices using singular value decomposition (SVD). Utilizing the MDGR-Net model, intelligent registration of the original and mirror point clouds were achieved, resulting in a combined point cloud. The principal component analysis (PCA) algorithm was applied to this combined point cloud to obtain the symmetry reference plane associated with the MDGR-Net methodology. Model evaluation for the translation and rotation matrices on the test set was performed using the coefficient of determination (R²). Angle error evaluations for the three-dimensional maxillofacial symmetry reference planes were constructed using the MDGR-Net-associated method and the "ground truth" iterative closest point (ICP)-associated method were conducted on 200 cases in the internal test set and 40 cases in an external test set.

Results: Based on testing with the three-dimensional maxillofacial data from the 200-case internal test set, the MDGR-Net model achieved an R² value of 0.91 for the rotation matrix and 0.98 for the translation matrix. The average angle error on the internal and external test sets were 0.84°±0.55° and 0.58°±0.43°, respectively. The construction of the three-dimensional maxillofacial symmetry reference plane for 40 clinical cases took only 3 seconds, with the model performing optimally in the patients with skeletal Class Ⅲ malocclusion, high angle cases, and Angle Class Ⅲ orthodontic patients.

Conclusion: This study proposed the MDGR-Net association method based on intelligent point cloud registration as a novel solution for constructing three-dimensional maxillofacial symmetry reference planes in clinical dental applications, which can significantly enhance diagnostic and therapeutic efficiency and outcomes, while reduce expert dependence.