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

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.

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.

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.

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.