# Adaptive Point Learning with Uncertainty Quantification to Generate Margin Lines on Prepared Teeth
###### Abstract  
During a crown generation procedure, dental technicians depend on commercial software to generate a margin line to define the design boundary for the crown. The margin line generation remains a non-reproducible, inconsistent, and challenging procedure. In this work, we propose to generate margin line points on prepared teeth meshes using adaptive point learning inspired by the AdaPointIrr model. We extracted ground truth margin lines as point clouds from the prepared teeth and crown bottom meshes. The chamfer distance (CD) and infoCD loss functions were used for training a supervised deep learning model that outputs a margin line as a point cloud. To enhance the generation results, the deep learning model was trained based on three different resolutions of the target margin lines, which were used to back-propagate the losses. Five folds were trained and an ensemble model was constructed. The training and test sets contained 913 and 134 samples, respectively, covering all teeth positions. Intraoral scanning was used to collect all samples. Our post-processing involves removing outlier points based on local point density and principal component analysis (PCA) followed by a spline prediction. Comparing our final spline predictions with the ground truth margin line using CD, we achieved a median distance of 0.137 mm. The median Hausdorff distance was 0.242 mm. We also propose a novel confidence metric for uncertainty quantification of generated margin lines during deployment. The metric was defined based on the percentage of removed outliers during the post-processing stage. The proposed end-to-end framework helps dental professionals in generating and evaluating margin lines consistently. The findings underscore the potential of deep learning to revolutionize the detection and extraction of 3D landmarks, offering personalized and robust methods to meet the increasing demands for precision and efficiency in the medical field. d 2024 14 9486 10.3390/app14209486 10.390/app14209486 10.  
crown to sit on the scanned die. The digital crown design procedure has several steps with the most important one being the accurate detection of the margin line on the surface of the die [1]. In this work, we propose an automated and personalized deep learning framework to extract margin lines from dental preparations. The proposed framework incorporates a novel uncertainty quantification metric to provide confidence level of the predicted margin lines. Margin lines constitute the boundaries of dental crowns. Current dental software use traditional search algorithms and optimization frameworks to detect appropriate margin lines that avoid undercuts. However, due to the huge variability in teeth among patients, the produced margin lines are not always precise [2]. Often, dental technicians need to manually intervene to correct margin lines before resuming the crown generation procedure, which constitutes an inconsistent and non repeatable step in the design process. The automated and accurate identification of margin lines on prepared teeth forms a bottleneck in the digital automation of dental restoration design [3]. The use of machine learning (ML) has been increasing in the field of digital dentistry [4; 5; 6]. Many problems in digital dentistry require personalized solutions that are difficult to automate using traditional computation methods. ML has the ability to learn from the huge amounts of available dental data to provide personalized solutions. ML has been used in prosthodonic-driven rehabilitation of patients [7], teeth classification [8; 9], teeth segmentation [10; 11; 12; 13; 14], caries and cavities detection [15; 16], arch registration [17], and crown generative tasks [18]. However, to the best of the authors' knowledge, there is a lack of research investigating the use of ML in detecting margin lines on dental preparations. Geometric methods have been proposed to automatically detect margin lines [19]. However, they highly depend on the presence of sharp features at the margin line.