Predicting build orientation for SLM dental parts: a comparison of rotation representations and direct vector regression
Authors: Felix Schmalzel, Reimar Waitz, Moritz Kronberger, Thorsten Schöler
Organizations: Technical University of Applied Sciences Augsburg, Augsburg, 86161, Germany · R. Waitz Data & Science, Kaufering, 86916, Germany
Abstract
Build orientation for selective laser melting (SLM) manufacturing of dental parts is usually chosen manually by technicians. We treat orientation prediction as supervised machine learning of the part's up-axis from technician-labeled production data, and test which rotation representations produce the best results. Using n≈2400 patient-specific dental parts, we trained a ResNet-50 multi-view image backbone and a PointNeXt-S point-cloud backbone, both pretrained and fine-tuned end-to-end, on 13 up-axis representations spanning six classical SO(3) parameterizations and seven representations defined directly on the unit sphere S2. We report the geodesic angular error between predicted and ground-truth up-axis on a test set, with and without test-time augmentation (TTA) over K=21 known rotations. With TTA, the octahedral map achieves the lowest mean angular error (10.6∘, ResNet-50). The three lowest-error results overall are direct S2 representations, though this may reflect label noise in the unsupervised in-plane component of the SO(3) targets rather than a topological advantage. von Mises-Fisher collapses to a near-constant prediction when trained with PointNeXt-S but not with ResNet-50. TTA reduces mean angular error by 31-73 % across almost every representation and backbone. Overall, test-time augmentation over a small set of known rotations is the most consistent driver of accuracy, whereas the best-performing representation is strongly backbone-dependent.
Prototype-based networks provide inherently interpretable classification by linking predictions to learned exemplars, but their use in 3D point clouds and clinical surface-pair reasoning remains limited. We introduce ProtoPointNet, a prototype-based model for dental occlusion classification from registered upper--lower intraoral arch pairs. Each point is encoded by a 14-dimensional descriptor combining local surface geometry, curvature, and explicit inter-arch displacement and clearance, exposing occlusal relationships to prototype matching. A shared multi-task point-cloud backbone learns axis-specific prototype heads for sagittal-left, sagittal-right, vertical, transverse, and midline classification. To support limited clinical data, we train prototypes from scratch using auxiliary supervision and encoder-freeze hand-off. On Bits2Bites, ProtoPointNet achieves mean test macro-F1 of 0.724 and AUROC of 0.825, with strongest performance on vertical (F1 0.828) and sagittal-left classification (F1 0.807). Projected prototype activations localise to anatomically plausible regions, including posterior molars and premolars for cross-bite evidence and anterior incisors for bite-depth evidence. These results support prototype-based reasoning as a transparent, spatially grounded alternative to black-box 3D classifiers for dental surface-pair analysis.
In our previous work, a deep learning-based framework for 3D intraoral reconstruction was proposed. The model directly predicts explicit 3D point cloud coordinates from ten fixed-angle intraoral images, employing MobileNetV2 and Multi-head Attention for multi-view feature fusion, with a combined L1 Loss and Chamfer Distance as the loss function. Although the model achieved an accuracy of 77.49%, predicted vertices tended to concentrate in high-density regions of the ground truth, leaving other regions largely uncovered. In this paper, an improved loss function is proposed to address this limitation. Hungarian matching with filtering and Repulsion Loss are introduced to enforce more uniform vertex distribution across the reconstructed model. The proposed model achieves an accuracy of 68.02%, which is numerically lower than the previous model. However, the vertex clustering issue observed in the prior work is substantially alleviated, with predicted vertices distributed more evenly across the entire reconstructed surface.
In the design of surgical guides for implant placement, determining the precise implant position is a critical step. However, the implant region itself is often characterized by a lack of distinctive texture in medical images. Consequently, artificial intelligence (AI) models must infer the correct implant position and angulation (slope) primarily by analyzing the texture of the surrounding teeth, which poses a significant challenge. To address this, we propose ImplantMamba, a network architecture designed for long-range sequential modeling to integrate texture information from adjacent teeth. Our approach explicitly couples the regression of the implant position with its slope. The core of ImplantMamba is a hybrid encoder that combines Convolutional Neural Networks (CNNs) with Mamba layers. This design enables the network to hierarchically extract local anatomical features through CNNs while simultaneously modeling global contextual dependencies across the entire scan volume via Mamba's selective scan operations, leading to a more comprehensive understanding of the implant site. Furthermore, we introduce a Slope-Coupled Prediction Branch (SCP). This branch is designed to connect the prediction of implant position with the slope, ensuring internal consistency and anatomical plausibility by thereby enforcing a coherent relationship between the predicted implant location and its angulation. Extensive experiments on a large-scale dental implant dataset demonstrate that the proposed ImplantMamba achieves superior performance compared to existing methods.