Predicting build orientation for SLM dental parts: a comparison of rotation representations and direct vector regression
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 $n\approx2400$ 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 $S^2$. 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 ($10.6^\circ$, ResNet-50). The three lowest-error results overall are direct $S^2$ 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.