# Predicting build orientation for SLM dental parts: a comparison of rotation representations and direct vector regression

arXiv: https://arxiv.org/abs/2609.15710 · HTML: https://mlsanity.com/paper/2609.15710/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Towards Fairer Datasets: Filtering and Balancing the Distribution of the People Subtree in the ImageNet Hierarchy](https://mlsanity.com/paper/1912.07726/) (2019)
- [Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation](https://mlsanity.com/paper/2109.09881/) (2021)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [Orient Anything: Learning Robust Object Orientation Estimation from Rendering 3D Models](https://mlsanity.com/paper/2412.18605/) (2024)
- [von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning](https://mlsanity.com/paper/2103.15718/) (2021)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [Probabilistic orientation estimation with matrix Fisher distributions](https://mlsanity.com/paper/2006.09740/) (2020)
- [Von Mises-Fisher Loss for Training Sequence to Sequence Models with Continuous Outputs](https://mlsanity.com/paper/1812.04616/) (2018)
- [Revisiting the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/2006.06234/) (2020)

## Abstract (arXiv)

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^circ, 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.