Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution
Yingda Yin, Jiangran Lyu, Yang Wang, Haoran Liu, He Wang, Baoquan Chen
TL;DR
This work introduces a rotation Laplace distribution on SO(3) to address robustness gaps in probabilistic rotation regression, where Gaussian-like models can be overly sensitive to outliers such as large-angle errors. By grounding the RL distribution in tangent-space Laplace behavior and offering a practical normalization via discretization (with a quaternion counterpart), the authors achieve strong single-prediction and semi-supervised performance, and extend the approach to a multimodal Rotation Laplace Mixture Model to handle symmetry-induced ambiguity. Empirical results on ModelNet10-SO3 and Pascal3D+ show state-of-the-art or competitive performance across probabilistic and non-probabilistic baselines, with improved robustness to outliers and noise, and tangible gains in 6DoF object pose estimation. The work also demonstrates practical benefits in SSL settings (FisherMatch integration) and multimodal prediction, highlighting the method’s utility for real-world robotics and vision tasks where uncertainty and multiple plausible poses matter.
Abstract
Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. As a popular approach, probabilistic rotation modeling additionally carries prediction uncertainty information, compared to single-prediction rotation regression. For modeling probabilistic distribution over SO(3), it is natural to use Gaussian-like Bingham distribution and matrix Fisher, however they are shown to be sensitive to outlier predictions, e.g. $180^\circ$ error and thus are unlikely to converge with optimal performance. In this paper, we draw inspiration from multivariate Laplace distribution and propose a novel rotation Laplace distribution on SO(3). Our rotation Laplace distribution is robust to the disturbance of outliers and enforces much gradient to the low-error region that it can improve. In addition, we show that our method also exhibits robustness to small noises and thus tolerates imperfect annotations. With this benefit, we demonstrate its advantages in semi-supervised rotation regression, where the pseudo labels are noisy. To further capture the multi-modal rotation solution space for symmetric objects, we extend our distribution to rotation Laplace mixture model and demonstrate its effectiveness. Our extensive experiments show that our proposed distribution and the mixture model achieve state-of-the-art performance in all the rotation regression experiments over both probabilistic and non-probabilistic baselines.