Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution

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 $\text{SO}(3)$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$180∘ 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 $\text{SO}(3)$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.