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.

本研究提出了一种新的基于 Laplace 分布的旋转概率模型，相较于高斯 Bingham 分布和 Matrix Fisher 模型更具鲁棒性，可以提高旋转回归任务的性能，并在半监督旋转回归和对称对象多解决方案空间等方面具有优势。