Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace
  Distribution
Yingda Yin Jiangran Lyu Yang Wang He Wang Baoquan Chen
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.