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.

翻译：从单张RGB图像估计3自由度旋转是一个重要且具有挑战性的问题。作为一种流行的方法，与单预测旋转回归相比，概率旋转建模额外携带了预测不确定性信息。为了在SO(3)上建模概率分布，自然可以使用类高斯分布，如Bingham分布和矩阵Fisher分布，然而它们被证明对异常值预测（例如$180^\circ$误差）敏感，因此不太可能以最优性能收敛。在本文中，我们从多元拉普拉斯分布中获得启发，并提出了一种新颖的SO(3)上的旋转拉普拉斯分布。我们的旋转拉普拉斯分布对异常值的干扰具有鲁棒性，并对低误差区域施加了更大的梯度，从而能够改进性能。此外，我们表明我们的方法对小噪声也表现出鲁棒性，因此能够容忍不完美的标注。得益于此，我们展示了其在半监督旋转回归中的优势，其中伪标签是带噪声的。为了进一步捕捉对称物体的多模态旋转解空间，我们将我们的分布扩展为旋转拉普拉斯混合模型，并证明了其有效性。我们的大量实验表明，我们提出的分布及其混合模型在所有旋转回归实验中，无论是与概率基线还是非概率基线相比，均取得了最先进的性能。