基于SO（3）的不确定性深度旋转学习的光滑信念表示
A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty
摘要：
准确的旋转估计是机器人感知任务的核心，例如视觉里程计和物体姿态估计。深度神经网络为执行这些任务提供了一种新的方法，旋转表示的选择是网络设计的重要组成部分。在这项工作中，我们提出了一种新的3D旋转群SO（3）的对称矩阵表示，具有两个重要的性质，使其特别适合于学习模型：（1）它满足在回归大的旋转目标时改进收敛和泛化的平滑特性，以及（2）它在单位四元数空间上编码对称Bingham信念，允许训练不确定性感知模型。我们通过在两种数据模式上训练深度神经旋转回归器来实证验证我们的公式的好处。首先，我们使用合成的点云数据表明，我们的表示导致优越的预测精度比现有的表示任意旋转目标。其次，我们使用的图像数据收集机载地面和空中车辆证明，我们的代表是服从一个有效的分布（OOD）拒绝技术，显着提高了旋转估计的鲁棒性看不见的环境影响和损坏的输入图像，而不需要使用显式的似然损失，随机采样，或辅助分类。这种能力对于安全关键型应用至关重要，在这些应用中，检测新的输入可以防止学习模型的灾难性故障。
英文摘要：
Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an important part of network design. In this work, we present a novel symmetric matrix representation of the 3D rotation group, SO(3), with two important properties that make it particularly suitable for learned models: (1) it satisfies a smoothness property that improves convergence and generalization when regressing large rotation targets, and (2) it encodes a symmetric Bingham belief over the space of unit quaternions, permitting the training of uncertainty-aware models. We empirically validate the benefits of our formulation by training deep neural rotation regressors on two data modalities. First, we use synthetic point-cloud data to show that our representation leads to superior predictive accuracy over existing representations for arbitrary rotation targets. Second, we use image data collected onboard ground and aerial vehicles to demonstrate that our representation is amenable to an effective out-of-distribution (OOD) rejection technique that significantly improves the robustness of rotation estimates to unseen environmental effects and corrupted input images, without requiring the use of an explicit likelihood loss, stochastic sampling, or an auxiliary classifier. This capability is key for safety-critical applications where detecting novel inputs can prevent catastrophic failure of learned models.
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