A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty

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.Comment: In Proceedings of Robotics: Science and Systems (RSS'20), Corvallis , Oregon, USA, Jul. 12-16, 202

Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects with multiple (sometimes infinite) correct poses. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability given the input image and a candidate pose. Grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the probability at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to showcase the rich expressive power, we introduce a dataset of challenging symmetric and nearly-symmetric objects. We require no supervision on pose uncertainty -- the model trains only with a single pose per example. Nonetheless, our implicit model is highly expressive to handle complex distributions over 3D poses, while still obtaining accurate pose estimation on standard non-ambiguous environments, achieving state-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks

A Probabilistic Rotation Representation for Symmetric Shapes With an Efficiently Computable Bingham Loss Function

In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation, it cannot represent the ambiguity of the observation. In order to handle the ambiguity, the Bingham distribution is one promising solution. However, it requires complicated calculation when yielding the negative log-likelihood (NLL) loss. An alternative easy-to-implement loss function has been proposed to avoid complex computations but has difficulty expressing symmetric distribution. In this paper, we introduce a fast-computable and easy-to-implement NLL loss function for Bingham distribution. We also create the inference network and show that our loss function can capture the symmetric property of target objects from their point clouds.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. arXiv admin note: substantial text overlap with arXiv:2203.0445

Ki-Pode: Keypoint-based Implicit Pose Distribution Estimation of Rigid Objects

The estimation of 6D poses of rigid objects is a fundamental problem in computer vision. Traditionally pose estimation is concerned with the determination of a single best estimate. However, a single estimate is unable to express visual ambiguity, which in many cases is unavoidable due to object symmetries or occlusion of identifying features. Inability to account for ambiguities in pose can lead to failure in subsequent methods, which is unacceptable when the cost of failure is high. Estimates of full pose distributions are, contrary to single estimates, well suited for expressing uncertainty on pose. Motivated by this, we propose a novel pose distribution estimation method. An implicit formulation of the probability distribution over object pose is derived from an intermediary representation of an object as a set of keypoints. This ensures that the pose distribution estimates have a high level of interpretability. Furthermore, our method is based on conservative approximations, which leads to reliable estimates. The method has been evaluated on the task of rotation distribution estimation on the YCB-V and T-LESS datasets and performs reliably on all objects.Comment: 11 pages, 2 figure