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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Abstract-We present a method for Simultaneous Localization and Mapping (SLAM) using a monocular camera that is capable of reconstructing dense 3D geometry online without the aid of a graphics processing unit (GPU).Our key contribution is a multi-resolution depth estimation and spatial smoothing process that exploits the correlation between low-texture image regions and simple planar structure to adaptively scale the complexity of the generated keyframe depthmaps to the texture of the input imagery. High-texture image regions are represented at higher resolutions to capture fine detail, while low-texture regions are represented at coarser resolutions for smooth surfaces. The computational savings enabled by this approach allow for significantly increased reconstruction density and quality when compared to the state-ofthe-art. The increased depthmap density also improves tracking performance as more constraints can contribute to the pose estimation. A video of experimental results is available at http:// groups.csail.mit.edu/rrg/multi_level_mapping.

We propose an efficient method for monocular simultaneous localization and mapping (SLAM) that is capable of estimating metrically-scaled motion without additional sensors or hardware acceleration by integrating metric depth predictions from a neural network into a geometric SLAM factor graph. Unlike learned end-to-end SLAM systems, ours does not ignore the relative geometry directly observable in the images. Unlike existing learned depth estimation approaches, ours leverages the insight that when used to estimate scale, learned depth predictions need only be coarse in image space. This allows us to shrink our network to the point that performing inference on a standard CPU becomes computationally tractable.We make several improvements to our network architecture and training procedure to address the lack of depth observability when using coarse images, which allows us to estimate spatially coarse, but depth-accurate predictions in only 30 ms per frame without GPU acceleration. At runtime we incorporate the learned metric data as unary scale factors in a Sim(3) pose graph. Our method is able to generate accurate, scaled poses without additional sensors, hardware accelerators, or special maneuvers and does not ignore or corrupt the observable epipolar geometry. We show compelling results on the KITTI benchmark dataset in addition to real-world experiments with a handheld camera.

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