Benchmarking mapping and motion estimation algorithms is established practice in robotics and computer vision. As the diversity of datasets increases, in terms of the trajectories, models, and scenes, it becomes a challenge to select datasets for a given benchmarking purpose. Inspired by the Wasserstein distance, this paper addresses this concern by developing novel metrics to evaluate trajectories and the environments without relying on any SLAM or motion estimation algorithm. The metrics, which so far have been missing in the research community, can be applied to the plethora of datasets that exist. Additionally, to improve the robotics SLAM benchmarking, the paper presents a new dataset for visual localization and mapping algorithms. A broad range of real-world trajectories is used in very high-quality scenes and a rendering framework to create a set of synthetic datasets with groundtruth trajectory and dense map which are representative of key SLAM applications such as virtual reality (VR), micro aerial vehicle (MAV) flight, and ground robotics.

As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage the formulation of variational inference in function space, where we associate Gaussian Processes (GPs) to both Bayesian CNN priors and variational family. Since GPs are fully determined by their mean and covariance functions, we are able to obtain predictive uncertainty estimates at the cost of a single forward pass through any chosen CNN architecture and for any supervised learning task. By leveraging the structure of the induced covariance matrices, we propose numerically efficient algorithms which enable fast training in the context of high-dimensional tasks such as depth estimation and semantic segmentation. Additionally, we provide sufficient conditions for constructing regression loss functions whose probabilistic counterparts are compatible with aleatoric uncertainty quantification.

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