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We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to…
Estimating the heightmaps of buildings and vegetation in single remotely sensed images is a challenging problem. Effective solutions to this problem can comprise the stepping stone for solving complex and demanding problems that require 3D…
The ability to recognize previously mapped locations is an essential feature for autonomous systems. Unstructured planetary-like environments pose a major challenge to these systems due to the similarity of the terrain. As a result, the…
In this investigation we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of…
When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular…
With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
This paper addresses the problem of single image depth estimation (SIDE), focusing on improving the quality of deep neural network predictions. In a supervised learning scenario, the quality of predictions is intrinsically related to the…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Recently, Gaussian Splatting (GS) has shown great potential for urban scene reconstruction in the field of autonomous driving. However, current urban scene reconstruction methods often depend on multimodal sensors as inputs, \textit{i.e.}…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
Safe navigation in new environments requires autonomous vehicles and robots to accurately interpret their surroundings, relying on LiDAR scene segmentation, out-of-distribution (OOD) obstacle detection, and uncertainty computation. We…
Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…
Autonomous 3D acquisition of outdoor environments poses special challenges. Different from indoor scenes, where the room space is delineated by clear boundaries and separations (e.g., walls and furniture), an outdoor environment is spacious…
Small Earth data are geoscience observations with limited short-term monitoring variability, providing sparse but meaningful measurements, typically exhibiting spatiotemporal correlations. Spatiotemporal forecasting on such data is crucial…
The equations of motion governing mobile robots are dependent on terrain properties such as the coefficient of friction, and contact model parameters. Estimating these properties is thus essential for robotic navigation. Ideally any map…
In order to retrieve cosmological parameters from photometric surveys, we need to estimate the distribution of the photometric redshift in the sky with excellent accuracy. We use and apply three different machine learning methods to…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…