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In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

3D scene graphs have recently emerged as a powerful high-level representation of 3D environments. A 3D scene graph describes the environment as a layered graph where nodes represent spatial concepts at multiple levels of abstraction and…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

We present LiDAR-GS, a Gaussian Splatting (GS) method for real-time, high-fidelity re-simulation of LiDAR scans in public urban road scenes. Recent GS methods proposed for cameras have achieved significant advancements in real-time…

Scene graphs have emerged as a powerful tool for robots, providing a structured representation of spatial and semantic relationships for advanced task planning. Despite their potential, conventional 3D indoor scene graphs face critical…

Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…

Both in terrestrial and extraterrestrial environments, the precise and informative model of the ground and the surface ahead is crucial for navigation and obstacle avoidance. The ground surface is not always flat and it may be sloped, bumpy…

This paper proposes a real-time multi-plane segmentation method based on GPU-accelerated high-resolution 3D voxel mapping for legged robot locomotion. Existing online planar mapping approaches struggle to balance accuracy and computational…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…

We introduce Consistent Instance Field, a continuous and probabilistic spatio-temporal representation for dynamic scene understanding. Unlike prior methods that rely on discrete tracking or view-dependent features, our approach disentangles…

Photorealistic reconstruction of street scenes is essential for developing real-world simulators in autonomous driving. While recent methods based on 3D/4D Gaussian Splatting (GS) have demonstrated promising results, they still encounter…

With the rapid development of indoor location-based services (LBSs), the demand for accurate localization keeps growing as well. To meet this demand, we propose an indoor localization algorithm based on graph convolutional network (GCN). We…

In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications…

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…

The widespread adoption of autonomous systems such as drones and assistant robots has created a need for real-time high-quality semantic scene segmentation. In this paper, we propose an efficient yet robust technique for on-the-fly dense…

Real-world objects and environments are predominantly composed of edge features, including straight lines and curves. Such edges are crucial elements for various applications, such as CAD modeling, surface meshing, lane mapping, etc.…

Interactive segmentation of 3D Gaussians opens a great opportunity for real-time manipulation of 3D scenes thanks to the real-time rendering capability of 3D Gaussian Splatting. However, the current methods suffer from time-consuming…

In order to deal with the scaling problem of volumetric map representations we propose spatially local methods for high-ratio compression of 3D maps, represented as truncated signed distance fields. We show that these compressed maps can be…