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Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…
Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…
Global localisation from visual data is a challenging problem applicable to many robotics domains. Prior works have shown that neural networks can be trained to map images of an environment to absolute camera pose within that environment,…
Segmentation from point cloud data is essential in many applications such as remote sensing, mobile robots, or autonomous cars. However, the point clouds captured by the 3D range sensor are commonly sparse and unstructured, challenging…
Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…
Visual localization is the task of estimating a camera pose in a known environment. In this paper, we utilize 3D Gaussian Splatting (3DGS)-based representations for accurate and privacy-preserving visual localization. We propose Gaussian…
The distributional analysis of Euclidean algorithms was carried out by Baladi and Vall\'{e}e. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the…
We develop an online probabilistic metric-semantic mapping approach for mobile robot teams relying on streaming RGB-D observations. The generated maps contain full continuous distributional information about the geometric surfaces and…
This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework that…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
This paper proposes a novel framework for large-scale scene reconstruction based on 3D Gaussian splatting (3DGS) and aims to address the scalability and accuracy challenges faced by existing methods. For tackling the scalability issue, we…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…
Simultaneous Localization and Mapping (SLAM) with dense representation plays a key role in robotics, Virtual Reality (VR), and Augmented Reality (AR) applications. Recent advancements in dense representation SLAM have highlighted the…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
In medical image visualization, path tracing of volumetric medical data like CT scans produces lifelike three-dimensional visualizations. Immersive VR displays can further enhance the understanding of complex anatomies. Going beyond the…
This paper introduces a novel framework for continuous 3D trajectory optimization in cluttered environments, leveraging online neural Euclidean Signed Distance Fields (ESDFs). Unlike prior approaches that rely on discretized ESDF grids with…
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer,…
Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the…