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Recent advances in 3D Gaussian Splatting (3D-GS) have shown remarkable success in representing 3D scenes and generating high-quality, novel views in real-time. However, 3D-GS and its variants assume that input images are captured based on…

In geostatistical problems with massive sample size, Gaussian processes can be approximated using sparse directed acyclic graphs to achieve scalable $O(n)$ computational complexity. In these models, data at each location are typically…

Traditional explicit 3D representations, such as point clouds and meshes, demand significant storage to capture fine geometric details and require complex indexing systems for surface lookups, making functional representations an efficient,…

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…

In this paper, we introduce \textbf{GS-SLAM} that first utilizes 3D Gaussian representation in the Simultaneous Localization and Mapping (SLAM) system. It facilitates a better balance between efficiency and accuracy. Compared to recent SLAM…

Sparse-view scene reconstruction often faces significant challenges due to the constraints imposed by limited observational data. These limitations result in incomplete information, leading to suboptimal reconstructions using existing…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…

This paper introduces a novel approach to improve robotic grasping in dynamic environments by integrating Gaussian Process Distance Fields (GPDF), SE(3) equivariant networks, and Riemannian Mixture Models. The aim is to enable robots to…

Angular data are commonly encountered in settings with a directional or orientational component. Regressing an angular response on real-valued features requires intrinsically capturing the circular or spherical manifold the data lie on, or…

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage. When the source data is noisy or…

Abstract representations of 3D scenes play a crucial role in computer vision, enabling a wide range of applications such as mapping, localization, surface reconstruction, and even advanced tasks like SLAM and rendering. Among these…

In recent years, parametric representations of point clouds have been widely applied in tasks such as memory-efficient mapping and multi-robot collaboration. Highly adaptive models, like spline surfaces or quadrics, are computationally…

3D Gaussian Splatting (3DGS) has made remarkable progress in RGBD SLAM. Current methods usually use 3D Gaussians or view-tied 3D Gaussians to represent radiance fields in tracking and mapping. However, these Gaussians are either too…

Accurately modeling light transport is essential for realistic image synthesis. Photon mapping provides physically grounded estimates of complex global illumination effects such as caustics and specular-diffuse interactions, yet its…

Surface roughness plays a critical role and has effects in, e.g. fluid dynamics or contact mechanics. For example, to evaluate fluid behavior at different roughness properties, real-world or numerical experiments are performed. Numerical…

Raw point cloud processing using capsule networks is widely adopted in classification, reconstruction, and segmentation due to its ability to preserve spatial agreement of the input data. However, most of the existing capsule based network…

We investigate the accuracy of conventional machine learning aided algorithms for the prediction of lateral land movement in an area using the precise position time series of permanent GNSS stations. The machine learning algorithms that are…

In this work, we introduce a spatio-temporal kernel for Gaussian process (GP) regression-based sound field estimation. Notably, GPs have the attractive property that the sound field is a linear function of the measurements, allowing the…