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Tracking non-stationary covariance matrices is fundamental to vision yet hindered by existing estimators that either neglect manifold constraints or rely on first-order updates, incurring inevitable phase lag during rapid evolution. We…
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…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
Phase-shifting profilometry (PSP) enables high-accuracy 3D reconstruction but remains highly susceptible to object motion. Although numerous studies have explored compensation for motion-induced errors, residual inaccuracies still persist,…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
Modelling individual objects in a scene as Neural Radiance Fields (NeRFs) provides an alternative geometric scene representation that may benefit downstream robotics tasks such as scene understanding and object manipulation. However, we…
Effective and efficient task planning is essential for mobile robots, especially in applications like warehouse retrieval and environmental monitoring. These tasks often involve selecting one location from each of several target clusters,…
Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…
Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can…
Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighbourhood structure of the model, and a precision, or…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
Using parts of existing models to rebuild new models, commonly termed as example-based modeling, is a classical methodology in the realm of computer graphics. Previous works mostly focus on shape composition, making them very hard to use…
We present a novel feature matching algorithm that systematically utilizes the geometric properties of features such as position, scale, and orientation, in addition to the conventional descriptor vectors. In challenging scenes with the…
In visual computing, 3D geometry is represented in many different forms including meshes, point clouds, voxel grids, level sets, and depth images. Each representation is suited for different tasks thus making the transformation of one…
Object-level mapping builds a 3D map of objects in a scene with detailed shapes and poses from multi-view sensor observations. Conventional methods struggle to build complete shapes and estimate accurate poses due to partial occlusions and…
We present Stochastic Gaussian Splatting (SGS): the first framework for uncertainty estimation using Gaussian Splatting (GS). GS recently advanced the novel-view synthesis field by achieving impressive reconstruction quality at a fraction…
This study addresses the challenge of accurately forecasting geometric deviations in manufactured components using advanced 3D surface analysis. Despite progress in modern manufacturing, maintaining dimensional precision remains difficult,…
Sparse-view novel view synthesis is fundamentally ill-posed due to severe geometric ambiguity. Current methods are caught in a trade-off: regressive models are geometrically faithful but incomplete, whereas generative models can complete…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
The Gaussian radial function-based Regression (RfR) method is a data-driven modeling approach that utilizes physically understandable variables from scalar time series, constructed using delay coordinates and Gaussian radial basis…