Related papers: Anisotropic Gaussian approximation in $L_2(\mathbb…
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…
We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the…
Despite the advancements in quality and efficiency achieved by 3D Gaussian Splatting (3DGS) in 3D scene rendering, aliasing artifacts remain a persistent challenge. Existing approaches primarily rely on low-pass filtering to mitigate…
3D Gaussian splatting (3DGS) has shown promising results in image rendering and surface reconstruction. However, its potential in volumetric reconstruction tasks, such as X-ray computed tomography, remains under-explored. This paper…
The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
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,…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
Modern vision language pipelines are driven by RGB vision encoders trained on massive image text corpora. While these pipelines have enabled impressive zero-shot capabilities and strong transfer across tasks, they still inherit two…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…
The multivariate generalised Gaussian distribution (MGGD) is commonly used to model high-dimensional vectors with non-Gaussian radial behaviour, ranging from sharp-peaked to heavy-tailed profiles. However, because many classical…
We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary…
Gaussian Splatting (GS) has proven to be highly effective in novel view synthesis, achieving high-quality and real-time rendering. However, its potential for reconstructing detailed 3D shapes has not been fully explored. Existing methods…
3D Gaussian Splatting (3DGS) has shown impressive results in real-time novel view synthesis. However, it often struggles under sparse-view settings, producing undesirable artifacts such as floaters, inaccurate geometry, and overfitting due…
In the field of 3D dynamic scene reconstruction, how to balance model convergence rate and rendering quality has long been a critical challenge that urgently needs to be addressed, particularly in high-precision modeling of scenes with…
Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…
For robots to robustly understand and interact with the physical world, it is highly beneficial to have a comprehensive representation - modelling geometry, physics, and visual observations - that informs perception, planning, and control…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ with error measured in the Gaussian-weighted space…
Recent works propose extending 3DGS with semantic feature vectors for simultaneous semantic segmentation and image rendering. However, these methods often treat the semantic and rendering branches separately, relying solely on 2D…