Related papers: Gaussian Blur and Relative Edge Response
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate…
The Gaussian splatting methods are getting popular. However, their loss function only contains the $\ell_1$ norm and the structural similarity between the rendered and input images, without considering the edges in these images. It is…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
In this paper, we address common error sources for 3D Gaussian Splatting (3DGS) including blur, imperfect camera poses, and color inconsistencies, with the goal of improving its robustness for practical applications like reconstructions…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
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…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Recent efforts in using 3D Gaussians for scene reconstruction and novel view synthesis can achieve impressive results on curated benchmarks; however, images captured in real life are often blurry. In this work, we analyze the robustness of…
Following the earlier verification for Gaussian model in \cite{ASaa2026}, this paper introduces a zero training forward computational framework for the model to realize it in real time applications. The framework is based on discrete…
Decomposing geometry, materials and lighting from a set of images, namely inverse rendering, has been a long-standing problem in computer vision and graphics. Recent advances in neural rendering enable photo-realistic and plausible inverse…
Open-vocabulary 3D scene understanding presents a significant challenge in computer vision, with wide-ranging applications in embodied agents and augmented reality systems. Existing methods adopt neurel rendering methods as 3D…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
While neural rendering has demonstrated impressive capabilities in 3D scene reconstruction and novel view synthesis, it heavily relies on high-quality sharp images and accurate camera poses. Numerous approaches have been proposed to train…
TL;DR: Gaussian Splatting is a widely adopted approach for 3D scene representation, offering efficient, high-quality reconstruction and rendering. A key reason for its success is the simplicity of representing scenes with sets of Gaussians,…
Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…
All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…