Related papers: An error estimate of Gaussian Recursive Filter in …
Aggregating deep convolutional features into a global image vector has attracted sustained attention in image retrieval. In this paper, we propose an efficient unsupervised aggregation method that uses an adaptive Gaussian filter and an…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC),…
We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to…
Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…
Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…
Due to the real-time rendering performance, 3D Gaussian Splatting (3DGS) has emerged as the leading method for radiance field reconstruction. However, its reliance on spherical harmonics for color encoding inherently limits its ability to…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it…
3D Gaussian Splatting (3DGS) is a recent explicit 3D representation that has achieved high-quality reconstruction and real-time rendering of complex scenes. However, the rasterization pipeline still suffers from unnecessary overhead…
Unmanned aerial vehicles are rapidly gaining popularity in a variety of environmental monitoring tasks. A key requirement for their autonomous operation is the ability to perform efficient environmental mapping online, given limited onboard…
Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is in numerical weather prediction where a previous forecast…
3D Gaussian Splatting (3DGS) has demonstrated impressive performance in 3D scene reconstruction. Beyond novel view synthesis, it shows great potential for multi-view surface reconstruction. Existing methods employ optimization-based…
Underwater 3D reconstruction and appearance restoration are hindered by the complex optical properties of water, such as wavelength-dependent attenuation and scattering. Existing Neural Radiance Fields (NeRF)-based methods struggle with…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view…