Related papers: An Operator-Splitting Method for the Gaussian Curv…
3D Gaussian Splatting (3D-GS) enables efficient novel view synthesis, but treats all frequencies uniformly, making it difficult to separate coarse structure from fine detail. Recent works have started to exploit frequency signals, but lack…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
High-fidelity reconstruction of dynamic scenes is an important yet challenging problem. While recent 4D Gaussian Splatting (4DGS) has demonstrated the ability to model temporal dynamics, it couples Gaussian motion and geometric attributes…
A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element based mean curvature flow algorithm based on a coupled partial differential equation system which…
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…
Gaussian Splatting (GS), a recent technique for converting discrete points into continuous spatial representations, has shown promising results in 3D scene modeling and 2D image super-resolution. In this paper, we explore its untapped…
We introduce G-Style, a novel algorithm designed to transfer the style of an image onto a 3D scene represented using Gaussian Splatting. Gaussian Splatting is a powerful 3D representation for novel view synthesis, as -- compared to other…
Generalizable 3D Gaussian Splatting reconstruction showcases advanced Image-to-3D content creation but requires substantial computational resources and large datasets, posing challenges to training models from scratch. Current methods…
Recent advances in computer vision have predominantly relied on data-driven approaches that leverage deep learning and large-scale datasets. Deep neural networks have achieved remarkable success in tasks such as stereo matching and…
Implicit Neural Representations (INR) have been successfully employed for Arbitrary-scale Super-Resolution (ASR). However, INR-based models need to query the multi-layer perceptron module numerous times and render a pixel in each query,…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
The mean curvature flow describes the evolution of a surface (a curve) with normal velocity proportional to the local mean curvature. It has many applications in mathematics, science and engineering. In this paper, we develop a numerical…
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…
To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
The discretization of velocity space plays a crucial role in the accuracy and efficiency of multiscale Boltzmann solvers. Conventional velocity space discretization methods suffer from uneven node distribution and mismatch issues, limiting…
We propose a discrete approach for approximating solutions to the prescribed Gaussian curvature problem in two-dimensional manifolds, based on the notion of discrete conformality. Our approach provides an efficient numerical method to…
We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…