Related papers: An Operator-Splitting Method for the Gaussian Curv…
3D Gaussian Splatting (3DGS) leverages densely distributed Gaussian primitives for high-quality scene representation and reconstruction. While existing 3DGS methods perform well in scenes with minor view variation, large view changes from…
Dynamic urban scene modeling is a rapidly evolving area with broad applications. While current approaches leveraging neural radiance fields or Gaussian Splatting have achieved fine-grained reconstruction and high-fidelity novel view…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
Image registration is one important task in many image processing applications. It aims to align two or more images so that useful information can be extracted through comparison, combination or superposition. This is achieved by…
A few recent works explored incorporating geometric priors to regularize the optimization of Gaussian splatting, further improving its performance. However, those early studies mainly focused on the use of low-order geometric priors (e.g.,…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
Reconstructing deformable endoscopic tissues is crucial for achieving robot-assisted surgery. However, 3D Gaussian Splatting-based approaches encounter challenges in achieving consistent tissue surface reconstruction, while existing…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
The Gaussian curvature of a two-dimensional Riemannian manifold is uniquely determined by the choice of the metric. The formulas for computing the curvature in terms of components of the metric, in isothermal coordinates, involve the…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
This paper presents a special type of distributed optimization problems, where the summation of agents' local cost functions (i.e., global cost function) is convex, but each individual can be non-convex. Unlike most distributed optimization…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
Gaussian Splatting has recently become one of the most popular frameworks for photorealistic 3D scene reconstruction and rendering. While current rasterizers allow for efficient mappings of 3D Gaussian splats onto 2D camera views, this work…
Accurate 3D reconstruction of dynamic surgical scenes from endoscopic video is essential for robotic-assisted surgery. While recent 3D Gaussian Splatting methods have shown promise in achieving high-quality reconstructions with fast…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results…
In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a weighted triangulation at the conic singularity. A discrete…