Related papers: Anisotropic Gauss Reconstruction for Unoriented Po…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
3D Gaussian Splatting has achieved impressive performance in novel view synthesis with real-time rendering capabilities. However, reconstructing high-quality surfaces with fine details using 3D Gaussians remains a challenging task. In this…
3D Gaussian Splatting (3DGS) is a powerful reconstruction technique, but it needs to be initialized from accurate camera poses and high-fidelity point clouds. Typically, the initialization is taken from Structure-from-Motion (SfM)…
We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…
We present a fully automatic approach for reconstructing compact 3D building models from large-scale airborne point clouds. A major challenge of urban reconstruction from airborne LiDAR point clouds lies in that the vertical walls are…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive…
We consider the extrinsic geometry of surfaces in simply isotropic space, a three-dimensional space equipped with a rank 2 metric of index zero. Since the metric is degenerate, a surface normal cannot be unequivocally defined based on…
Reconstructing desired objects and scenes has long been a primary goal in 3D computer vision. Single-view point cloud reconstruction has become a popular technique due to its low cost and accurate results. However, single-view…
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…
We introduce a statistical extension of the classic Poisson Surface Reconstruction algorithm for recovering shapes from 3D point clouds. Instead of outputting an implicit function, we represent the reconstructed shape as a modified Gaussian…
Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…
The accurate reconstruction of dynamic street scenes is critical for applications in autonomous driving, augmented reality, and virtual reality. Traditional methods relying on dense point clouds and triangular meshes struggle with moving…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
We present a novel compression framework for 3D Gaussian splatting (3DGS) data that leverages transform coding tools originally developed for point clouds. Contrary to existing 3DGS compression methods, our approach can produce compressed…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…
Recently, Gaussian splatting has demonstrated significant success in novel view synthesis. Current methods often regress Gaussians with pixel or point cloud correspondence, linking each Gaussian with a pixel or a 3D point. This leads to the…