Related papers: Least squares surface reconstruction on arbitrary …
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent…
In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on…
We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…
Detailed analysis of scanning probe microscopy (SPM) data acquired for faceted and non-flat surfaces is usually complicated due to the presence of a large number of surface areas tilted by large/variable angles relative to the scanning…
We present 3D Surface Splatting (3DSS), the first differentiable surface splatting renderer for physically-based inverse rendering from multi-view images. Our central insight is that the surface separation problem at the heart of surface…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
Joint camera pose and dense geometry estimation from a set of images or a monocular video remains a challenging problem due to its computational complexity and inherent visual ambiguities. Most dense incremental reconstruction systems…
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces from sparse,…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
Lightweight building surface models are crucial for digital city, navigation, and fast geospatial analytics, yet conventional multi-view geometry pipelines remain cumbersome and quality-sensitive due to their reliance on dense…
Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual…