Related papers: Least squares surface reconstruction on arbitrary …
Iterative least-squares MR reconstructions typically use the Conjugate Gradient algorithm, despite known numerical issues. This paper demonstrates that the more recent LSMR algorithm has favourable numerical properties, and is to be…
It is an important task to reconstruct surfaces from 3D point clouds. Current methods are able to reconstruct surfaces by learning Signed Distance Functions (SDFs) from single point clouds without ground truth signed distances or point…
In this paper, we present an implicit surface reconstruction method with 3D Gaussian Splatting (3DGS), namely 3DGSR, that allows for accurate 3D reconstruction with intricate details while inheriting the high efficiency and rendering…
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusing on least squares and deep learning-based methods. First,…
It is vital to infer a signed distance function (SDF) in multi-view based surface reconstruction. 3D Gaussian splatting (3DGS) provides a novel perspective for volume rendering, and shows advantages in rendering efficiency and quality.…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on…
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…
A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations…
Neural signed distance functions (SDFs) have shown powerful ability in fitting the shape geometry. However, inferring continuous signed distance fields from discrete unoriented point clouds still remains a challenge. The neural network…
Implicit surface representations such as the signed distance function (SDF) have emerged as a promising approach for image-based surface reconstruction. However, existing optimization methods assume solid surfaces and are therefore unable…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
Recent works on implicit neural representations have made significant strides. Learning implicit neural surfaces using volume rendering has gained popularity in multi-view reconstruction without 3D supervision. However, accurately…
Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
Surface reconstruction and novel view rendering from sparse-view images are challenging. Signed Distance Function (SDF)-based methods struggle with fine details, while 3D Gaussian Splatting (3DGS)-based approaches lack global geometry…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…
The most common problem in data reconstruction is to fit a function based on the observations of some sample (guiding) points. This paper provides a methodological point of view of digital-discrete surface reconstruction. We explain our…