Related papers: A Closed-Form Formulation of HRBF-Based Surface Re…

Reconstruction of high-fidelity 3D objects or scenes is a fundamental research problem. Recent advances in RGB-D fusion have demonstrated the potential of producing 3D models from consumer-level RGB-D cameras. However, due to the discrete…

We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear…

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set)…

In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. The applicability of RBF methods is hindered by its computational demand, that requires the solution of linear systems of…

Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for…

We propose a fast and accurate surface reconstruction algorithm for unorganized point clouds using an implicit representation. Recent learning methods are either single-object representations with small neural models that allow for high…

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…

We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus we develop an efficient local scheme via the well-known Partition of Unity (PU)…

Neural implicit representations have emerged as a powerful paradigm for 3D reconstruction. However, despite their success, existing methods fail to capture fine geometric details and thin structures, especially in scenarios where only…

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…

Neural implicit surface reconstruction using volume rendering techniques has recently achieved significant advancements in creating high-fidelity surfaces from multiple 2D images. However, current methods primarily target scenes with…

Neural rendering can be used to reconstruct implicit representations of shapes without 3D supervision. However, current neural surface reconstruction methods have difficulty learning high-frequency geometry details, so the reconstructed…

Neural reconstruction and rendering strategies have demonstrated state-of-the-art performances due, in part, to their ability to preserve high level shape details. Existing approaches, however, either represent objects as implicit surface…

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

High-order surface reconstruction is an important technique for CAD-free, mesh-based geometric and physical modeling, and for high-order numerical methods for solving partial differential equations (PDEs) in engineering applications. In…

Recovering high-quality surfaces from irregular point cloud is ill-posed unless strong geometric priors are available. We introduce an implicit self-prior approach that distills a shape-specific prior directly from the input point cloud…

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…