Related papers: Radial Basis Function Techniques for Neural Field …

Neural Radiance Fields (NeRFs) have emerged as powerful tools for capturing detailed 3D scenes through continuous volumetric representations. Recent NeRFs utilize feature grids to improve rendering quality and speed; however, these…

In this paper, we study the problem of continuous 3D shape representations. The majority of existing successful methods are coordinate-based implicit neural representations. However, they are inefficient to render novel views or recover…

Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution…

We propose to tackle the multiview photometric stereo problem using an extension of Neural Radiance Fields (NeRFs), conditioned on light source direction. The geometric part of our neural representation predicts surface normal direction,…

Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D…

Neural Radiance Fields (NeRF), as a pioneering technique in computer vision, offer great potential to revolutionize medical imaging by synthesizing three-dimensional representations from the projected two-dimensional image data. However,…

In this paper, we discuss the problem of constructing Radial Basis In this paper, we discuss the problem of constructing Radial Basis Function (RBF)-based Partition of Unity (PU) interpolants that are positive if data values are positive.…

Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…

Neural Radiance Fields (NeRF) have demonstrated exceptional capabilities in reconstructing complex scenes with high fidelity. However, NeRF's view dependency can only handle low-frequency reflections. It falls short when handling complex…

We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or statistical interpretations. Focusing on the prototype…

We introduce Neural Radiosity, an algorithm to solve the rendering equation by minimizing the norm of its residual similar as in traditional radiosity techniques. Traditional basis functions used in radiosity techniques, such as piecewise…

Derivative boundary conditions introduce challenges for mesh-free discretizations of PDEs on surfaces, especially when the domain is represented by randomly sampled point clouds. The recently developed two-step tangent-space RBF-generated…

We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…

For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He…

Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…

This paper proposes a data-driven method to solve the fixed-energy inverse scattering problem for radially symmetric potentials using radial basis function (RBF) neural networks in an open-loop control system. The method estimates the…

The purpose of this article is to introduce radial basis function, (RBFs), methods for solving null control problems for the Stokes system with few internal scalar controls and Dirichlet or Navier slip boundary conditions. To the best of…

Existing neural reconstruction schemes such as Neural Radiance Field (NeRF) are largely focused on modeling opaque objects. We present a novel neural refractive field(NeReF) to recover wavefront of transparent fluids by simultaneously…

Cortical surface registration is a fundamental tool for neuroimaging analysis that has been shown to improve the alignment of functional regions relative to volumetric approaches. Classically, image registration is performed by optimizing a…