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We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies…

Numerical Analysis · Mathematics 2025-09-19 Sage B Shaw , Zachary P Kilpatrick , Daniele Avitabile

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

Numerical Analysis · Mathematics 2018-06-13 Zuzana Majdisova , Vaclav Skala

Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…

Numerical Analysis · Mathematics 2018-03-29 G. Garmanjani , R. Cavoretto , M. Esmaeilbeigi

We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the…

Numerical Analysis · Mathematics 2018-04-11 Vidhi Zala , Varun Shankar , Shankar P. Sastry , Robert M. Kirby

We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…

Numerical Analysis · Mathematics 2026-04-02 Alex Shiu Lun Chu , Leevan Ling , Ka Chun Cheung

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…

Numerical Analysis · Mathematics 2015-10-20 Roberto Cavoretto , Alessandra De Rossi

This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…

Numerical Analysis · Mathematics 2026-02-26 Adrijan Rogan , Andrej Kolar-Požun , Gregor Kosec

This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…

Numerical Analysis · Mathematics 2025-12-23 Rajesh Dachiraju

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

Numerical Analysis · Mathematics 2018-06-12 Pankaj K Mishra , Sankar K Nath , Mrinal K Sen , Gregory E Fasshauer

Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…

Numerical Analysis · Mathematics 2021-02-18 Kathryn P. Drake , Edward J. Fuselier , Grady B. Wright

Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many…

Numerical Analysis · Mathematics 2025-08-27 Maria Han Veiga , Faezeh Nassajian Mojarrad , Fatemeh Nassajian Mojarrad

Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…

Numerical Analysis · Mathematics 2017-02-24 Elisabeth Larsson , Victor Shcherbakov , Alfa Heryudono

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…

Graphics · Computer Science 2015-07-13 Shengjun Liu , Charlie C. L. Wang , Guido Brunnett , Jun Wang

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,…

Computer Vision and Pattern Recognition · Computer Science 2024-02-13 Atharva Pandey , Vishal Yadav , Rajendra Nagar , Santanu Chaudhury

In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using radial basis functions. Bayesian optimization is a…

Numerical Analysis · Mathematics 2023-11-09 Roberto Cavoretto , Alessandra De Rossi , Sandro Lancellotti , Federico Romaniello

Realistic digital models of plant leaves are crucial to fluid dynamics simulations of droplets for optimising agrochemical spray technologies. The presence and nature of small features (on the order of 100$\mathrm{\mu m}$) such as ridges…

The fundamental purpose of the present work is to constitute an enhanced Euler method with adaptive inverse-quadratic and inverse-multi-quadratic radial basis function (RBF) interpolation technique to solve initial value problems. These…

Numerical Analysis · Mathematics 2023-02-21 Samala Rathan , Deepit Shah

We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding…

Numerical Analysis · Mathematics 2018-05-09 Varun Shankar , Grady Wright

We propose united implicit functions (UNIF), a part-based method for clothed human reconstruction and animation with raw scans and skeletons as the input. Previous part-based methods for human reconstruction rely on ground-truth part labels…

Computer Vision and Pattern Recognition · Computer Science 2022-07-21 Shenhan Qian , Jiale Xu , Ziwei Liu , Liqian Ma , Shenghua Gao

Preserving details in restoring images highly corrupted by impulse noise remains a challenging problem. We proposed an algorithm based on radial basis functions (RBF) interpolation which estimates the intensities of corrupted pixels by…

Multimedia · Computer Science 2017-02-17 Fariborz Taherkhani , Mansour Jamzad