Related papers: Minimum-norm interpolation for unknown surface rec…

We propose a novel method that renders point clouds as if they are surfaces. The proposed method is differentiable and requires no scene-specific optimization. This unique capability enables, out-of-the-box, surface normal estimation,…

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…

Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the…

Surface reconstruction from point clouds is a crucial task in the fields of computer vision and computer graphics. SDF-based methods excel at reconstructing smooth meshes with minimal error and artefacts but struggle with representing open…

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and…

In deep learning models, learning more with less data is becoming more important. This paper explores how neural networks with normalized Radial Basis Function (RBF) kernels can be trained to achieve better sample efficiency. Moreover, we…

This paper studies the influence of scaling on the behavior of Radial Basis Function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The most important questions are: How does the error of a…

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…

We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…

This paper presents an approach for compressing point cloud geometry by leveraging a lightweight super-resolution network. The proposed method involves decomposing a point cloud into a base point cloud and the interpolation patterns for…

We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural…

Point cloud registration is a task to estimate the rigid transformation between two unaligned scans, which plays an important role in many computer vision applications. Previous learning-based works commonly focus on supervised…

We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…

Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…

The Partition of Unity (PU) method, performed with local Radial Basis Function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good…

The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…

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…

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…