Related papers: Minimum-norm interpolation for unknown surface rec…
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)…
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…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
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…
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…
Volumetric neural rendering methods like NeRF generate high-quality view synthesis results but are optimized per-scene leading to prohibitive reconstruction time. On the other hand, deep multi-view stereo methods can quickly reconstruct…
Reconstructing a continuous surface from a raw 3D point cloud is a challenging task. Recent methods usually train neural networks to overfit on single point clouds to infer signed distance functions (SDFs). However, neural networks tend to…
LiDAR point cloud frame interpolation, which synthesizes the intermediate frame between the captured frames, has emerged as an important issue for many applications. Especially for reducing the amounts of point cloud transmission, it is by…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
Reconstruction of geometric structures from images using supervised learning suffers from limited available amount of accurate data. One type of such data is accurate real-world RGB-D images. A major challenge in acquiring such ground truth…
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…