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

Compressing a set of unordered points is far more challenging than compressing images/videos of regular sample grids, because of the difficulties in characterizing neighboring relations in an irregular layout of points. Many researchers…

Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…

Surface reconstruction for point clouds is an important task in 3D computer vision. Most of the latest methods resolve this problem by learning signed distance functions from point clouds, which are limited to reconstructing closed…

Pseudo-LiDAR point cloud interpolation is a novel and challenging task in the field of autonomous driving, which aims to address the frequency mismatching problem between camera and LiDAR. Previous works represent the 3D spatial motion…

Real-world 3D data may contain intricate details defined by salient surface gaps. Automated reconstruction of these open surfaces (e.g., non-watertight meshes) is a challenging problem for environment synthesis in mixed reality…

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…

The Mixup method (Zhang et al. 2018), which uses linearly interpolated data, has emerged as an effective data augmentation tool to improve generalization performance and the robustness to adversarial examples. The motivation is to curtail…

Recent years we have witnessed rapid development in NeRF-based image rendering due to its high quality. However, point clouds rendering is somehow less explored. Compared to NeRF-based rendering which suffers from dense spatial sampling,…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

Feature lines are important geometric cues in characterizing the structure of a CAD model. Despite great progress in both explicit reconstruction and implicit reconstruction, it remains a challenging task to reconstruct a polygonal surface…

Point clouds offer an attractive source of information to complement images in neural scene representations, especially when few images are available. Neural rendering methods based on point clouds do exist, but they do not perform well…

In recent years, point cloud normal estimation, as a classical and foundational algorithm, has garnered extensive attention in the field of 3D geometric processing. Despite the remarkable performance achieved by current Neural Network-based…

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…

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…

Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…

We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, PUM). This approach gives a promising alternative to other…

We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Previous methods focus on learning point weights to fit neighborhoods into a geometric…

Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we…