Related papers: Rational RBF-based partition of unity method for e…

This paper aims to survey our recent work relating to the radial basis function (RBF) from some new views of points. In the first part, we established the RBF on numerical integration analysis based on an intrinsic relationship between the…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined.…

Majority of the perception methods in robotics require depth information provided by RGB-D cameras. However, standard 3D sensors fail to capture depth of transparent objects due to refraction and absorption of light. In this paper, we…

Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…

One of the main challenges in point cloud compression (PCC) is how to evaluate the perceived distortion so that the codec can be optimized for perceptual quality. Current standard practices in PCC highlight a primary issue: while…

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…

Neural implicit modeling permits to achieve impressive 3D reconstruction results on small objects, while it exhibits significant limitations in large indoor scenes. In this work, we propose a novel neural implicit modeling method that…

While NeRF has shown great success for neural reconstruction and rendering, its limited MLP capacity and long per-scene optimization times make it challenging to model large-scale indoor scenes. In contrast, classical 3D reconstruction…

We present a novel derivative-free interpolation based optimization algorithm. A trust-region method is used where a surrogate model is realized via an interpolation framework. The framework for interpolation is provided by Universal…

Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However,…

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the…

Real-time 3D reconstruction from RGB-D sensor data plays an important role in many robotic applications, such as object modeling and mapping. The popular method of fusing depth information into a truncated signed distance function (TSDF)…

The main purpose of this work is the one of providing an efficient scheme for constructing reduced interpolation models for kernel bases. In literature such problem is mainly addressed via the well-established knot insertion or knot removal…

Image-based lighting (IBL) is a widely used technique that renders objects using a high dynamic range image or environment map. However, aggregating the irradiance at the object's surface is computationally expensive, in particular for…

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…

Accurate 3D reconstruction from multi-view images is essential for downstream robotic tasks such as navigation, manipulation, and environment understanding. However, obtaining precise camera poses in real-world settings remains challenging,…

We mainly concerned with a decoupled fractional Laplacian wave equation in this paper. A new time-space domain radial basis function (RBF) collocation method is introduced to solve the fractional wave equation, which describes seismic wave…

In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing…