Related papers: Laplace-Beltrami based Multi-Resolution Shape Reco…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Mechanically reconfigurable metasurfaces capable of translation, rotation, and permutation have attracted considerable attention for high-capacity optical information storage and full-color holographic displays, owing to their low-power and…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
One important property of imaging modalities and related applications is the resolution of image reconstructions which relies on various factors such as instrumentation or data processing. Restrictions in resolution can have manifold…
In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami…
We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
We give estimates for the $L^p$ norm ($2\leq p \leq +\infty$) of the restriction to a curve of the eigenfunctions of the Laplace Beltrami operator on a Riemannian surface. If the curve is a geodesic, we show that on the sphere these…
In this paper we shall assume that the ambient manifold is a pseudo-Riemannian space form $N^{m+1}_t(c)$ of dimension $m+1$ and index $t$ ($m\geq2$ and $1 \leq t\leq m$). We shall study hypersurfaces $M^{m}_{t'}$ which are polyharmonic of…
Despite recent advancements in the Large Reconstruction Model (LRM) demonstrating impressive results, when extending its input from single image to multiple images, it exhibits inefficiencies, subpar geometric and texture quality, as well…
Optical prisms are made of glass and map temporal frequencies into spatial frequencies by decomposing incident white light into its constituent colors and refract them into different directions. Conventional prisms suffer from their…
This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field.…
Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs…
Maps between Riemannian manifolds which are submersions on a dense subset, are studied by means of the eigenvalues of the pull-back of the target metrics, the first fundamental form. Expressions for the derivatives of these eigenvalues…
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…
This paper investigates links between the eigenvalues and eigenfunctions of the Laplace-Beltrami operator, and the higher Cheeger constants of smooth Riemannian manifolds, possibly weighted and/or with boundary. The higher Cheeger constants…
In this paper, we put forth the idea of metaprism, a passive and non-reconfigurable metasurface acting as a metamirror with frequency-dependent reflecting properties within the signal bandwidth. We show that, with an appropriate design of…
Multipath effects significantly influence the quality of microwave imaging in highly reflective environments, while the physical measurement aperture size constrains resolution. It is shown that by exploiting multipath reflections, improved…