Related papers: Surface Eigenvalues with Lattice-Based Approximati…

We give a sufficient condition for branched minimal immersions of spheres into ellipsoids to be embedded: we show that if the coordinate functions of the branched minimal immersion are first or second eigenfunctions with respect to a…

We introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first $k$ Dirichlet eigenvalues of the fractional…

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The…

Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…

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…

We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…

A novel mesh refinement sensor is proposed for lattice Boltzmann methods (LBMs) applicable to either static or dynamic mesh refinement algorithms. The sensor exploits the kinetic nature of LBMs by evaluating the departure of distribution…

In this paper, we introduce Point2Mesh, a technique for reconstructing a surface mesh from an input point cloud. Instead of explicitly specifying a prior that encodes the expected shape properties, the prior is defined automatically using…

Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…

We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…

Here, we present a least-squares based spectral element formulation for one-dimensional eigenvalue problems with interface conditions. First we develop the method for without interface case, then we extend it to interface case. Convergence…

We consider a non compact, complete manifold {\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\bf{X}}\times ]1,+\infty [$ with metric $ds^2=(h+dy^2)/y^{2\delta}.$ {\bf{X}} is a compact manifold with nonzero…

This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…

The spectral structure of the Laplacian-Beltrami operator (LBO) on manifolds has been widely used in many applications, include spectral clustering, dimensionality reduction, mesh smoothing, compression and editing, shape segmentation,…

We demonstrate an application of the closest point method where the truncated spectrum of the Laplace--Beltrami operator of an object is used to identify the object. The effectiveness of the method is analyzed as well as the default…

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…

For a $d$-dimensional hypersurface of class $C^3$ without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplacians. We then use this elliptic reformulation as a basis for…

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…

We propose an auto-encoding network architecture for point clouds (PC) capable of extracting shape signatures without supervision. Building on this, we (i) design a loss function capable of modelling data variance on PCs which are…

The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on a flat disc than on any other surface of revoltuion immersed in Euclidean space with the same boundary.