Related papers: Laplace-Beltrami based Multi-Resolution Shape Reco…

The purpose of this note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained in a previous work in dimension 2. We also give some related…

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to…

We present a method for generating high-quality watertight manifold meshes from multi-view input images. Existing volumetric rendering methods are robust in optimization but tend to generate noisy meshes with poor topology. Differentiable…

Reflective and textureless surfaces remain a challenge in multi-view 3D reconstruction. Both camera pose calibration and shape reconstruction often fail due to insufficient or unreliable cross-view visual features. To address these issues,…

Magnetic particle imaging (MPI) offers unparalleled contrast and resolution for tracing magnetic nanoparticles. A common imaging procedure calibrates a system matrix (SM) that is used to reconstruct data from subsequent scans. The ill-posed…

With the rising popularity of virtual worlds, the importance of data-driven parametric models of 3D meshes has grown rapidly. Numerous applications, such as computer vision, procedural generation, and mesh editing, vastly rely on these…

3D surface reconstruction from multi-view images is essential for scene understanding and interaction. However, complex indoor scenes pose challenges such as ambiguity due to limited observations. Recent implicit surface representations,…

Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…

The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate…

Birefringent metasurfaces are two-dimensional structures capable of independently controlling the amplitude, phase and polarization of orthogonally polarized incident waves. In this work, we propose a in-depth discussion on the mathematical…

Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…

3D reassembly is a fundamental geometric problem, and in recent years it has increasingly been challenged by deep learning methods rather than classical optimization. While learning approaches have shown promising results, most still rely…

We prove new a posteriori error estimates for surface finite element methods (SFEM). Surface FEM approximate solutions to PDE posed on surfaces. Prototypical examples are elliptic PDE involving the Laplace-Beltrami operator. Typically the…

In this paper, we study the Radial Basis Function (RBF) approximation to differential operators on smooth tensor fields defined on closed Riemannian submanifolds of Euclidean space, identified by randomly sampled point cloud data. {The…

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace-Beltrami operator on functions and the Laplacian on powers of the cotangent bundle.…

Magnetic resonance imaging (MRI) reconstruction is a fundamental task aimed at recovering high-quality images from undersampled or low-quality MRI data. This process enhances diagnostic accuracy and optimizes clinical applications. In…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…

Holography has emerged as a vital approach to fully engineer the wavefronts of light since its invention dating back to the last century. However, the typically large pixel size, small field of view and limited space-bandwidth impose…

We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements,…

Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…