Related papers: New efficient algorithm for the isometric embeddin…
Photometric Stereo methods seek to reconstruct the 3d shape of an object from motionless images obtained with varying illumination. Most existing methods solve a restricted problem where the physical reflectance model, such as Lambertian…
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large…
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical significance and wide-ranging applications. Despite extensive…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\mathcal M}^2$ which can be realized as isometric immersions into $\R^3$. This problem can be formulated as…
We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve…
In this paper, we study the problem of local isometric immersion of pseudospherical surfaces determined by the solutions of a class of third order nonlinear partial differential equations with the type $u_t - u_{xxt} = \lambda u^2 u_{xxx} +…
We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid…