Related papers: Geometric Tomography With Topological Guarantees

This paper considers the approximate reconstruction of points, x \in R^D, which are close to a given compact d-dimensional submanifold, M, of R^D using a small number of linear measurements of x. In particular, it is shown that a number of…

In this article, we derive a topological obstruction to the removal of a isolated degenerate complex tangent to an embedding of a 3-manifold into $\mathbb{C}^3$ (without affecting the structure of the remaining complex tangents). We…

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…

Monocular 3D object detection is of great significance for autonomous driving but remains challenging. The core challenge is to predict the distance of objects in the absence of explicit depth information. Unlike regressing the distance as…

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…

Tomography is the area of reconstructing objects from projections. Here we wish to reconstruct a set of cells in a two dimensional grid, given the number of cells in every row and column. The set is required to be an hv-convex polyomino,…

We present STITCH, a novel approach for neural implicit surface reconstruction of a sparse and irregularly spaced point cloud while enforcing topological constraints (such as having a single connected component). We develop a new…

Traditional sampling schemes often assume that the sampling locations are known. Motivated by the recent bioimaging technique known as cryogenic electron microscopy (cryoEM), we consider the problem of reconstructing an unknown 3D structure…

Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…

We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These two problems are: the local isometric embedding problem for two-dimensional Riemannian…

We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a…

One major challenge in 3D reconstruction is to infer the complete shape geometry from partial foreground occlusions. In this paper, we propose a method to reconstruct the complete 3D shape of an object from a single RGB image, with…

A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…

We present SAM 3D, a generative model for visually grounded 3D object reconstruction, predicting geometry, texture, and layout from a single image. SAM 3D excels in natural images, where occlusion and scene clutter are common and visual…

Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…

The goal of discrete tomography is to reconstruct an unknown function $f$ via a given set of line sums. In addition to requiring accurate reconstructions, it is favourable to be able to perform the task in a timely manner. This is…

Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different…

In this paper, we prove a geometrization conjecture, every orientable smooth closed 3-manifold with finite fundamental group is homeomorphic to $S^3/G$ for some finite cyclic subgroup $G\subset {Isom}^+(S^3)$.

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of…

We present a novel method for 6-DoF object tracking and high-quality 3D reconstruction from monocular RGBD video. Existing methods, while achieving impressive results, often struggle with complex objects, particularly those exhibiting…