Related papers: 3D Well-composed Polyhedral Complexes
A tetrahedral curve is a (usually nonreduced) curve in P^3 defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph to each curve and, using…
This paper presents a novel method for the reconstruction of 3D edges in multi-view stereo scenarios. Previous research in the field typically relied on video sequences and limited the reconstruction process to either straight…
Recent advancements in 3D reconstruction, especially through neural rendering approaches like Neural Radiance Fields (NeRF) and Plenoxel, have led to high-quality 3D visualizations. However, these methods are optimized for digital…
3D Lidar imaging can be a challenging modality when using multiple wavelengths, or when imaging in high noise environments (e.g., imaging through obscurants). This paper presents a hierarchical Bayesian algorithm for the robust…
Recent advances in 3D generation have been remarkable, with methods such as DreamFusion leveraging large-scale text-to-image diffusion-based models to guide 3D object generation. These methods enable the synthesis of detailed and…
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of such decompositions approximates the homotopy of the simplicial…
A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here directly, to describe "spaces" whose geometric realisation can…
Objective quality assessment of stereoscopic panoramic images becomes a challenging problem owing to the rapid growth of 360-degree contents. Different from traditional 2D image quality assessment (IQA), more complex aspects are involved in…
Numerous techniques have been proposed for reconstructing 3D models for opaque objects in past decades. However, none of them can be directly applied to transparent objects. This paper presents a fully automatic approach for reconstructing…
We propose to recover 3D shape structures from single RGB images, where structure refers to shape parts represented by cuboids and part relations encompassing connectivity and symmetry. Given a single 2D image with an object depicted, our…
One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues…
We call a 3-manifold Platonic if it can be decomposed into isometric Platonic solids. Generalizing an earlier publication by the author and others where this was done in case of the hyperbolic ideal tetrahedron, we give a census of…
Plane Wave imaging enables many applications that require high frame rates, including localisation microscopy, shear wave elastography, and ultra-sensitive Doppler. To alleviate the degradation of image quality with respect to conventional…
Given any connected, open 3-manifold $U$ having finitely many ends, a non-compact 3-manifold $M$ is constructed having the following properties: the interior of $M$ is homeomorphic to $U$; the boundary of $M$ is the disjoint union of…
Low-cost autonomous agents including autonomous driving vehicles chiefly adopt monocular 3D object detection to perceive surrounding environment. This paper studies 3D intermediate representation methods which generate intermediate 3D…
3D dense reconstruction refers to the process of obtaining the complete shape and texture features of 3D objects from 2D planar images. 3D reconstruction is an important and extensively studied problem, but it is far from being solved. This…
In this article, a family of $H^2$-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3D. In the family, the $P_\ell$ polynomial space is enriched by some high order polynomials for all…
Existing methods for reconstructing objects and humans from a monocular image suffer from severe mesh collisions and performance limitations for interacting occluding objects. This paper introduces a method to obtain a globally consistent…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
We give a homotopy classification of the global defects in ordered media, and explain it via the example of biaxial nematic liquid crystals, i.e., systems where the order parameter space is the quotient of the $3$-sphere $S^3$ by the…