Related papers: 3D Well-composed Polyhedral Complexes
Existing works on single-image 3D reconstruction mainly focus on shape recovery. In this work, we study a new problem, that is, simultaneously recovering 3D shape and surface color from a single image, namely "colorful 3D reconstruction".…
We construct infinitely many examples of pairs of isospectral but non-isometric $1$-cusped hyperbolic $3$-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an…
The accurate computation of the electrostatic capacity of three dimensional objects is a fascinating benchmark problem with a long and rich history. In particular, the capacity of the unit cube has widely been studied, and recent advances…
We introduce POP3D, a novel framework that creates a full $360^\circ$-view 3D model from a single image. POP3D resolves two prominent issues that limit the single-view reconstruction. Firstly, POP3D offers substantial generalizability to…
Perceptual image restoration seeks for high-fidelity images that most likely degrade to given images. For better visual quality, previous work proposed to search for solutions within the natural image manifold, by exploiting the latent…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
Automatic methods for reconstructing buildings from airborne LiDAR point clouds focus on producing accurate 3D models in a fast and scalable manner, but they overlook the problem of delivering simple and regularized models to practitioners.…
Quantitative photoacoustic computed tomography (qPACT) is a promising imaging modality for estimating physiological parameters such as blood oxygen saturation. However, developing robust qPACT reconstruction methods remains challenging due…
We call a polytope P of dimension 3 admissible if it has the following two properties: (1) for each vertex of P the set of its first-neighbours is coplanar; (2) all planes determined by the first-neighbours are distinct. It is shown that…
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…
A perfect Euler cuboid is a rectangular parallelepiped with integer edges, with integer face diagonals, and with integer space diagonal as well. Finding such parallelepipeds or proving their non-existence is an old unsolved mathematical…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
Several new constructions of 3-dimensional optical orthogonal codes are presented here. In each case the codes have ideal autocorrelation $\mathbf{ \lambda_a=0} $, and in all but one case a cross correlation of $ \mathbf{\lambda_c=1} $. All…
We construct compact polyhedra with $m$-gonal faces whose links are generalized 3-gons. It gives examples of cocompact hyperbolic bildings of type $P(m,3)$. For $m=3$ we get compact spaces covered by Euclidean buildings of type $A_2$.
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors,…
This paper develops a simple and fast method to reconstruct reality from stereoscopic images. We bring together ideas from robust optical flow techniques, morphing deformations and lightfield 3D rendering in order to create unsupervised…
In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…
Voxel art is a distinctive stylization widely used in games and digital media, yet automated generation from 3D meshes remains challenging due to conflicting requirements of geometric abstraction, semantic preservation, and discrete color…
We establish the method of holomorphic handle attaching to the strongly pseudoconcave boundary of a complex surface. We use this for proving the following statements: (1) every closed connected oriented contact 3-manifold can be filled as…
One of the most common methods for reconstructing three-dimensional (3D) images of real objects is digital holography. This technique relies on the use of electro-optical devices that modify the phase or amplitude of light fields in a…