Related papers: 3D Well-composed Polyhedral Complexes

Simultaneous reconstruction of geometry and reflectance properties in uncontrolled environments remains a challenging problem. In this paper, we propose an efficient method to reconstruct the scene's 3D geometry and reflectance from…

We present a numerically efficient method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. Our method is based on a template…

Let $M$ be a non-compact hyperbolic $3$-manifold with finite volume and totally geodesic boundary components. By subdividing mixed ideal polyhedral decompositions of $M$, under some certain topological conditions, we prove that $M$ has an…

This paper examines the representations of hyperbolic integral homology spheres into the binary icosahedral group $2I$. We specifically give a geometric meaning to $2I$ representations by relating them to Larsen's notion of quotient…

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we…

The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface…

We show that the following algorithmic problem is decidable: given a $2$-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in $\mathbf{R}^3$? By a known reduction, it suffices to decide…

We propose a hybrid image-space/object-space solution to the classical hidden surface removal problem: Given n disjoint triangles in Real^3 and p sample points (``pixels'') in the xy-plane, determine the first triangle directly behind each…

We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our main goal is to produce a reconstruction of a scene that is adapted to…

We propose a novel method to reconstruct the 3D shapes of transparent objects using hand-held captured images under natural light conditions. It combines the advantage of explicit mesh and multi-layer perceptron (MLP) network, a hybrid…

Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…

In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

We propose pix2pix3D, a 3D-aware conditional generative model for controllable photorealistic image synthesis. Given a 2D label map, such as a segmentation or edge map, our model learns to synthesize a corresponding image from different…

A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can…

Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are…

Three-dimensional (3D) reconstruction from a single image is an ill-posed problem with inherent ambiguities, i.e. scale. Predicting a 3D scene from text description(s) is similarly ill-posed, i.e. spatial arrangements of objects described.…

Point cloud completion aims to reconstruct complete 3D shapes from partial observations, which is a challenging problem due to severe occlusions and missing geometry. Despite recent advances in multimodal techniques that leverage…

Color encoding of depth is shown to occur naturally in holograms that are reconstructed under white light illumination. It can be registered in a common color photograph, allowing a simple method of visual decoding by means of ordinary…

3D reconstruction from 2D images is a central problem in computer vision. Recent works have been focusing on reconstruction directly from a single image. It is well known however that only one image cannot provide enough information for…