Related papers: Recovering the polyhedral geometry of fragments
A well-known result in the study of convex polyhedra, due to Minkowski, is that a convex polyhedron is uniquely determined (up to translation) by the directions and areas of its faces. The theorem guarantees existence of the polyhedron…
This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
This paper studies the straight skeleton of polyhedra in three dimensions. We first address voxel-based polyhedra (polycubes), formed as the union of a collection of cubical (axis-aligned) voxels. We analyze the ways in which the skeleton…
The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…
Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional…
What's the most accurate 3D model of your face you can obtain while sitting at your desk? We attempt to answer this question in our work. High fidelity face reconstructions have so far been limited to either studio settings or through…
Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
While the problem of estimating shapes and diffuse reflectances of human faces from images has been extensively studied, there is relatively less work done on recovering the specular albedo. This paper presents a lightweight solution for…
Three-dimensional restoration of complex structural models has become a recognized validation method. Bringing a sedimentary structural model back in time to various deposition stages may also help understand the geological history of a…
Existing works on motion deblurring either ignore the effects of depth-dependent blur or work with the assumption of a multi-layered scene wherein each layer is modeled in the form of fronto-parallel plane. In this work, we consider the…
We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut…
3D face reconstruction from a single image is a classical and challenging problem, with wide applications in many areas. Inspired by recent works in face animation from RGB-D or monocular video inputs, we develop a novel method for…
We explore the potential of our novel triaxial modeling machinery in recovering the viewing angles, the shape and the orbit distribution of galaxies by using a high-resolution $N$-body merger simulation. Our modelling technique includes…
We analyze polyhedra composed of hexagons and triangles with three faces around each vertex, and their 3-regular planar graphs of edges and vertices, which we call "trihexes". Trihexes are analogous to fullerenes, which are 3-regular planar…
This research proposes a novel adjustable algorithm for reconstructing 3D body shapes from front and side silhouettes. Most recent silhouette-based approaches use a deep neural network trained by silhouettes and key points to estimate the…