Related papers: Shape Reconstruction of Trapezoidal Surfaces

We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…

We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in…

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…

Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…

This paper introduces a novel method for reconstructing meshes from sparse point clouds by predicting edge connection. Existing implicit methods usually produce superior smooth and watertight meshes due to the isosurface extraction…

Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…

Reconstructing hand-held objects in 3D from monocular images remains a significant challenge in computer vision. Most existing approaches rely on implicit 3D representations, which produce overly smooth reconstructions and are…

The most common problem in data reconstruction is to fit a function based on the observations of some sample (guiding) points. This paper provides a methodological point of view of digital-discrete surface reconstruction. We explain our…

We present Hybrid-CSR, a geometric deep-learning model that combines explicit and implicit shape representations for cortical surface reconstruction. Specifically, Hybrid-CSR begins with explicit deformations of template meshes to obtain…

Dexterous manipulation enables complex tasks but suffers from self-occlusion, severe depth noise, and depth information loss when manipulating transparent objects. To solve this problem, this paper proposes TransDex, a 3D visuo-tactile…

We describe a new approach to fit the polyhedron describing a 3D building model to the point cloud of a Digital Elevation Model (DEM). We introduce a new kinetic framework that hides to its user the combinatorial complexity of determining…

Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…

A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge…

The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also…

Topology and geometry are deeply intertwined in the study of surfaces, though their interaction manifests differently in smooth and discrete settings. In the smooth category, a classical result asserts that any closed smooth surface…