Related papers: Flat Delaunay Complexes for Homeomorphic Manifold …

Generation of 3D data by deep neural network has been attracting increasing attention in the research community. The majority of extant works resort to regular representations such as volumetric grids or collection of images; however, these…

We present a new paradigm for rigid alignment between point clouds based on learnable weighted consensus which is robust to noise as well as the full spectrum of the rotation group. Current models, learnable or axiomatic, work well for…

Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and…

For a non-compact n-manifold M let H(M) denote the group of homeomorphisms of M endowed with the Whitney topology and H_c(M) the subgroup of H(M) consisting of homeomorphisms with compact support. It is shown that the group H_c(M) is…

Four constructions of constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere are given, which should be considered analogues of `classical' constructions that are possible for CMC hypersurfaces in Euclidean space. First,…

We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…

PointNet has recently emerged as a popular representation for unstructured point cloud data, allowing application of deep learning to tasks such as object detection, segmentation and shape completion. However, recent works in literature…

Semantic scene understanding from point clouds is particularly challenging as the points reflect only a sparse set of the underlying 3D geometry. Previous works often convert point cloud into regular grids (e.g. voxels or bird-eye view…

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a…

We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a…

We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

Adversarial attacks on point clouds often impose strict geometric constraints to preserve plausibility; however, such constraints inherently limit transferability and undefendability. While deformation offers an alternative, existing…

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural…

The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…

This paper focuses on the task of 4D shape reconstruction from a sequence of point clouds. Despite the recent success achieved by extending deep implicit representations into 4D space, it is still a great challenge in two respects, i.e. how…

The restricted Delaunay triangulation of a closed surface $\Sigma$ and a finite point set $V \subset \Sigma$ is a subcomplex of the Delaunay tetrahedralization of $V$ whose triangles approximate $\Sigma$. It is well known that if $V$ is a…

Point cloud surface reconstruction has improved in accuracy with advances in deep learning, enabling applications such as infrastructure inspection. Recent approaches that reconstruct from small local regions rather than entire point clouds…

We propose an efficient framework for point cloud and measure registration using bi-Lipschitz homeomorphisms, achieving O(n log n) complexity, where n is the number of points. By leveraging the Energy-Distance (ED) kernel, which can be…

Point clouds obtained from capture devices or 3D reconstruction techniques are often noisy and interfere with downstream tasks. The paper aims to recover the underlying surface of noisy point clouds. We design a novel model, NoiseTrans,…