Related papers: Point set stratification and Delaunay depth

Fully exploring correlation among points in point clouds is essential for their feature modeling. This paper presents a novel end-to-end graph model, named Point2Node, to represent a given point cloud. Point2Node can dynamically explore…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…

Point cloud denoising task aims to recover the clean point cloud from the scanned data coupled with different levels or patterns of noise. The recent state-of-the-art methods often train deep neural networks to update the point locations…

This paper presents a new O(nlog(n)) algorithm for computing the convex hull of a set of 3 dimensional points. The algorithm first sorts the point in (x,y,z) then incrementally adds sorted points to the convex hull using the constraint that…

In this paper, we present a polynomial dynamic programming algorithm that tests whether a $n$-vertex directed tree $T$ has an upward planar embedding into a convex point-set $S$ of size $n$. Further, we extend our approach to the class of…

We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.

Traditional algorithms of point set registration minimizing point-to-plane distances often achieve a better estimation of rigid transformation than those minimizing point-to-point distances. Nevertheless, recent deep-learning-based methods…

We extend the classical notion of the spherical depth in \mathbb{R}^k, to the important setup of data on a Riemannian manifold. We show that this notion of depth satisfies a set of desirable properties. For the empirical version of this…

Quantification of sputter depth profiles is frequently done by fitting the convolution integral over concentration and depth resolution function. For a thin delta layer, there exist analytical solutions. The analytical depth resolution…

We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.

In this paper, we address the problem of estimating dense depth from a sequence of images using deep neural networks. Specifically, we employ a dense-optical-flow network to compute correspondences and then triangulate the point cloud to…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

We present a neural-network-based architecture for 3D point cloud denoising called neural projection denoising (NPD). In our previous work, we proposed a two-stage denoising algorithm, which first estimates reference planes and follows by…

The development of practical applications, such as autonomous driving and robotics, has brought increasing attention to 3D point cloud understanding. While deep learning has achieved remarkable success on image-based tasks, there are many…

The local flow field and seepage induced drag obtained from Pore Network Models (PNM) is compared to Immersed Boundary Method (IBM) simulations, for a range of linear graded and bimodal samples. PNM were generated using a weighted Delaunay…

Point cloud completion is a generation and estimation issue derived from the partial point clouds, which plays a vital role in the applications in 3D computer vision. The progress of deep learning (DL) has impressively improved the…

In this paper we propose a rotation-invariant deep network for point clouds analysis. Point-based deep networks are commonly designed to recognize roughly aligned 3D shapes based on point coordinates, but suffer from performance drops with…

In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…

Implicit function based surface reconstruction has been studied for a long time to recover 3D shapes from point clouds sampled from surfaces. Recently, Signed Distance Functions (SDFs) and Occupany Functions are adopted in learning-based…