Related papers: A fast and robust algorithm to count topologically…

Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD). Previously, there has been…

The problem faced in this paper concerns the recognition of simple and complex geometric primitives in point clouds resulting from scans of mechanical CAD objects. A large number of points, the presence of noise, outliers, missing or…

Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a…

Point clouds, as a form of Lagrangian representation, allow for powerful and flexible applications in a large number of computational disciplines. We propose a novel deep-learning method to learn stable and temporally coherent feature…

Dense point cloud generation from a sparse or incomplete point cloud is a crucial and challenging problem in 3D computer vision and computer graphics. So far, the existing methods are either computationally too expensive, suffer from…

We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…

We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…

The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a…

In recent years, three-dimensional point clouds are used increasingly to document natural environments. Each dataset contains a diverse set of objects, at varying shapes and sizes, distributed throughout the data and intricately intertwined…

The continual improvement of 3D sensors has driven the development of algorithms to perform point cloud analysis. In fact, techniques for point cloud classification and segmentation have in recent years achieved incredible performance…

In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in Euclidean space given by image. Carlsson et al. proposed a…

With the development of 3D sensing technologies, point clouds have attracted increasing attention in a variety of applications for 3D object representation, such as autonomous driving, 3D immersive tele-presence and heritage reconstruction.…

As a popular representation of 3D data, point cloud may contain noise and need to be filtered before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distribution in the filtered…

Plane detection in 3D point clouds is a crucial pre-processing step for applications such as point cloud segmentation, semantic mapping and SLAM. In contrast to many recent plane detection methods that are only applicable on organized point…

As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation and heritage reconstruction.…

Ears are a particularly difficult region of the human face to model, not only due to the non-rigid deformations existing between shapes but also to the challenges in processing the retrieved data. The first step towards obtaining a good…

In this paper, we propose novel edge and corner detection algorithms for unorganized point clouds. Our edge detection method evaluates symmetry in a local neighborhood and uses an adaptive density based threshold to differentiate 3D edge…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of…

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…