Related papers: Continuation of Point Clouds via Persistence Diagr…

We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, \etc. Nevertheless, dynamic point…

Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…

Point cloud registration is a fundamental technique in 3-D computer vision with applications in graphics, autonomous driving, and robotics. However, registration tasks under challenging conditions, under which noise or perturbations are…

Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes…

In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical…

In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate…

To achieve point cloud denoising, traditional methods heavily rely on geometric priors, and most learning-based approaches suffer from outliers and loss of details. Recently, the gradient-based method was proposed to estimate the gradient…

The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are…

This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4.…

The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…

We present a novel, effective method for global point cloud registration problems by geometric topology. Based on many point cloud pairwise registration methods (e.g ICP), we focus on the problem of accumulated error for the composition of…

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…

3D dynamic point clouds provide a discrete representation of real-world objects or scenes in motion, which have been widely applied in immersive telepresence, autonomous driving, surveillance, etc. However, point clouds acquired from…

This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…

Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in unorganized clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary…

In this paper, we introduce a novel conditional generative adversarial network that creates dense 3D point clouds, with color, for assorted classes of objects in an unsupervised manner. To overcome the difficulty of capturing intricate…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…