Related papers: Continuation of Point Clouds via Persistence Diagr…

Noisy 3D point clouds arise in many applications. They may be due to errors when constructing a 3D model from images or simply to imprecise depth sensors. Point clouds can be given geometrical structure using graphs created from the…

Point cloud super-resolution is a fundamental problem for 3D reconstruction and 3D data understanding. It takes a low-resolution (LR) point cloud as input and generates a high-resolution (HR) point cloud with rich details. In this paper, we…

This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

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…

In this paper, we introduce a Point Recurrent Neural Network (PointRNN) for moving point cloud processing. At each time step, PointRNN takes point coordinates $\boldsymbol{P} \in \mathbb{R}^{n \times 3}$ and point features $\boldsymbol{X}…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning…

Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…

3D point cloud registration is a fundamental problem in computer vision and robotics. Recently, learning-based point cloud registration methods have made great progress. However, these methods are sensitive to outliers, which lead to more…

Topological Data Analysis (TDA) provides a toolkit for the study of the shape of high dimensional and complex data. While operating on a space of persistence diagrams is cumbersome, persistence norms provide a simple real value measure of…

In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…

A point cloud serves as a representation of the surface of a three-dimensional (3D) shape. Deep generative models have been adapted to model their variations typically using a map from a ball-like set of latent variables. However, previous…

With the development of 3D laser scanning techniques and depth sensors, 3D dynamic point clouds have attracted increasing attention as a representation of 3D objects in motion, enabling various applications such as 3D immersive…

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

Explaining decisions made by deep neural networks is a rapidly advancing research topic. In recent years, several approaches have attempted to provide visual explanations of decisions made by neural networks designed for structured 2D image…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…