Related papers: Continuation of Point Clouds via Persistence Diagr…

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…

Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…

In this paper, we propose a method to segment regions in three-dimensional point clouds. We assume that (i) the shape and the number of regions in the point cloud are not known and (ii) the point cloud may be noisy. The method consists of…

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

Contemporary deep neural networks offer state-of-the-art results when applied to visual reasoning, e.g., in the context of 3D point cloud data. Point clouds are important datatype for precise modeling of three-dimensional environments, but…

Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…

There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling…

The task of point cloud completion aims to predict the missing part for an incomplete 3D shape. A widely used strategy is to generate a complete point cloud from the incomplete one. However, the unordered nature of point clouds will degrade…

Point cloud filtering is a fundamental problem in geometry modeling and processing. Despite of significant advancement in recent years, the existing methods still suffer from two issues: 1) they are either designed without preserving sharp…

We introduce a new model for planar point point processes, with the aim of capturing the structure of point interaction and spread in persistence diagrams. Persistence diagrams themselves are a key tool of TDA (topological data analysis),…

In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist of a dense sampling of the object's surface, containing many…

Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…

The processing, storage and transmission of large-scale point clouds is an ongoing challenge in the computer vision community which hinders progress in the application of 3D models to real-world settings, such as autonomous driving, virtual…

We propose a systematic approach for registering cross-source point clouds. The compelling need for cross-source point cloud registration is motivated by the rapid development of a variety of 3D sensing techniques, but many existing…

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…

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used…

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to…