Related papers: Recognizing Rigid Patterns of Unlabeled Point Clou…

A basic representation of any real molecule is a finite cloud of unordered atoms, many of which are chemically indistinguishable. A natural equivalence on point clouds in any metric space is defined by isometries that are…

Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point clouds of different sizes. Hence the isometry shape…

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…

Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model…

This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete…

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…

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…

Point clouds have grown in importance in the way computers perceive the world. From LIDAR sensors in autonomous cars and drones to the time of flight and stereo vision systems in our phones, point clouds are everywhere. Despite their…

Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…

Despite significant progress in image-based 3D scene flow estimation, the performance of such approaches has not yet reached the fidelity required by many applications. Simultaneously, these applications are often not restricted to…

The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…

LiDAR point clouds provide rich geometric information, which is particularly useful for the analysis of complex scenes of urban regions. Finding structural and semantic differences between two different three-dimensional point clouds, say,…

This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for justifying the novelty of solid crystalline materials…

We provide a dynamical perspective on the classical problem of 3D point cloud registration with correspondences. A point cloud is considered as a rigid body consisting of particles. The problem of registering two point clouds is formulated…

This paper reports on a novel nonparametric rigid point cloud registration framework that jointly integrates geometric and semantic measurements such as color or semantic labels into the alignment process and does not require explicit data…

We can use a method called registration to integrate some point clouds that represent the shape of the real world. In this paper, we propose highly accurate and stable registration method. Our method detects keypoints from point clouds and…

Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…

This paper introduces a robust unsupervised SE(3) point cloud registration method that operates without requiring point correspondences. The method frames point clouds as functions in a reproducing kernel Hilbert space (RKHS), leveraging…

Visual imitation learning with 3D point clouds has advanced robotic manipulation by providing geometry-aware, appearance-invariant observations. However, point cloud-based policies remain highly sensitive to sensor noise, pose…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…