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

Surface reconstruction from an unorganized point cloud is an important problem due to its widespread applications. White noise, possibly clustered outliers, and noisy perturbation may be generated when a point cloud is sampled from a…

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…

For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of $n$ points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of…

We present MonteBoxFinder, a method that, given a noisy input point cloud, fits cuboids to the input scene. Our primary contribution is a discrete optimization algorithm that, from a dense set of initially detected cuboids, is able to…

In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point…

We address the problem of estimating the poses of multiple instances of the source point cloud within a target point cloud. Existing solutions require sampling a lot of hypotheses to detect possible instances and reject the outliers, whose…

Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…

The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…

The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ of…

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…

This paper presents a new algorithm for filling holes in Level of Detail 2 (LoD2) building mesh models, addressing the challenges posed by geometric inaccuracies and topological errors. Unlike traditional methods that often alter the…

Data Science aims to extract meaningful knowledge from unorganised data. Real datasets usually come in the form of a cloud of points with only pairwise distances. Numerous applications require to visualise an overall shape of a noisy cloud…

This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…

Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat.…

We analyze the problem of determining whether 2 given point clouds in 2D, with any distinct cardinality and any number of outliers, have subsets of the same size that can be matched via a rigid motion. This problem is important, for…

We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…

We use a deep neural network to detect and place region-of-interest boxes around ultracold atom clouds in absorption and fluorescence images---with the ability to identify and bound multiple clouds within a single image. The neural network…

Point clouds are vital in computer vision tasks such as 3D reconstruction, autonomous driving, and robotics. However, TLS-acquired point clouds often contain virtual points from reflective surfaces, causing disruptions. This study presents…