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

We address the problem of crowd localization, i.e., the prediction of dots corresponding to people in a crowded scene. Due to various challenges, a localization method is prone to spatial semantic errors, i.e., predicting multiple dots…

Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…

Data clustering with uneven distribution in high level noise is challenging. Currently, HDBSCAN is considered as the SOTA algorithm for this problem. In this paper, we propose a novel clustering algorithm based on what we call graph of…

In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…

Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Discrete point cloud objects lack sufficient shape descriptors of 3D geometries. In this paper, we present a novel method for aggregating hypothetical curves in point clouds. Sequences of connected points (curves) are initially grouped by…

In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…

Unsupervised point cloud completion aims at estimating the corresponding complete point cloud of a partial point cloud in an unpaired manner. It is a crucial but challenging problem since there is no paired partial-complete supervision that…

We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…

Air travel is one of the fastest growing modes of transportation, however, the effects of aircraft noise on populations surrounding airports is hindering its growth. In an effort to study and ultimately mitigate the impact that this noise…

We present a scheme to improve the noise threshold for the fault-tolerant topological one-way computation with a constant overhead. Certain cluster states of finite size, say star clusters, are constructed with logical qubits through an…

Point clouds are widely used representations of 3D data, but determining the visibility of points from a given viewpoint remains a challenging problem due to their sparse nature and lack of explicit connectivity. Traditional methods, such…

We propose a new method for segmentation-free joint estimation of orthogonal planes, their intersection lines, relationship graph and corners lying at the intersection of three orthogonal planes. Such unified scene exploration under…

We study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied…

Current 3D object detection methods are heavily influenced by 2D detectors. In order to leverage architectures in 2D detectors, they often convert 3D point clouds to regular grids (i.e., to voxel grids or to bird's eye view images), or rely…

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…

Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE (Structure-preserving High-dimensional Analysis with Density-based Exploration), the first deep…

We study the problem of differentially private continual counting in the unbounded setting where the input size $n$ is not known in advance. Current state-of-the-art algorithms based on optimal instantiations of the matrix mechanism cannot…

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…