Related papers: The Dual Degree Cech Bifiltration
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Point cloud filtering, the main bottleneck of which is removing noise (outliers) while preserving geometric features, is a fundamental problem in 3D field. The two-step schemes involving normal estimation and position update have been shown…
This paper presents two techniques for characterisation of cloud-feeding coherent boundary layer structures through analysis of large-eddy simulations of shallow cumulus clouds, contrasting conditions with and without ambient shear. The…
We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…
Local density of point clouds is crucial for representing local details, but has been overlooked by existing point cloud compression methods. To address this, we propose a novel deep point cloud compression method that preserves local…
We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
Point clouds, which directly record the geometry and attributes of scenes or objects by a large number of points, are widely used in various applications such as virtual reality and immersive communication. However, due to the huge data…
Point clouds are a basic data type that is increasingly of interest as 3D content becomes more ubiquitous. Applications using point clouds include virtual, augmented, and mixed reality and autonomous driving. We propose a more efficient…
We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and…
Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in unorganized clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary…
Rigid registration of partial observations is a fundamental problem in various applied fields. In computer graphics, special attention has been given to the registration between two partial point clouds generated by scanning devices.…
The degree-Rips bifiltration is the most computable of the parameter-free, density-sensitive bifiltrations in topological data analysis. It is known that this construction is stable to small perturbations of the input data, but its…
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris-Rips, Cech and witness complexes) built on top of precompact spaces. Using recent developments in the theory of topological…
As human-machine interaction continues to evolve, the capacity for environmental perception is becoming increasingly crucial. Integrating the two most common types of sensory data, images, and point clouds, can enhance detection accuracy.…
This paper devises, implements and benchmarks a novel shape retrieval method that can accurately match individual labelled point clusters (instances) of existing industrial facilities with their respective CAD models. It employs a…
Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…
We propose an alternative formulation of the well-known Hough transform to detect lines in point clouds. Replacing the discretized voting scheme of the classical Hough transform by a continuous score function, its persistent features in the…