Related papers: The Dual Degree Cech Bifiltration

Network centrality measures play a crucial role in understanding graph structures, assessing the importance of nodes, paths, or cycles based on directed or reciprocal interactions encoded by vertices and edges. Estrada and Ross extended…

We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…

Thanks to the application of deep learning technology in point cloud processing of the remote sensing field, point cloud segmentation has become a research hotspot in recent years, which can be applied to real-world 3D, smart cities, and…

Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet…

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…

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a…

The common occurrence of occlusion-induced incompleteness in point clouds has made point cloud completion (PCC) a highly-concerned task in the field of geometric processing. Existing PCC methods typically produce complete point clouds from…

Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…

We propose a new method for fine registering multiple point clouds simultaneously. The approach is characterized by being dense, therefore point clouds are not reduced to pre-selected features in advance. Furthermore, the approach is robust…

Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

Classical methods to model topological properties of point clouds, such as the Vietoris-Rips complex, suffer from the combinatorial explosion of complex sizes. We propose a novel technique to approximate a multi-scale filtration of the Rips…

Pre-trained point cloud analysis models have shown promising advancements in various downstream tasks, yet their effectiveness is typically suffering from low-quality point cloud (i.e., noise and incompleteness), which is a common issue in…

In recent decades, the use of 3D point clouds has been widespread in computer industry. The development of techniques in analyzing point clouds is increasingly important. In particular, mapping of point clouds has been a challenging…

Point clouds have become increasingly vital across various applications thanks to their ability to realistically depict 3D objects and scenes. Nevertheless, effectively compressing unstructured, high-precision point cloud data remains a…

The complexity of clouds, particularly in terms of texture detail at high resolutions, has not been well explored by most existing cloud detection networks. This paper introduces the High-Resolution Cloud Detection Network (HR-cloud-Net),…

We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-$k$ in persistent homology, for a either the \cech or the Vietoris--Rips filtration built…

Bifiltered graphs are a versatile tool for modelling relations between data points across multiple grades of a two-dimensional scale. They are especially popular in topological data analysis, where the homological properties of the induced…

Hyperspectral point clouds (HPCs) can simultaneously characterize 3D spatial and spectral information of ground objects, offering excellent 3D perception and target recognition capabilities. Current approaches for generating HPCs often…

Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such…