Related papers: Graph skeletonization of high-dimensional point cl…

Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has…

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…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

Point cloud compression (PCC) is a key enabler for various 3-D applications, owing to the universality of the point cloud format. Ideally, 3D point clouds endeavor to depict object/scene surfaces that are continuous. Practically, as a set…

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…

Classifying whole images is a classic problem in machine learning, and graph neural networks are a powerful methodology to learn highly irregular geometries. It is often the case that certain parts of a point cloud are more important than…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

With the development of 3D sensing technologies, point clouds have attracted increasing attention in a variety of applications for 3D object representation, such as autonomous driving, 3D immersive tele-presence and heritage reconstruction.…

Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims…

Curve skeleton extraction from unorganized point cloud is a fundamental task of computer vision and three-dimensional data preprocessing and visualization. A great amount of work has been done to extract skeleton from point cloud. but the…

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

3D reconstruction from images is a core problem in computer vision. With recent advances in deep learning, it has become possible to recover plausible 3D shapes even from single RGB images for the first time. However, obtaining detailed…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

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…

Reconstructing a high-resolution 3D model of an object is a challenging task in computer vision. Designing scalable and light-weight architectures is crucial while addressing this problem. Existing point-cloud based reconstruction…

Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…