Related papers: Graph skeletonization of high-dimensional point cl…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
The growing size of point clouds enlarges consumptions of storage, transmission, and computation of 3D scenes. Raw data is redundant, noisy, and non-uniform. Therefore, simplifying point clouds for achieving compact, clean, and uniform…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…
We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
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…
Graph convolutional networks (GCNs) are nowadays becoming mainstream in solving many image processing tasks including skeleton-based recognition. Their general recipe consists in learning convolutional and attention layers that maximize…
In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream…
Efficient processing and feature extraction of largescale point clouds are important in related computer vision and cyber-physical systems. This work investigates point cloud resampling based on hypergraph signal processing (HGSP) to better…
3D point cloud registration is a fundamental problem in computer vision and robotics. Recently, learning-based point cloud registration methods have made great progress. However, these methods are sensitive to outliers, which lead to more…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Understanding the dynamic processes of the glassy system continues to be challenging. Recent advances have shown the power of graph neural networks (GNNs) for determining the correlation between structure and dynamics in the glassy system.…
Graph Convolutional Networks (GCN) which typically follows a neural message passing framework to model dependencies among skeletal joints has achieved high success in skeleton-based human motion prediction task. Nevertheless, how to…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
Graph convolutional networks (GCNs) aim at extending deep learning to arbitrary irregular domains, namely graphs. Their success is highly dependent on how the topology of input graphs is defined and most of the existing GCN architectures…
A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…