Related papers: Topological Signal Processing for 3D Point Cloud D…

Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore,…

The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…

3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can…

The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…

Three-dimensional (3D) point clouds are important data representations in visualization applications. The rapidly growing utility and popularity of point cloud processing strongly motivate a plethora of research activities on large-scale…

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…

Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…

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…

Point cloud models with neural network architectures have achieved great success and have been widely used in safety-critical applications, such as Lidar-based recognition systems in autonomous vehicles. However, such models are shown…

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…

Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their…

Along with increasingly popular virtual reality applications, the three-dimensional (3D) point cloud has become a fundamental data structure to characterize 3D objects and surroundings. To process 3D point clouds efficiently, a suitable…

One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical…

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…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…

One of the key challenges in many research fields is uncovering how different interconnected systems interact within complex networks, typically represented as multi-layer networks. Capturing the intra- and cross-layer interactions among…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

3D sensing and content capture have made significant progress in recent years and the MPEG standardization organization is launching a new project on immersive media with point cloud compression (PCC) as one key corner stone. In this work,…

We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…