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

Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to…

Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop TSP theories for the case where observations belong to general…

3D Gaussian Splatting (3DGS) excels at producing highly detailed 3D reconstructions, but these scenes often require specialised renderers for effective visualisation. In contrast, point clouds are a widely used 3D representation and are…

We propose a new method for the reconstruction of simplicial complexes (combining points, edges and triangles) from 3D point clouds from Mobile Laser Scanning (MLS). Our main goal is to produce a reconstruction of a scene that is adapted to…

Point cloud based 3D visual representation is becoming popular due to its ability to exhibit the real world in a more comprehensive and immersive way. However, under a limited network bandwidth, it is very challenging to communicate this…

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in…

Point cloud has been the mainstream representation for advanced 3D applications, such as virtual reality and augmented reality. However, the massive data amounts of point clouds is one of the most challenging issues for transmission and…

Wireless transmission of high-dimensional 3D point clouds (PCs) is increasingly required in industrial collaborative robotics systems. Conventional compression methods prioritize geometric fidelity, although many practical applications…

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…

Recent years have witnessed the growth of point cloud based applications because of its realistic and fine-grained representation of 3D objects and scenes. However, it is a challenging problem to compress sparse, unstructured, and…

Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…

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…

Current point cloud registration methods are mainly based on local geometric information and usually ignore the semantic information contained in the scenes. In this paper, we treat the point cloud registration problem as a semantic…

Acquisition and processing of point clouds (PCs) is a crucial enabler for many emerging applications reliant on 3D spatial data, such as robot navigation, autonomous vehicles, and augmented reality. In most scenarios, PCs acquired by remote…

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…

Given the rapid development of 3D scanners, point clouds are becoming popular in AI-driven machines. However, point cloud data is inherently sparse and irregular, causing significant difficulties for machine perception. In this work, we…

High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…

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.…

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence…

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…