Related papers: The Dual Degree Cech Bifiltration
Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. However, conventional methods for…
The Rips filtration over a finite metric space and its corresponding persistent homology are prominent methods in TDA to summarise the shape of data. Crucial to their use is the bottleneck stability result. A generalisation of the Rips…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
Feature Descriptors and Detectors are two main components of feature-based point cloud registration. However, little attention has been drawn to the explicit representation of local and global semantics in the learning of descriptors and…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid…
The alpha complex efficiently computes persistent homology of a point cloud $X$ in Euclidean space when the dimension $d$ is low. Given a subset $A$ of $X$, relative persistent homology can be computed as the persistent homology of the…
Multi-view multi-instance feature association constitutes a crucial step in 3D reconstruction, facilitating the consistent grouping of object instances across various camera perspectives. The presence of multiple identical objects within a…
Recent advancements in Diffusion Transformer (DiT) models have significantly improved 3D point cloud generation. However, existing methods primarily focus on local feature extraction while overlooking global topological information, such as…
Recent advances in computer vision and deep learning have shown promising performance in estimating rigid/similarity transformation between unregistered point clouds of complex objects and scenes. However, their performances are mostly…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
A novel method performing 3D PTV from double frame multi-camera images is introduced. Particle velocities are estimated by following three steps. Firstly, separate particle reconstructions with a sparsity-based algorithm are performed on a…
With the rapid advancement of 3D sensing technologies, obtaining 3D shape information of objects has become increasingly convenient. Lidar technology, with its capability to accurately capture the 3D information of objects at long…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
We define a new framework that unifies the filtration and mapper approaches from TDA, and present efficient algorithms to compute it. Termed the box filtration of a PCD, we grow boxes (hyperrectangles) that are not necessarily centered at…
Point cloud registration has seen significant advancements with the application of deep learning techniques. However, existing approaches often overlook the potential of integrating radiometric information from RGB images. This limitation…
Point cloud compression plays a crucial role in reducing the huge cost of data storage and transmission. However, distortions can be introduced into the decompressed point clouds due to quantization. In this paper, we propose a novel…
Point cloud (PCD) anomaly detection steadily emerges as a promising research area. This study aims to improve PCD anomaly detection performance by combining handcrafted PCD descriptions with powerful pre-trained 2D neural networks. To this…
The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…