Related papers: A Persistent Homology Design Space for 3D Point Cl…

Persistent homology has been widely used to study the topology of point clouds in $\mathbb{R}^n$. Standard approaches are very sensitive to outliers, and their computational complexity depends badly on the number of data points. In this…

This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…

In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to…

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…

Deep learning on point clouds has made a lot of progress recently. Many point cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have shown advantages in accuracy and speed comparing to those using traditional 3D…

We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,lines, circles, and B-splines). Accordingly, our deep neural…

In this paper, we propose PCPNet, a deep-learning based approach for estimating local 3D shape properties in point clouds. In contrast to the majority of prior techniques that concentrate on global or mid-level attributes, e.g., for shape…

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

Persistent homology (PH) is a crucial concept in computational topology, providing a multiscale topological description of a space. It is particularly significant in topological data analysis, which aims to make statistical inference from a…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

The latest trends in the research field of single-view human reconstruction devote to learning deep implicit functions constrained by explicit body shape priors. Despite the remarkable performance improvements compared with traditional…

LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent…

The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…

How to extract significant point cloud features and estimate the pose between them remains a challenging question, due to the inherent lack of structure and ambiguous order permutation of point clouds. Despite significant improvements in…

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…

We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract…

Point clouds have become increasingly vital across various applications thanks to their ability to realistically depict 3D objects and scenes. Nevertheless, effectively compressing unstructured, high-precision point cloud data remains a…