Related papers: Bifunction and Interlevel Delaunay Trifiltrations

The recent surge in 3D data acquisition has spurred the development of geometric deep learning models for point cloud processing, boosted by the remarkable success of transformers in natural language processing. While point cloud…

Object recognition in 3D point clouds is a challenging task, mainly when time is an important factor to deal with, such as in industrial applications. Local descriptors are an amenable choice whenever the 6 DoF pose of recognized objects…

Deep neural networks are known to be vulnerable to adversarial examples which are carefully crafted instances to cause the models to make wrong predictions. While adversarial examples for 2D images and CNNs have been extensively studied,…

Many types of 3D acquisition sensors have emerged in recent years and point cloud has been widely used in many areas. Accurate and fast registration of cross-source 3D point clouds from different sensors is an emerged research problem in…

Classical methods to model topological properties of point clouds, such as the Vietoris-Rips complex, suffer from the combinatorial explosion of complex sizes. We propose a novel technique to approximate a multi-scale filtration of the Rips…

Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…

Nonlinear state estimation under noisy observations is rapidly intractable as system dimension increases. We introduce an improved Yau-Yau filtering framework that breaks the curse of dimensionality and extends real-time nonlinear filtering…

Establishing accurate and representative matches is a crucial step in addressing the point cloud registration problem. A commonly employed approach involves detecting keypoints with salient geometric features and subsequently mapping these…

In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in Euclidean space given by image. Carlsson et al. proposed a…

Change detection and irregular object extraction in 3D point clouds is a challenging task that is of high importance not only for autonomous navigation but also for updating existing digital twin models of various industrial environments.…

We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…

Learning local descriptors is an important problem in computer vision. While there are many techniques for learning local patch descriptors for 2D images, recently efforts have been made for learning local descriptors for 3D points. The…

In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points.…

This paper proposes a computationally efficient approach to detecting objects natively in 3D point clouds using convolutional neural networks (CNNs). In particular, this is achieved by leveraging a feature-centric voting scheme to implement…

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…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

Recent studies that incorporate geometric features and transformers into 3D point cloud feature learning have significantly improved the performance of 3D deep-learning models. However, their robustness against adversarial attacks has not…

We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…

Recently, deep neural networks have made remarkable achievements in 3D point cloud classification. However, existing classification methods are mainly implemented on idealized point clouds and suffer heavy degradation of per-formance on…

With the help of the deep learning paradigm, many point cloud networks have been invented for visual analysis. However, there is great potential for development of these networks since the given information of point cloud data has not been…