Related papers: Delaunay Bifiltrations of Functions on Point Cloud…

Cloud segmentation amounts to separating cloud pixels from non-cloud pixels in an image. Current deep learning methods for cloud segmentation suffer from three issues. (a) Constrain on their receptive field due to the fixed size of the…

A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…

Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to…

The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization,…

In this paper, we propose an algorithm for registering sequential bounding boxes with point cloud streams. Unlike popular point cloud registration techniques, the alignment of the point cloud and the bounding box can rely on the properties…

Point clouds are often the default choice for many applications as they exhibit more flexibility and efficiency than volumetric data. Nevertheless, their unorganized nature -- points are stored in an unordered way -- makes them less suited…

In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a…

We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.

Airborne Laser Scanning (ALS) point clouds have complex structures, and their 3D semantic labeling has been a challenging task. It has three problems: (1) the difficulty of classifying point clouds around boundaries of objects from…

Clustering is a fundamental task in machine learning. One of the most successful and broadly used algorithms is DBSCAN, a density-based clustering algorithm. DBSCAN requires $\epsilon$-nearest neighbor graphs of the input dataset, which are…

Adversarial attacks pose serious challenges for deep neural network (DNN)-based analysis of various input signals. In the case of three-dimensional point clouds, methods have been developed to identify points that play a key role in network…

Point clouds are unstructured and unordered data, as opposed to images. Thus, most machine learning approach developed for image cannot be directly transferred to point clouds. In this paper, we propose a generalization of discrete…

Masked autoencoding and generative pretraining have achieved remarkable success in computer vision and natural language processing, and more recently, they have been extended to the point cloud domain. Nevertheless, existing point cloud…

The paper introduces DelTriC (Delaunay Triangulation Clustering), a clustering algorithm which integrates PCA/UMAP-based projection, Delaunay triangulation, and a novel back-projection mechanism to form clusters in the original…

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…

Given a fixed $n\times d$ matrix $\mathbf{X}$, where $n\gg d$, we study the complexity of sampling from a distribution over all subsets of rows where the probability of a subset is proportional to the squared volume of the parallelepiped…

Fine-grained geometry, captured by aggregation of point features in local regions, is crucial for object recognition and scene understanding in point clouds. Nevertheless, existing preeminent point cloud backbones usually incorporate…

Point clouds have been recognized as a crucial data structure for 3D content and are essential in a number of applications such as virtual and mixed reality, autonomous driving, cultural heritage, etc. In this paper, we propose a set of…

Point clouds are an increasingly ubiquitous input modality and the raw signal can be efficiently processed with recent progress in deep learning. This signal may, often inadvertently, capture sensitive information that can leak semantic and…

For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…