Related papers: Generating Large Convex Polytopes Directly on Poin…

Transformer, as an alternative to CNN, has been proven effective in many modalities (e.g., texts and images). For 3D point cloud transformers, existing efforts focus primarily on pushing their accuracy to the state-of-the-art level.…

Autonomous exploration is a crucial aspect of robotics that has numerous applications. Most of the existing methods greedily choose goals that maximize immediate reward. This strategy is computationally efficient but insufficient for…

While point-based neural architectures have demonstrated their efficacy, the time-consuming sampler currently prevents them from performing real-time reasoning on scene-level point clouds. Existing methods attempt to overcome this issue by…

A two-step model for generating random polytopes is considered. For parameters $d$, $m$, and $p$, the first step is to generate a simple polytope $P$ whose facets are given by $m$ uniform random hyperplanes tangent to the unit sphere in…

The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine…

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,…

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…

3D object detection from point clouds plays a critical role in autonomous driving. Currently, the primary methods for point cloud processing are voxel-based and pillar-based approaches. Voxel-based methods offer high accuracy through…

The simplest way to generate a lattice of convex sets is to consider an initial set of points and draw segments, triangles, and any convex hull from it, then intersect them to obtain new points, and so forth. The result is an infinite…

3D Gaussian Splatting (3DGS) has demonstrated its advantages in achieving fast and high-quality rendering. As point clouds serve as a widely-used and easily accessible form of 3D representation, bridging the gap between point clouds and…

In point cloud generation and completion, previous methods for transforming latent features to point clouds are generally based on fully connected layers (FC-based) or folding operations (Folding-based). However, point clouds generated by…

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…

Large-scale terrain scans are the basis for many important tasks, such as topographic mapping, forestry, agriculture, and infrastructure planning. The resulting point cloud data sets are so massive in size that even basic tasks like viewing…

We present a framework for creating navigable space from sparse and noisy map points generated by sparse visual SLAM methods. Our method incrementally seeds and creates local convex regions free of obstacle points along a robot's…

This paper presents Polylidar, an efficient algorithm to extract non-convex polygons from 2D point sets, including interior holes. Plane segmented point clouds can be input into Polylidar to extract their polygonal counterpart, thereby…

An alternative generating function is proposed to enumerate row-convex polyominoes without internal holes on a discrete grid. The approach is based on integer partitions of the total area, where each partition corresponds to a sequence of…

Point clouds are a very efficient way to represent volumetric data in medical imaging. First, they do not occupy resources for empty spaces and therefore can avoid trade-offs between resolution and field-of-view for voxel-based 3D…

We propose Convexity-Driven Projection (CDP), a boundary-free linear method for dimensionality reduction of point clouds that targets preserving detour-induced local non-convexity. CDP builds a $k$-NN graph, identifies admissible pairs…

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…

Efficiently generating energetically stable crystal structures has long been a challenge in material design, primarily due to the immense arrangement of atoms in a crystal lattice. To facilitate the discovery of stable material, we present…