SearcharxivSearch

arXiv · 2502.11602

Cheesemap: A High-Performance Point-Indexing Data Structure for Neighbor Search in LiDAR Data

Abstract

Point cloud data, as the representation of three-dimensional spatial information, is a fundamental piece of information in various domains where indexing and querying these point clouds efficiently is crucial for tasks such as object recognition, autonomous navigation, and environmental modeling. In this paper, we present a comprehensive comparative analysis of various data structures combined with neighboring search methods across different types of point clouds. Additionally, we introduce a novel data structure, cheesemap, to handle 3D LiDAR point clouds. Exploring the sparsity and irregularity in the distribution of points, there are three flavors of the cheesemap: dense, sparse, and mixed. Results show that the cheesemap can outperform state-of-the-art data structures in terms of execution time per query, particularly for ALS (Aerial Laser Scanning) point clouds. Memory consumption is also minimal, especially in the sparse and mixed representations, making the cheesemap a suitable choice for applications involving three-dimensional point clouds.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ruben Laso, Miguel Yermo. 2025-02-17. Cheesemap: A High-Performance Point-Indexing Data Structure for Neighbor Search in LiDAR Data. https://arxiv.org/abs/2502.11602

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS