Gaussian Linear Functional Manifold Method for Massive Point Cloud Data
Abstract
Reconstructing continuous terrain manifolds from massive, unstructured airborne LiDAR point clouds remains challenging in complex Wildland-Urban Interface (WUI) environments, where deep neural networks require costly point-wise annotations and nonparametric surface reconstruction methods often lack structural interpretability. This paper introduces the Gaussian Linear Functional Manifold (GLFM), a physics-informed statistical framework that represents continuous surface topography using deterministic linear functional bases while modeling microscale diffuse laser backscatter as an isotropic Gaussian process. To avoid the quadratic computational cost of exact constrained maximum likelihood estimation, we develop an algebraic singular value decomposition (SVD) rank-reduction algorithm that enables linear-time parameter estimation and closed-form quadric classification. Evaluated on 35.2 km^2 of real-world aerial LiDAR data, GLFM automatically filters ground points and extracts morphological features, achieving an adjusted Rand index (ARI) of 0.9933 against field-verified ground truth and outperforming four leading baselines while maintaining an out-of-core memory footprint. The framework provides a rigorous, interpretable, and scalable foundation for large-scale point cloud analytics.
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BibTeX
@misc{zhao2026gaussian,
title = {{Gaussian Linear Functional Manifold Method for Massive Point Cloud Data}},
author = {Hong Zhao and Tonglin Zhang and Baijian Yang and Jin Wei-Kocsis and Songlin Fei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05744},
eprint = {2609.05744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05744},
}
RIS
TY - UNPB
TI - Gaussian Linear Functional Manifold Method for Massive Point Cloud Data
AU - Hong Zhao
AU - Tonglin Zhang
AU - Baijian Yang
AU - Jin Wei-Kocsis
AU - Songlin Fei
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05744
UR - https://arxiv.org/abs/2609.05744
AB - Reconstructing continuous terrain manifolds from massive, unstructured airborne LiDAR point clouds remains challenging in complex Wildland-Urban Interface (WUI) environments, where deep neural networks require costly point-wise annotations and nonparametric surface reconstruction methods often lack structural interpretability. This paper introduces the Gaussian Linear Functional Manifold (GLFM), a physics-informed statistical framework that represents continuous surface topography using deterministic linear functional bases while modeling microscale diffuse laser backscatter as an isotropic Gaussian process. To avoid the quadratic computational cost of exact constrained maximum likelihood estimation, we develop an algebraic singular value decomposition (SVD) rank-reduction algorithm that enables linear-time parameter estimation and closed-form quadric classification. Evaluated on 35.2 km^2 of real-world aerial LiDAR data, GLFM automatically filters ground points and extracts morphological features, achieving an adjusted Rand index (ARI) of 0.9933 against field-verified ground truth and outperforming four leading baselines while maintaining an out-of-core memory footprint. The framework provides a rigorous, interpretable, and scalable foundation for large-scale point cloud analytics.
ER -