用统计模型高效重建大规模激光点云地形，精度高且可解释。
Gaussian Linear Functional Manifold Method for Massive Point Cloud Data
- 用线性函数基加高斯过程建模地形与激光散射
- 在35.2平方公里数据上达ARI 0.9933，优于4个基准方法
- 适合需要可解释性与大规模处理的地理信息分析
从复杂城野交界区的大规模无结构机载激光雷达点云中重建连续地形面仍具挑战，因深度神经网络需昂贵逐点标注，非参数方法又常缺乏结构可解释性。本文提出高斯线性函数流形（GLFM），一种融合物理先验的统计框架：用确定性线性函数基表示连续地表形态，同时将微尺度激光回波散射建模为各向同性高斯过程。为避免精确约束最大似然估计的二次计算开销，提出基于代数奇异值分解（SVD）的降秩算法，实现线性时间参数估计与闭式二次曲面分类。在35.2平方公里真实航空激光雷达数据上评估，GLFM可自动滤除地面点并提取形态特征，相较实地验证真值达到调整兰德指数（ARI）0.9933，超越四个领先基线方法，且保持外存级内存占用。该框架为大规模点云分析提供了严谨、可解释、可扩展的基础。
原文摘要 · Abstract (English)
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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