发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对大规模LiDAR点云地形重建难题，提出物理信息统计框架GLFM，结合线性函数基与高斯过程，采用SVD秩约简实现线性时间估计，在35.2平方公里数据上ARI达0.9933，优于四个基线。
AI 中文摘要
从大规模、非结构化的机载LiDAR点云中重建连续地形流形，在复杂的野地-城市交界区（WUI）环境中仍然具有挑战性，其中深度神经网络需要昂贵的逐点标注，而非参数化表面重建方法往往缺乏结构可解释性。本文提出了高斯线性函数流形（GLFM），一种物理信息统计框架，它使用确定性线性函数基表示连续地表地形，同时将微尺度漫射激光后向散射建模为各向同性高斯过程。为了避免精确约束最大似然估计的二次计算成本，我们开发了一种代数奇异值分解（SVD）秩约简算法，该算法能够实现线性时间参数估计和闭式二次曲面分类。在35.2平方公里的真实航空LiDAR数据上评估，GLFM自动过滤地面点并提取形态特征，与实地验证的地面真值相比，调整兰德指数（ARI）达到0.9933，在保持核外内存占用的情况下优于四个领先基线。该框架为大规模点云分析提供了严谨、可解释且可扩展的基础。
英文摘要
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.
