Physics-Constrained Variational Autoencoders for Density Compensation in High-Rise LiDAR Point Clouds

High-rise LiDAR scanning produces vertically sparse point clouds where upper-layer defects are hardest to detect due to inverse-square ranging law (1/r2) density gradients, noise contamination, and complex geometries. This paper presents PC-TowerNet, a physics-aware AI pipeline that achieves state-of-the-art reconstruction through sequential modules: (1) 50D geometric feature classification outperforming CloudCompare SOR (100% accuracy vs. 91.3% retention); (2) Physics-Constrained VAE (PC-VAE) recovering 28.7 ± 2.1% upper density vs. 8.3 ± 1.7% standard VAE; (3) multi-modal PointNet++/GNN/Transformer fusion; and (4) Bayesian uncertainty maps (ECE = 0.042 ± 0.008). Synthetic tower evaluation (10 × 5 seeds) demonstrates 48.9% surface smoothness improvement and 38.2% volume error reduction over tuned RANSAC baselines, with clear paths to real-data validation.