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MS-DGCNN++: Multi-Scale Dynamic Graph Convolution with Scale-Dependent Normalization for Robust LiDAR Tree Species Classification

Graph-based deep learning on LiDAR point clouds encodes geometry through edge features, yet standard implementations use the same encoding at every scale. In tree species classification, where point density varies by orders of magnitude between trunk and canopy, this is particularly limiting. We prove it is suboptimal: normalized directional features have mean squared error decaying as $\mathcal{O}(1/s^2)$ with inter-point distance~$s$, while raw displacement error is constant, implying each encoding suits a different signal-to-noise ratio (SNR) regime. We propose MS-DGCNN++, a multi-scale dynamic graph convolutional network with \emph{scale-dependent edge encoding}: raw vectors at the local scale (low SNR) and hybrid raw-plus-normalized vectors at the intermediate scale (high SNR). Five ablations validate this design: encoding ablation confirms $+4$--$6\%$ overall accuracy (OA) gain; density dropout shows the flattest degradation under canopy thinning; a noise sweep locates the theoretical crossover near $\text{SNR}_2 \approx 1.22$; max-pooling provenance reveals far neighbors win $85\%$ of competitions under raw encoding, a bias eliminated by normalization; and isotropy analysis shows normalization nearly doubles effective rank. On STPCTLS (seven species, terrestrial laser scanning), MS-DGCNN++ achieves the highest OA ($92.91\%$) among 56 models, surpassing self-supervised methods with $7$--$24\times$ more parameters using only $1.81$M parameters. On HeliALS (nine species, airborne laser scanning, geometry-only), it achieves $73.66\%$ OA with the best balanced accuracy ($50.28\%$), matching FGI-PointTransformer which uses $4\times$ more points. Robustness analysis across five perturbation types reveals complementary variant strengths for deployment in heterogeneous forest environments. Code: https://github.com/said-ohamouddou/MS-DGCNN2.

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