HMeMD-Net: A Hybrid Network for Inverting Tree Diameter at Breast Height in Dense Mixed Forests With Airborne Laser Scanning

Tree diameter at breast height (DBH) is a key indicator for assessing forest ecosystems, biomass, and resources. Airborne laser scanning enables large-scale DBH inversion with high accuracy and point density. In mixed forests, existing methods can be categorized into regression-after-classification (RAC) and direct-regression-without-classification (DRWC) ones. However, the RAC methods exhibit excessive complexity and may lose common information among species, and the DRWC methods struggle with appropriately handling varying distributions of tree structural data. Therefore, this study proposes a hierarchical multi-experts mixture density network (HMeMD-Net) that integrates RAC and DRWC for accurate DBH inversion. First, an integrated feature optimization strategy is presented to handle complexity in feature construction. Subsequently, a hierarchical mixture of experts (HMoE) structure is designed to extract deep features through synergistic classification-regression task interactions. Innovatively, this paper designs a reinforcement mechanism for information collaboration utilizing Markov random fields. It optimizes information flow and feature representation across tasks. Finally, the model predicts the structural data distributions across tree species through a mixture density network, capturing the data heterogeneity via a Gaussian mixture model. Experimental results on large-scale public datasets <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SYSSIFOSS</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FOR-instance</i> demonstrate that HMeMD-Net outperforms existing methods that are commonly used in forestry (R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>:0.93/0.88, RMSE:3.35/3.83cm, rRMSE:15.01/15.83%, MAE:2.54/2.82cm, sMAPE:13.79/13.15%), significantly improving the accuracy of DBH inversion and providing an innovative technical pathway for precise assessment and management of forest resources.