Extraction of tree heights in mountainous natural forests from UAV leaf-on stereoscopic imagery based on approximation of ground surfaces

The application of high-resolution stereoscopic imagery acquired by Unmanned Aerial Vehicle (UAV) on the extraction of forest heights has grown rapidly in recent years. Most existing studies either required auxiliary terrain data, e.g., Digital Terrain Model (DTM) provided by lidar data, or focused on flat terrains. It is still a great challenge to extract tree heights in mountainous forests only using UAV leaf-on stereoscopic imagery. An al-gorithm referred to as AGAR (i.e., Approximation of Ground using Allometric Relationship) is proposed in this study to estimate individual heights of visible trees on UAV stereoscopic imagery in mountainous natural forests. The central idea of the AGAR algorithm is firstly to approximate the understory terrain elevations (i.e., DTM) based on attributes of tree crowns (e.g., crown area) and the iterative adjustment of allometric equation co-efficients. Then individual tree heights are determined by differencing the elevation of crown tops with that of the approximated ground surface. The proposed algorithm was demonstrated at five sites with different terrain conditions by taking field measurements and ICESat-2 data as references, respectively. Results showed that the AGAR algorithm worked well on the estimation of tree heights at all sites. In contrast, the classical progressive triangulation filter (PTF) algorithm was susceptible to terrains and forest structures. The root mean square error (RMSE) and relative RMSE (rRMSE) of tree heights estimated by the PTF algorithm were 4.4 m -6.3 m and 32.6% -37.6%, respectively. They were decreased by the AGAR algorithm to 1.7 m -2.5 m and 12.6% -15.2%, respectively. The AGAR algorithm will substantially advance the application of UAV stereoscopic im-agery on the extraction of tree heights in the absence of other available terrain data, and will also open new horizons for application of decimeter or even centimeter spaceborne stereoscopic imagery on forest vertical structures in the future.