Estimating branch angle distributions from terrestrial laser scanning data using an instance segmentation-based contraction method

Tree branch angles and their distributions (BADs) are key structural traits influencing light interception, resource allocation, and canopy architecture. However, measuring them accurately remains challenging. We present BASeg, a novel method based on instance segmentation to automatically quantify branch angles and BADs from terrestrial laser scanning (TLS) data. BASeg segments individual branches using Voronoi partitioning, fits branch diameters via non-linear least squares, downsamples branch point clouds of varying diameter to different resolutions, and skeletonizes branches using the Laplacian algorithm. Branch angles are then calculated through a cluster-based nearest neighbor graph. We validated BASeg using leaf-off TLS data from six sycamore trees and using simulated data from nine trees (aspen, birch, and maple), spanning various sizes. Additionally, we evaluated its sensitivity to TLS scanning protocols—scanning angular resolution, scanning distance between different locations, and number of scan positions—using 107 field-measured angles from two large beech trees. BASeg achieved a root mean square error (RMSE) of 9.96° (14.64 %) and a concordance correlation coefficient (CCC) of 0.89 for branch angle estimation. For estimating BADs, BASeg achieved mean absolute error (MAE) ranging from 2.2 to 381.1 (25.2 % to 69.3 %), outperforming TreeQSM, Laplacian, TreeGraph, L1-tree, and WOODSKE. Neither scanning distance (10–20 m) nor the number of scan positions (3–6) affected the accuracy of branch angles or BADs traits, while scanning angular resolution (0.01°–0.04°) did impact these traits. This study offers an effective approach for quantifying BADs and improves the understanding of fine-scale tree architecture within TLS frameworks.