A double-constrained convex hull approach for tree crown volume estimation: A mobile laser scanning case study of Catalpa bungei

: Individual tree crown volume (CV) is an important three-dimensional indicator of tree growth, crown architecture, and physio-ecological functioning, but its quantification remains challenging because tree crowns are irregular and porous, often with indistinct boundaries, internal gaps, and multi-branched structures. This study developed a double-constrained convex hull (DB) algorithm for CV estimation from mobile laser scanning (MLS) point clouds, using 100 Catalpa bungei trees with clearly delineated crowns as a case study. The algorithm combines a triangulation length threshold (TL) to separate weakly connected crown components with a convex hull length threshold (CHL) to refine slice-level crown boundaries. To provide a controlled geometric reference, four algorithms were tested on 100,000-point clouds uniformly sampled from four tree-shaped 3D mesh models with known computational volumes. DB achieved the lowest error (mean absolute percentage error (MAPE) = 4.00%, normalized root mean square error (nRMSE) = 4.73%), compared with MAPE values of 68.71%, 13.81%, and 30.62% for voxel, Graham convex hull, and 3D convex hull methods, respectively. For the high-density MLS crowns extracted after manual segmentation correction, uniform random downsampling yielded mean absolute relative differences of 0.87% and 2.53% from full-density estimates at 75% and 50% point retention. The 49-combination CHL/TL sensitivity analysis showed that TL controlled crown component separation while CHL regulated boundary refinement and runtime, identifying a dataset-specific candidate range of CHL = 0.04–0.08 m and TL = 0.30–0.60 m. These results support DB’s geometric performance in the controlled benchmark and demonstrate its representation of irregular, multi-branched crowns in the present case study. Broader application remains conditional on reliable crown extraction and parameter selection, while its operational advantage under overlapping crowns, natural occlusion, or incomplete observations remains unverified.