Estimation of fractal dimension of trees using LiDAR point data with sequential data decimation

Abstract

Fractal dimensions of trees provide key ecological information regarding tree and forest stand structure. Although LiDAR scanning has the potential to reduce the intensive labor required to estimate fractal dimensions with manual measurements, neither an accuracy assessment comparing with true dimensions nor a guide or method for accurately measuring the dimensions using LiDAR scanners has been presented. This study examined the accuracy of fractal dimensions estimated using terrestrial LiDAR scanning (TLS) and unmanned aerial LiDAR scanning (ULS) through computer simulations and developed an approach to reduce the estimation bias. The true fractal dimensions of digitized trees of red pine (Pinus densiflora), ubame oak (Quercus phillyreoides), and giant timber bamboo (Phyllostachys bambusoides) in 18 site scenarios were calculated by applying the box-counting method to the tree object data. The true fractal dimensions were compared with the estimated dimensions in four TLS and ULS scenarios. Furthermore, a method to reduce the estimation bias was developed by introducing sequential point decimation and modeling the acquisition rate decay, thereby extrapolating the number of voxels before decay. Simple box-counting on highly dense and precise TLS data collected from four positions could retrieve the true fractal dimensions for all 18 site scenarios. However, sparse and less accurate TLS underestimated fractal dimensions in 8 out of 18 cases, and ULS overestimated the dimensions in 29 of 36 cases. The change in the relationship between the number of voxels and mesh size on a log-log plot with sequential decimation could be used to judge whether a set of TLS data can retrieve accurate fractal dimensions by applying simple box-counting to the TLS data. The developed method improved the estimations of fractal dimensions for 30 of the 37 cases where the simple box-counting on the TLS and ULS data provided biased estimations. In contrast, the estimation bias increased in 27 of the 35 cases where the simple box-counting on the TLS and ULS data successfully retrieved the true fractal dimensions.