Authors: Rasmus Larsen and Teodor Malmgren Supervisors: Mikael Nilsson, Centre for Mathematical Sciences David Gillsjö, Nordic Forestry Automation (NFA) AB Martin Ahrnbom, Nordic Forestry Automation (NFA) AB Examiner: Karl Åström, Centre for Mathematical Sciences

Abstract
The development of decision-assisting tools for use in forestry operations has the potential to improve the adherence to forest management best practices, which could benefit biodiversity and increase the economic efficiency of the forest industry. Nordic Forestry Automation AB is developing a system that leverages information about the forest environment extracted from data collected with harvester-mounted light detection and ranging (LiDAR) scanners to inform various decisions made during thinning.
Extracting the shapes of individual trees is of particular interest for this application, as defects such as crookedness negatively affect the economic value of trees. We have developed a stem shape estimation procedure that finds a spline representation of the centerline and radius of a tree using LiDAR point cloud data. Points corresponding to the stem are first segmented using a density-based clustering method. A graph-based approach is then used to fit the centerline spline to the stem points. Finally, the radius is estimated by fitting circles to the stem points at intervals along the centerline. To allow comparison of our results to ground truth, we created a synthetic dataset consisting of 2000 point clouds from simulated LiDAR scans of generated 3D tree models. Our dataset is divided into two subsets, with and without simulated odometry errors due to uncertainty in the position of the moving LiDAR sensor. The overlap of the reconstructed stems and the true model stems measured as mean intersection over union (IoU) and the volume estimation error measured as volume root mean square error (RMSE) are among the metrics used for evaluation. Without odometry errors we achieved a mean IoU of 0.92 and a volume RMSE of 4.2% and with odometry errors we achieved a mean IoU of 0.83 and a volume RMSE of 8.2%. Although there is some impact on the results from odometry errors, our procedure is overall successful in estimating the shape of stems when applied to both data subsets.