Exploring trees in three dimensions: VoxR, a novel voxel-based R package dedicated to analysing the complex arrangement of tree crowns.

Background: Interest in tree form assessments using the terrestrial laser scanner (TLS) has increased in recent years. Yet many existing methods are limited to small-sized trees, principally due to noise and occlusion phenomena. In this paper, a novel voxel-based program that is dedicated to the analyses of large tree structures is presented. The method is based on the assumption that architectural trait variations (i.e. branching angle, bifurcation ratio, biomass allocation, etc.) influence the way a tree explores space. This method uses the concept of space exploration that considers a voxel as a portion of space explored by the tree. Once the TLS scene is voxelized, the program provides tools that extract qualitative (geometrical) and quantitative (volumetric) metrics. These tools measure (1) voxel dispersion in three dimensions (3-D), (2) projections of the voxel cloud in 2-D and (3) multi-temporal changes within a single tree crown. Scope: To test algorithm capabilities of measuring larger tree architectural traits, two application studies were conducted using point clouds that were either generated by a tree growth simulation model, thereby allowing algorithm application in a perfectly controlled environment, or acquired in the field with a TLS device. The space exploration concept makes it possible to take advantage of the volumetric nature of voxels to compensate for occlusion. The hypothesis that large-sized voxels can be used to reduce occlusion in the original point cloud was tested, as well as the consequences of voxel size on quantification of tree volume and on precision of derived metrics. Conclusions: Results show that space exploration is well adapted to highlight architectural differences among trees. They also suggest that large-sized voxels are efficient for occlusion compensation at the expense of metrics precision in some cases. The best resolution to choose depending on the research objectives and quality of the TLS scan is discussed.