Constructing tree stem form from digitized surface measurements by a programming approach within discrete mathematics

Key message The main message of this work is the demonstration of possibility of creation of stem shape from digitized points using integer-programming approach. The points are digitized by magnetic motion tracker which in contrast to the laser scanning allows the reconstruction of complete cross-section of stem even in the "hidden (invisible)" part. Three-dimensional information on tree stem form plays an important role in understanding the structure and strength of a standing tree against the forces of wind, snow, and other natural pressure. It also contributes to precision in volume measurement compared to conventional two-dimensional measurement. We investigate approaches for obtaining three-dimensional information of tree stem form from partially organized surface measurements, acquired using a three-dimensional digitizing device (Polhemus FASTRAK(A (R)) motion tracking device). We then propose a new programming approach from discrete mathematics to construct tree stem form. Our method is based on an optimal connection of neighbor triangles for surface construction, which is created by locally possible combination of three digitized points on the stem surface. We compare the proposed method to the existing heuristic methods of contour tracing and region growing. Our analysis shows that the proposed method provides a consistent construction of tree stem form, for even stems with extremely irregular structure such as those from bent trees and mangrove trees with unique root spread, while the other methods are incapable for constructing such tree stems.