Mathematically optimized trajectory for terrestrial close-range photogrammetric 3D reconstruction of forest stands

Abstract

Terrestrial close-range photogrammetry offers a low-cost method of three-dimensional (3D) reconstruction of forest stands that provides automatically processable 3D data that can be used to evaluate inventory parameters of forest stands and individual trees. However, fundamental methodological problems in image acquisition and processing remain. This study enhances the methodology of photogrammetric Structure from Motion reconstruction of forest stands by determining the best photographer's trajectory for image acquisition. The study comprises 1) mathematical optimization of the route in a square grid using integer programming, 2) evaluation of point clouds derived from sequences of real photographs, simulating different trajectories, and 3) verification on real trajectories. In a forest research plot, we established a 1 m square grid of 625 (i.e., 25 × 25) photographic positions, and at each position, we captured 16 photographs in uniformly spaced directions. We adopted real tree positions and diameters, and the coordinates of the photographic positions, including orientation angles of captured images, were recorded. We then formulated an integer programming optimization model to find the most efficient trajectory that provided coverage of all sides of all trees with sufficient counts of images. Subsequently, we used the 10,000 captured images to produce image subsets simulating image sequences acquired during the photographer's movement along 84 different systematic trajectories of seven patterns based on either parallel lines or concentric orbits. 3D point clouds derived from the simulated image sequences were evaluated for their suitability for automatic tree detection and estimation of diameters at breast height. The results of the integer programming model indicated that the optimal trajectory consisted of parallel line segments if the camera is pointed forward – in the travel direction, or concentric orbits if the camera is pointed to a side – perpendicular to the travel direction. With point clouds derived from the images of the simulated trajectories, the best diameter estimates on automatically detected trees were achieved with trajectories consisting of parallel lines in two perpendicular directions where each line was passed in both opposite directions. For efficient image acquisition, resulting in point clouds of reasonable quality with low counts of images, a trajectory consisting of concentric orbits, including the plot perimeter with the camera pointed towards the plot center, proved to be the best. Results of simulated trajectories were verified with the photogrammetric reconstruction of the forest stand based on real trajectories for six patterns. The mathematical optimization was consistent with the results of the experiment, which indicated that mathematical optimization may represent a valid tool for planning trajectories for photogrammetric 3D reconstruction of scenes in general.