On solving Exterior Orientation of an Image with Particle Swarm Optimization

Abstract. Solving the exterior orientation of images is a fundamental component in photogrammetric mapping and 3D restitution processes. Additionally, it is essential in photogrammetric tasks such as visual odometry, camera-based visual simultaneous localization and mapping, camera calibration, camera-based 3D tracking of movement, and change detection. The aim of this research was to evaluate whether particle swarm optimization is suitable for finding the exterior orientation parameters of a single image using image resection. In addition, we developed a robustified particle swarm optimization by adding an iteratively changing stochastic model to the optimization criteria by attaching a weight matrix with residual vectors. The method was compared to the solution from the least squares method using both simulated ideal and noisy data. Solving the exterior orientation parameters reliably with particle swarm optimization was possible after fine-tuning the algorithm's options. The non-robustified version of particle swarm optimization provided identical results to the non-robustified least squares method. However, in the case of the robustified particle swarm optimization, only 60% of attempts resulted in the same outcome as the corresponding robustified least squares method, with sub-millimeter accuracy. In 40% of cases, the results achieved millimeter accuracy. The sub-millimeter accuracy was achieved in every case with sequential robustified particle swarm optimization, where the algorithm was rerun using stricter bounds for unknown parameters if the evaluation criteria were too large. The implementation of particle swarm optimization is easier than that of the nonlinear least squares method. However, the computation time for particle swarm optimization was significantly longer.