Angle Damping in Bundle Adjustment

Abstract: Bundle Adjustment is a common fine-tuning step used in photogrammetry. It uses different types of parameters, some of which can be considered to be almost linear while others can be considered to be highly nonlinear, e.g. the rotational parameters. However, in the Bundle Adjustment process all parameters are treated equal. In concert with a poor initial estimate, this might cause Bundle Adjustment to diverge. In this report, two novel methods based on the damped Gauss-Newton with Armijo linesearch, modified by giving rotational parameters a special treatment, are tested. These methods, Clamped Alpha and Linear Exponential Search, are compared to Gauss-Newton with Armijo linesearch, as well as to the undamped Gauss-Newton method, also known as the Gauss-Markov method. Parameter sweeps over different perturbation levels for the angular parameters show that each of the three damped methods outperform the Gauss-Newton method. Notably, the Clamped Alpha method also outperforms the other two damped methods, with as much as 16 times as many convergent cases for a given perturbation level. Meanwhile, the average number of iterations is increased by only 1.8 times that of the Gauss-Newton with Armijo linesearch. The results add to existing research arguing for the use of damped methods in Bundle Adjustment. In particular, the simple and cheap Clamped Alpha method is potentially attractive for problems where the uncertainty of the camera angles is significant. While the Clamped Alpha method show promising results, it should be noted that the experiments in this study are on synthetic data. In order to solidify these results, further investigations into the performance of Clamped Alpha using real-world data should be conducted.