A Globally Convergent Gauss-newton Algorithm for the Bundle Adjustment Problem with Functional Constraints

This paper describes a Gauss-Newton-based algorithm for the bundle adjustment problem with functional constraints (GNC). The GNC algorithm has superior theoretical convergence properties compared to the conventional bundle algorithm. Both algorithms were applied to simulated measurements of a sphere with 2–3 cameras and 4–9 points. For 2 cameras and 4–5 points, the GNC converged in substantially more cases. For the other configurations, the convergence properties were similar. The added cost for the GNC algorithm was less than 0.01 iterations on average. The GNC algorithm need to be evaluated on real-world problems, but the results suggest that the algorithm will be more reliable for minimum data problems and have a minimal overhead for easy problems.