Enhancing the motion estimate in bundle adjustment using projective newton-type optimization on the manifold

Bundle adjustment is a minimization method frequently used to refine the structure and motion parameters of a moving camera. In this work, we present a Newton-based approach to enhance the accuracy of the estimated motion parameters in the bundle adjustment framework. The key issue is to first parameterize the motion variables of a camera on the manifold of the Euclidean motion by using the underlying Lie group structure of the motion representation. Second, it is necessary to formulate the bundle adjustment cost function and derive the corresponding gradient and the Hessian formulation on the manifold using the concepts of differential geometry. This results in a more compact derivation of the Hessian which allows us to use its complete form in the minimization process. Compared to the Levenberg-Marquardt scheme, the proposed algorithm is shown to provide more accurate results while having a comparable complexity although the latter uses an approximate form of the Hessian. The experimental results we performed on simulated and real image sets are evidence that demonstrate our claims.