Intrinsic second-order geometric optimization for robust point set registration without correspondence

Abstract

Determining Euclidean transformations for the robust registration of noisy unstructured point sets is a key problem of model-based computer vision and numerous industrial applications. Key issues include accuracy of the registration, robustness with respect to outliers and initialization, and computational speed. In this paper, we consider objective functions for robust point registration without correspondence. We devise a numerical algorithm that fully exploits the intrinsic manifold geometry of the underlying Special Euclidean Group SE(3) in order to efficiently determine a local optimum. This leads to a quadratic convergence rate that compensates the moderately increased computational costs per iteration. Exhaustive numerical experiments demonstrate that our approach exhibits significantly enlarged domains of attraction to the correct registration. Accordingly, our approach outperforms a range of state-of-the-art methods in terms of robustness against initialization while being comparable with respect to registration accuracy and speed. © 2009 Springer.