Global Motion Estimation from Relative Measurements in the Presence of Outliers

This work addresses the generic problem of global motion estimation (homographies, camera poses, orientations, etc.) from relative measurements in the presence of outliers. We propose an efficient and robust framework to tackle this problem when motion parameters belong to a Lie group manifold. It exploits the graph structure of the problem as well as the geometry of the manifold. It is based on the recently proposed iterated extended Kalman filter on matrix Lie groups. Our algorithm iteratively samples a minimum spanning tree of the graph, applies Kalman filtering along this spanning tree and updates the graph structure, until convergence. The graph structure update is based on computing loop errors in the graph and applying a proposed statistical inlier test on Lie groups. This is done efficiently, taking advantage of the covariance matrix of the estimation errors produced by the filter. The proposed formalism is applied on both synthetic and real data, for a camera pose registration problem, an automatic image mosaicking problem and a partial 3D reconstruction merging problem. In these applications, the framework presented in this paper efficiently recovers the global motions while the state of the art algorithms fail due to the presence of a large proportion of outliers.

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