In this paper we propose a new data fitting method which, similar to RANSAC, fits data to a model using sample and consensus. The application of interest is fitting 3D point clouds to a prior geometric model. Where the RANSAC process uses random samples of points in the fitting trials, we propose a novel method which directs the sampling by ordering the points according to their contribution to the solution's constraints. This is particularly important when the data is quasi-degenerate. In this case, the standard RANSAC algorithm often fails to find the correct solution. Our approach selects points based on a Mutual Information criterion, which allows us to avoid redundant points that result in degenerate sample sets. We demonstrate our approach on simulated and real data and show that in the case of quasi-degenerate data, the proposed algorithm significantly outperforms RANSAC.
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