Multibody structure-and-motion segmentation by branch-and-bound model selection

An efficient and robust framework is proposed for two-view multiple structure-and-motion segmentation of unknown number of rigid objects. The segmentation problem has three unknowns, namely the object memberships, the corresponding fundamental matrices, and the number of objects. To handle this otherwise recursive problem, hypotheses for fundamental matrices are generated through local sampling. Once the hypotheses are available, a combinatorial selection problem is formulated to optimize a model selection cost which takes into account the hypotheses likelihoods and the model complexity. An explicit model for outliers is also added for robust segmentation. The model selection cost is minimized through the branch-and-bound technique of combinatorial optimization. The proposed branch-and-bound approach efficiently searches the solution space and guaranties optimality over the current set of hypotheses. The efficiency and the guarantee of optimality of the method is due to its ability to reject solutions without explicitly evaluating them. The proposed approach was validated with synthetic data, and segmentation results are presented for real images.