A global optimization approach to robust multi-model fitting

We present a novel Quadratic Program (QP) formulation for robust multi-model fitting of geometric structures in vision data. Our objective function enforces both the fidelity of a model to the data and the similarity between its associated inliers. Departing from most previous optimization-based approaches, the outcome of our method is a ranking of a given set of putative models, instead of a pre-specified number of “good” candidates (or an attempt to decide the right number of models). This is particularly useful when the number of structures in the data is a priori unascertainable due to unknown intent and purposes. Another key advantage of our approach is that it operates in a unified optimization framework, and the standard QP form of our problem formulation permits globally convergent optimization techniques. We tested our method on several geometric multi-model fitting problems on both synthetic and real data. Experiments show that our method consistently achieves state-of-the-art results.