A Branch and Bound Approach to Correspondence and Grouping Problems
Résumé
Data correspondence/grouping is a fundamental topic in computer vision. Finding feature correspondences is probably the most popular application of this topic and constitutes our main motivation. It is a key ingredient for various tasks including 3D reconstruction and object recognition. Existing feature correspondence methods are based on either local appearance similarity, or global geometric consistency, or a combination of both in some heuristic manner. None of these methods is fully satisfactory, especially with repetitive image textures or mis-matches. In this paper, we present a new algorithm that combines the benefits of both appearance-based and geometry-based methods, and mathematically guarantees a global optimization. Our algorithm accepts the two sets of features as input, and outputs the largest set of feature correspondences verifying both the appearance and geometric constraints. We formulate the problem as a mixed integer program, and solve it efficiently by a series of linear programs via branch-and-bound. We subsequently generalize our framework in the context of data correspondence/grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems. Our algorithm has been validated successfully on synthesized data and challenging real images.