Decomposed global optimization for robust point matching with low-dimensional branching

We propose a new methodology for reliably solving the correspondence problem between points of two or more images. This is a key step in most problems of Computer Vision and, so far, no general method exists to solve it. Our methodology is able to handle most of the commonly used assumptions in a unique formulation, independent of the domain of application and type of features. It performs correspondence and outlier rejection in a single step, and achieves global optimality with feasible computation. Feature selection and correspondence are first formulated as an integer optimization problem. This is a blunt formulation, which considers the whole combinatorial space of possible point selections and correspondences. To find its global optimal solution we build a concave objective function and relax the search domain into its convex-hull. The special structure of this extended problem assures its equivalence to the original one, but it can be optimally solved by efficient algorithms that avoid combinatorial search.

3-Points Convex Hull Matching (3PCHM) for fast and robust point set registration