Optimal correspondences from pairwise constraints

Correspondence problems are of great importance in computer vision. They appear as subtasks in many applications such as object recognition, merging partial 3D reconstructions and image alignment. Automatically matching features from appearance only is difficult and errors are frequent. Thus, it is necessary to use geometric consistency to remove incorrect correspondences. Typically heuristic methods like RANSAC or EM-like algorithms are used, but they risk getting trapped in local optima and are in no way guaranteed to find the best solution. This paper illustrates how pairwise constraints in combination with graph methods can be used to efficiently find optimal correspondences. These ideas are implemented on two basic geometric problems, 3D-3D registration and 2D-3D registration. The developed scheme can handle large rates of outliers and cope with multiple hypotheses. Despite the combinatorial explosion, the resulting algorithm which has been extensively evaluated on real data, yields competitive running times compared to state of the art.