LAUSR

Simultaneously determining the relative pose and correspondence between a set of 3D points and its 2D projection is a fundamental problem in computer vision, and the problem becomes more difficult when the point sets are contaminated by noise and outliers. Traditionally, this problem is solved by local optimization methods, which usually start from an initial guess of the pose and alternately optimize the pose and the correspondence. In this paper, we formulate the problem as optimizing the pose of the 3D points in the SE(3) space to make its 2D projection best align with the 2D point set, which is measured by the cardinality of the inlier set on the 2D projection plane. We propose four geometric bounds for the position of the projection of a 3D point on the 2D projection plane and solve the 2D–3D point set registration problem by combining a global optimal rotation search and a grid search of translation. Compared with existing global optimization approaches, the proposed method utilizes a different problem formulation and more efficiently searches the translation space, which improves the registration speed. Experiments with synthetic and real data showed that the proposed approach significantly outperformed the state-of-the-art local and global methods.