A Fast and Accurate Solution for Pose Estimation from 3D Correspondences

Estimating pose from given 3D correspondences, including point-to-point, point-to-line and point-to-plane correspondences, is a fundamental task in computer vision with many applications. We present a fast and accurate solution for the least-squares problem of this task. Previous works mainly focus on studying the way to find the global minimizer of the least-squares problem. However, existing works that show the ability to achieve the global minimizer are still unsuitable for real-time applications. Furthermore, as one of contributions of this paper, we prove that there exist ambiguous configurations for any number of lines and planes. These configurations have several solutions in theory, which makes the correct solution may come from a local minimizer when the data are with noise. Previous works based on convex optimization which is unable to find local minimizers do not work in the ambiguous configuration. Our algorithm is efficient and able to reveal local minimizers. We employ the Cayley-Gibbs-Rodriguez (CGR) parameterization of the rotation to derive a general rational cost for the three cases of 3D correspondences. The main contribution of this paper is to solve the first-order optimality conditions of the least-squares problem, which are of a complicated rational form. The central idea of our algorithm is to introduce some intermediate unknowns to simplify the problem. Extensive experimental results show that our algorithm is more stable than previous algorithms when the number N of correspondences is small. Besides, when N is large, our algorithm achieves the same accuracy as the state-of-the-art algorithm [1], but our algorithm is about 7 times faster than [1] in real applications.