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Estimating pose from given 3D correspondences, including point-to-point,point-to-line and point-to-plane correspondences, is a fundamental task incomputer vision with many applications. We present a complete solution for thistask, including a solution for the minimal problem and the least-squaresproblem of this task. Previous works mainly focused on finding the globalminimizer to address the least-squares problem. However, existing works thatshow the ability to achieve global minimizer are still unsuitable for real-timeapplications. Furthermore, as one of contributions of this paper, we prove thatthere exist ambiguous configurations for any number of lines and planes. Theseconfigurations have several solutions in theory, which makes the correctsolution may come from a local minimizer. Our algorithm is efficient and ableto reveal local minimizers. We employ the Cayley-Gibbs-Rodriguez (CGR)parameterization of the rotation to derive a general rational cost for thethree cases of 3D correspondences. The main contribution of this paper is tosolve the resulting equation system of the minimal problem and the first-orderoptimality conditions of the least-squares problem, both of which are ofcomplicated rational forms. The central idea of our algorithm is to introduceintermediate unknowns to simplify the problem. Extensive experimental resultsshow that our algorithm significantly outperforms previous algorithms when thenumber of correspondences is small. Besides, when the global minimizer is thesolution, our algorithm achieves the same accuracy as previous algorithms thathave guaranteed global optimality, but our algorithm is applicable to real-timeapplications.

Do not Omit Local Minimizer: a Complete Solution for Pose Estimation from 3D Correspondences