An Accurate, Efficient, and Stable Perspective-n-Point Algorithm in 3D Space

Abstract

The Perspective-n-Point problem is usually addressed by means of a projective imaging model of 3D points, but the spatial distribution and quantity of 3D reference points vary, making it difficult for the Perspective-n-Point algorithm to balance accuracy, robustness, and computational efficiency. To address this issue, this paper introduces Hidden PnP, a hidden variable method. Following the parameterization of the rotation matrix by CGR parameters, the method, unlike the existing best matrix synthesis technique (Gröbner technology), does not require construction of a larger matrix elimination template in the polynomial solution phase. Therefore, it is able to solve CGR parameter rapidly, and achieve an accurate location of the solution using the Gauss–Newton method. According to the synthetic data test, the PnP algorithm solution, based on hidden variables, outperforms the existing best Perspective-n-Point method in accuracy and robustness, under cases of Ordinary 3D, Planar Case, and Quasi-Singular. Furthermore, its computational efficiency can be up to seven times that of existing excellent algorithms when the spatially redundant reference points are increased to 500. In physical experiments on pose reprojection from monocular cameras, this algorithm even showed higher accuracy than the best existing algorithm.

Keywords

• Perspective-n-Point problem
• CGR parameter matrix
• Gröbner technology
• hidden PnP