A Versatile Approach for Solving PnP, PnPf, and PnPfr Problems
This paper proposes a versatile approach for solving three kinds of absolute camera pose estimation problem: PnP problem for calibrated cameras, PnPf problem for cameras with unknown focal length, and PnPfr problem for cameras with unknown focal length an
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Abstract. This paper proposes a versatile approach for solving three kinds of absolute camera pose estimation problem: PnP problem for calibrated cameras, PnPf problem for cameras with unknown focal length, and PnPfr problem for cameras with unknown focal length and unknown radial distortion. This is not only the first least squares solution to PnPfr problem, but also the first approach formulating three problems in the same theoretical manner. We show that all problems have a common subproblem represented as multivariate polynomial equations. Solving these equations by Gr¨ obner basis method, we derive a linear form for the remaining parameters of each problem. Finally, we apply root polishing to strictly satisfy the original KKT condition. The proposed PnP and PnPf solvers have comparable performance to the state-of-the-art methods on synthetic distortion-free data. Moreover, the novel PnPfr solver gives the best result on distorted point data and demonstrates real image rectification against significant distortion. Keywords: Absolute camera pose estimation Length · Radial distortion
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PnP Problem
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Focal
Introduction
Camera parameter estimation from n pairs of 2D-3D point correspondence in a single image has been a fundamental problem in computer vision and photogrammetry community. The camera parameters consist of two kinds of parameters. One is the extrinsic parameters which determine the position and the orientation of the camera, i.e., 3D rotation and translation. The other is the intrinsic parameters which are optical properties of the camera unaffected by the extrinsic parameters, i.e., focal length, skew, principal point, aspect ratio, lens distortion, etc. The name of the parameter estimation problem is different depending on unknown parameters: Perspective-n-Point (PnP) problem when the extrinsic parameters are unknown and all the intrinsic parameters are calibrated in advance, PnPf problem for partially calibrated cameras when only focal length is known, PnPfr problem when radial distortion of the lens is additionally unknown. Electronic supplementary material The online version of this chapter (doi:10. 1007/978-3-319-46487-9 21) contains supplementary material, which is available to authorized users. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part III, LNCS 9907, pp. 338–352, 2016. DOI: 10.1007/978-3-319-46487-9 21
A Versatile Approach for Solving PnP, PnPf, and PnPfr Problems
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It is well discussed that n = 3 is the minimal number of the points required to solve PnP problem [1–3]. The trend of the latest PnP solvers is to find the global optimal solution for n ≥ 3 case in linear complexity O(n) without considering planar or non-planar scene. The first O(n) method is EPnP [4], but it does not assure the global optimality. Hesch and Roumeliotis [5] proposed Direct Least Square method (DLS) which finds all stationary points of the first optimality condition, also known as the Karush–Kuhn–Tucker (KKT) condition, by solving a system of nonlinear multivariate poly
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