EPnP
EPnP: An Accurate O(n) Solution to the PnP Problem. We propose a non-iterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n≥4 and handles properly both planar and non-planar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12×12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data.
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References in zbMATH (referenced in 8 articles )
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Sorted by year (- Yao, Kunpeng; Billard, Aude: An inverse optimization approach to understand human acquisition of kinematic coordination in bimanual fine manipulation tasks (2020)
- Boutteau, Rémi; Sturm, Peter; Vasseur, Pascal; Demonceaux, Cédric: Circular laser/camera-based attitude and altitude estimation: minimal and robust solutions (2018)
- Steger, Carsten: Algorithms for the orthographic-(n)-point problem (2018)
- Briales, Jesus; Gonzalez-Jimenez, Javier: A minimal closed-form solution for the perspective three orthogonal angles (P3oA) problem: application to visual odometry (2016)
- Zhou, Jie; Wang, Dingkang: Solving the perspective-three-point problem using comprehensive Gröbner systems (2016)
- Park, Hyun Soo; Shiratori, Takaaki; Matthews, Iain; Sheikh, Yaser: 3D trajectory reconstruction under perspective projection (2015)
- Collins, Toby; Bartoli, Adrien: Infinitesimal plane-based pose estimation (2014)
- Guo, Yang: A novel solution to the P4P problem for an uncalibrated camera (2013)