In real-world applications the Perspective-n-Point (PnP) problem should generally be applied in a sequence of images which a set of drift-prone features are tracked over time. In this paper, we consider both the temporal dependency of camera poses and the uncertainty of features for the sequential camera pose estimation. Using the Extended Kalman Filter (EKF), a priori estimate of the camera pose is calculated from the camera motion model and then corrected by minimizing the reprojection error of the reference points. Experimental results, using both simulated and real data, demonstrate that the proposed method improves the robustness of the camera pose estimation, in the presence of noise, compared to the state-of-the-art.
P3P @cite_8 is one of the first algorithms for the pose estimation of calibrated cameras from 3 correspondences between 3D reference points and their 2D projections. In addition, there is a variety of PnP algorithms deriving closed-form solutions from a limited number of points, namely P4P @cite_8 and P5P @cite_6 . Since these algorithms are only applicable to a small portion of correspondences, they are sensitive to noise. Although other traditional PnP solutions have no restriction on the number of points, they are computationally expensive. For example, the time complexity of @cite_24 as the lowest complexity method is @math while it is very sensitive to noise. The time complexity of more robust methods like @cite_19 and @cite_27 are significantly increased to @math and @math respectively.
@cite_8 @cite_6 @cite_24 @cite_19 @cite_27
2039032788 1991544872 2155056756 2048382330
We propose a real-time and accurate solution to the Perspective-n-Point (PnP) problem –estimating the pose of a calibrated camera from n 3D-to-2D point correspondences– that exploits the fact that in practice the 2D position of not all 2D features is estimated with the same accuracy. Assuming a model of such feature uncertainties is known in advance, we reformulate the PnP problem as a maximum likelihood minimization approximated by an unconstrained Sampson error function, which naturally penalizes the most noisy correspondences. The advantages of this approach are thoroughly demonstrated in synthetic experiments where feature uncertainties are exactly known. Pre-estimating the features uncertainties in real experiments is, though, not easy. In this paper we model feature uncertainty as 2D Gaussian distributions representing the sensitivity of the 2D feature detectors to different camera viewpoints. When using these noise models with our PnP formulation we still obtain promising pose estimation results that outperform the most recent approaches. 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. The Perspective-Three-Point (P3P) problem aims at determining the position and orientation of the camera in the world reference frame from three 2D-3D point correspondences. This problem is known to provide up to four solutions that can then be disambiguated using a fourth point. All existing solutions attempt to first solve for the position of the points in the camera reference frame, and then compute the position and orientation of the camera in the world frame, which alignes the two point sets. In contrast, in this paper we propose a novel closed-form solution to the P3P problem, which computes the aligning transformation directly in a single stage, without the intermediate derivation of the points in the camera frame. This is made possible by introducing intermediate camera and world reference frames, and expressing their relative position and orientation using only two parameters. The projection of a world point into the parametrized camera pose then leads to two conditions and finally a quartic equation for finding up to four solutions for the parameter pair. A subsequent backsubstitution directly leads to the corresponding camera poses with respect to the world reference frame. We show that the proposed algorithm offers accuracy and precision comparable to a popular, standard, state-of-the-art approach but at much lower computational cost (15 times faster). Furthermore, it provides improved numerical stability and is less affected by degenerate configurations of the selected world points. The superior computational efficiency is particularly suitable for any RANSAC-outlier-rejection step, which is always recommended before applying PnP or non-linear optimization of the final solution. We present a new method for solving the problem of camera pose and calibration from a limited number of correspondences between noisy 2D and 3D features. We show that the probabilistic estimation problem can be expressed as a partially linear problem, where point and line correspondences are mixed using a common formulation. Our Sampling-Solving algorithm enables to robustly estimate the parameters and evaluate the probability distribution of the estimated parameters. It solves the problem of pose estimation with unknown focal length using a minimum of only four correspondences (five if the principal point is also unknown). To our knowledge, this is the first calibration method using so few correspondences of both points and lines. Experimental results on minimal data sets show that the algorithm is very robust to Gaussian noise. Experimental comparisons show that our method is much more stable than existing camera calibration methods for small data sets. Finally, some tests show the potential of global uncertainty estimates on real data sets.