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.
We propose a real-time, robust to outliers and accurate solution to the Perspective-n-Point (PnP) problem. The main advantages of our solution are twofold: first, it in- tegrates the outlier rejection within the pose estimation pipeline with a negligible computational overhead, and sec- ond, its scalability to arbitrarily large number of correspon- dences. Given a set of 3D-to-2D matches, we formulate pose estimation problem as a low-rank homogeneous sys- tem where the solution lies on its 1D null space. Outlier correspondences are those rows of the linear system which perturb the null space and are progressively detected by projecting them on an iteratively estimated solution of the null space. Since our outlier removal process is based on an algebraic criterion which does not require computing the full-pose and reprojecting back all 3D points on the image plane at each step, we achieve speed gains of more than 100× compared to RANSAC strategies. An extensive exper- imental evaluation will show that our solution yields accu- rate results in situations with up to 50 of outliers, and can process more than 1000 correspondences in less than 5ms. 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. A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing