Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world data
@cite_36: Augmented reality (AR) allows to seamlessly insert virtual objects in an image sequence. In order to accomplish this goal, it is important that synthetic elements are rendered and aligned in the scene in an accurate and visually acceptable way. The solution of this problem can be related to a pose estimation or, equivalently, a camera localization process. This paper aims at presenting a brief but almost self-contented introduction to the most important approaches dedicated to vision-based camera localization along with a survey of several extension proposed in the recent years. For most of the presented approaches, we also provide links to code of short examples. This should allow readers to easily bridge the gap between theoretical aspects and practical implementations.
@cite_27: In this paper, we revisit the classical perspective-n-point (PnP) problem, and propose the first non-iterative O(n) solution that is fast, generally applicable and globally optimal. Our basic idea is to formulate the PnP problem into a functional minimization problem and retrieve all its stationary points by using the Gr"obner basis technique. The novelty lies in a non-unit quaternion representation to parameterize the rotation and a simple but elegant formulation of the PnP problem into an unconstrained optimization problem. Interestingly, the polynomial system arising from its first-order optimality condition assumes two-fold symmetry, a nice property that can be utilized to improve speed and numerical stability of a Grobner basis solver. Experiment results have demonstrated that, in terms of accuracy, our proposed solution is definitely better than the state-of-the-art O(n) methods, and even comparable with the reprojection error minimization method.
@cite_7: A large number of absolute pose algorithms have been presented in the literature. Common performance criteria are computational complexity, geometric optimality, global optimality, structural degeneracies, and the number of solutions. The ability to handle minimal sets of correspondences, resulting solution multiplicity, and generalized cameras are further desirable properties. This paper presents the first PnP solution that unifies all the above desirable properties within a single algorithm. We compare our result to state-of-the-art minimal, non-minimal, central, and non-central PnP algorithms, and demonstrate universal applicability, competitive noise resilience, and superior computational efficiency. Our algorithm is called Unified PnP (UPnP).
@cite_24: 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 camera pose problem has been studied for more than a century, and there is a large body of literature on the absolute pose estimation problem @cite_36 . Here, we first review the PnP algorithm without mismatches. When the observations include no outliers, the PnP problem has a closed solution ( @math ). To reduce the sensitivity to noise and consider a larger point set, the Efficient PnP (EPnP) @cite_24 , Optimal PnP (OPnP) @cite_27 , and Unified PnP (UPnP) @cite_7 methods have been developed to produce accurate results with a linear complexity. These algorithms are applied in many related areas and can be regarded as state-of-the-art outlier-free PnP techniques.