Abstract This work is concerned with camera pose estimation from correspondences of 3D 2D lines, i. e. with the Perspective-n-Line (PnL) problem. We focus on large line sets, which can be efficiently solved by methods using linear formulation of PnL. We propose a novel method “DLT-Combined-Lines” based on the Direct Linear Transformation (DLT) algorithm, which benefits from a new combination of two existing DLT methods for pose estimation. The method represents 2D structure by lines, and 3D structure by both points and lines. The redundant 3D information reduces the minimum required line correspondences to 5. A cornerstone of the method is a combined projection matrix estimated by the DLT algorithm. It contains multiple estimates of camera rotation and translation, which can be recovered after enforcing constraints of the matrix. Multiplicity of the estimates is exploited to improve the accuracy of the proposed method. For large line sets (10 and more), the method is comparable to the state-of-the-art in accuracy of orientation estimation. It achieves state-of-the-art accuracy in estimation of camera position and it yields the smallest reprojection error under strong image noise. The method achieves top-3 results on real world data. The proposed method is also highly computationally effective, estimating the pose of 1000 lines in 12 ms on a desktop computer.
The task of camera pose estimation from line correspondences has been receiving attention for more than a quarter of century. Some of the earliest works are those by @cite_9 and @cite_7 . They introduce two different ways to deal with the PnL problem -- algebraic and iterative approaches -- both of which have different properties and thus also different uses. A specific subset of algebraic approaches are the methods based on linear formulation of the PnL problem.
@cite_9 @cite_7
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In this paper we deal with the camera pose estimation problem from a set of 2D 3D line correspondences, which is also known as PnL (Perspective-n-Line) problem. We carry out our study by comparing PnL with the well-studied PnP (Perspective-n-Point) problem, and our contributions are three-fold: (1) We provide a complete 3D configuration analysis for P3L, which includes the well-known P3P problem as well as several existing analyses as special cases. (2) By exploring the similarity between PnL and PnP, we propose a new subset-based PnL approach as well as a series of linear-formulation-based PnL approaches inspired by their PnP counterparts. (3) The proposed linear-formulation-based methods can be easily extended to deal with the line and point features simultaneously. We propose a non-iterative solution for the Perspective-n-Line (PnL) problem, which can efficiently and accurately estimate the camera pose for both small number and large number of line correspondences. By selecting a rotation axis in the camera framework, the reference lines are divided into triplets to form a sixteenth order cost function, and then the optimum is retrieved from the roots of the derivative of the cost function by evaluating the orthogonal errors and the reprojected errors of the local minima. The final pose estimation is normalized by a 3D alignment approach. The advantages of the proposed method are as follows: (1) it stably retrieves the optimum of the solution with very little computational complexity and high accuracy; (2) small line sets can be robustly handled to achieve highly accurate results and; (3) large line sets can be efficiently handled because it is O(n). Estimation of camera pose from an image of n points or lines with known correspondence is a thoroughly studied problem in computer vision. Most solutions are iterative and depend on nonlinear optimization of some geometric constraint, either on the world coordinates or on the projections to the image plane. For real-time applications, we are interested in linear or closed-form solutions free of initialization. We present a general framework which allows for a novel set of linear solutions to the pose estimation problem for both n points and n lines. We then analyze the sensitivity of our solutions to image noise and show that the sensitivity analysis can be used as a conservative predictor of error for our algorithms. We present a number of simulations which compare our results to two other recent linear algorithms, as well as to iterative approaches. We conclude with tests on real imagery in an augmented reality setup. The determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is well-known that from three corresponding points there are at most four algebraic solutions. Less appears to be known about the cases of four and five corresponding points. We propose a family of linear methods that yield a unique solution to 4- and 5-point pose determination for generic reference points. We first review the 3-point algebraic method. Then we present our two-step, 4-point and one-step, 5-point linear algorithms. The 5-point method can also be extended to handle more than five points. Finally, we demonstrate our methods on both simulated and real images. We show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice.