text: 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.
  @cite_9: A method for finding analytical solutions to the problem of determining the attitude of a 3D object in space from a single perspective image is presented. Its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model, and on the search for the model attitude consistent with these projections. The geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight-degree equation in the general case. Using simple logical rules, it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3D objects because few admissible hypotheses are retained from the interpolation of the three line segments. Line matching by the prediction-verification procedure is thus less complex. >
  @cite_7: A method for the determination of camera location from two-dimensional (2-D) to three-dimensional (3-D) straight line or point correspondences is presented. With this method, the computations of the rotation matrix and the translation vector of the camera are separable. First, the rotation matrix is found by a linear algorithm using eight or more line correspondences, or by a nonlinear algorithm using three or more line correspondences, where the line correspondences are either given or derived from point correspondences. Then, the translation vector is obtained by solving a set of linear equations based on three or more line correspondences, or two or more point correspondences. Eight 2-D to 3-D line correspondences or six 2-D to 3-D point correspondences are needed for the linear approach; three 2-D to 3-D line or point correspondences for the nonlinear approach. Good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used. >
summary: 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.