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_17: A class of pose determination problems in which the sensory data are lines and the corresponding reference data are planes is discussed. The lines considered are different from edge lines in that they are not the intersection of boundary faces of the object. The author describes a polynomial approach that does not require a priori knowledge about the object location. Closed-form solutions for orthogonal, parallel, and coplanar feature configurations of critical importance in real applications are derived. Findings concerning the necessary and sufficient conditions under which the line-to-plane pose determination problem can be solved are described. >
summary: Among the earliest efforts in this field are those of @cite_9 and @cite_17 . Both methods solve the minimal problem of pose estimation from 3 line correspondences in a closed form. Solutions of the P3L problem are multiple: up to 8 solutions may exist . Unfortunately, neither method is able to exploit more measurements to remove the ambiguity, and both methods are sensitive to presence of image noise.