Correspondences between 3D lines and their 2D images captured by a camera are often used to determine position and orientation of the camera in space. In this work, we propose a novel algebraic algorithm to estimate the camera pose. We parameterize 3D lines using Plucker coordinates that allow linear projecti on of the lines into the image. A line projection matrix is estimated using Linear Least Squares and the camera pose is then extracted from the matrix. An algebraic approach to handle mismatched line correspondences is also included. The proposed algorithm is an order of magnitude faster yet comparably accurate and robust to the state-of-the-art, it does not require initialization, and it yields only one solution. The described method requires at least 9 lines and is particularly suitable for scenarios with 25 and more lines, as also shown in the results.
Recently, two major improvements of algebraic approaches have been achieved. First, Mirzaei and Roumeliotis @cite_4 proposed a method which is both efficient (linear computational complexity depending on the number of lines) and robust in the presence of image noise. The cases with 3 or more lines can be handled. A polynomial system with 27 candidate solutions is constructed and solved through the eigendecomposition of a multiplication matrix. Camera orientations having the least square error are considered to be the optimal ones. Camera positions are obtained separately using the Linear Least Squares. Nonetheless, the problem of this algorithm is that it often yields multiple solutions.
@cite_4
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Correspondences between 2D lines in an image and 3D lines in the surrounding environment can be exploited to determine the camera's position and attitude (pose). In this paper, we introduce a novel approach to estimate the camera's pose by directly solving the corresponding least-squares problem algebraically. Specifically, the optimality conditions of the least-squares problem form a system of polynomial equations, which we efficiently solve through the eigendecomposition of a so-called multiplication matrix. Contrary to existing methods, the proposed algorithm (i) is guaranteed to find the globally optimal estimate in the least-squares sense, (ii) does not require initialization, and (iii) has computational cost only linear in the number of measurements. The superior performance of the proposed algorithm compared to previous approaches is demonstrated through extensive simulations and experiments.