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.
The estimate the camera pose by solving a system of (usually polynomial) equations, minimizing an algebraic error. Dhome al @cite_21 and Chen @cite_15 solve the minimal problem of pose estimation from 3 line correspondences whereas Ansar and Daniilidis @cite_19 work with 4 or more lines. Their algorithm has quadratic computational complexity depending on the number of lines and it may fail if the polynomial system has more than 1 solution. More crucial disadvantage of these methods is that they become unstable in the presence of image noise and must be plugged into a RANSAC or similar loop.
@cite_19 @cite_15 @cite_21
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Estimating the absolute pose of a camera relative to a 3D representation of a scene is a fundamental step in many geometric Computer Vision applications. When the camera is calibrated, the pose can be computed very efficiently. If the calibration is unknown, the problem becomes much harder, resulting in slower solvers or solvers requiring more samples and thus significantly longer run-times for RANSAC. In this paper, we challenge the notion that using minimal solvers is always optimal and propose to compute the pose for a camera with unknown focal length by randomly sampling a focal length value and using an efficient pose solver for the now calibrated camera. Our main contribution is a novel sampling scheme that enables us to guide the sampling process towards promising focal length values and avoids considering all possible values once a good pose is found. The resulting RANSAC variant is significantly faster than current state-of-the-art pose solvers, especially for low inlier ratios, while achieving a similar or better pose accuracy. We present an algorithm for calibrated camera relative pose estimation from lines. Given three lines with two of the lines parallel and orthogonal to the third we can compute the relative rotation between two images. We can also compute the relative translation from two intersection points. We also present a framework in which such lines can be detected. We evaluate the performance of the algorithm using synthetic and real data. The intended use of the algorithm is with robust hypothesize-and-test frameworks such as RANSAC. Our approach is suitable for urban and indoor environments where most lines are either parallel or orthogonal to each other. We present a new method for solving the problem of camera pose and calibration from a limited number of correspondences between noisy 2D and 3D features. We show that the probabilistic estimation problem can be expressed as a partially linear problem, where point and line correspondences are mixed using a common formulation. Our Sampling-Solving algorithm enables to robustly estimate the parameters and evaluate the probability distribution of the estimated parameters. It solves the problem of pose estimation with unknown focal length using a minimum of only four correspondences (five if the principal point is also unknown). To our knowledge, this is the first calibration method using so few correspondences of both points and lines. Experimental results on minimal data sets show that the algorithm is very robust to Gaussian noise. Experimental comparisons show that our method is much more stable than existing camera calibration methods for small data sets. Finally, some tests show the potential of global uncertainty estimates on real data sets. This paper identifies and fills the probably last two missing items in minimal pose estimation algorithms using points and lines. Pose estimation refers to the problem of recovering the pose of a calibrated camera given known features (points or lines) in the world and their projections on the image. There are four minimal configurations using point and line features: 3 points, 2 points and 1 line, 1 point and 2 lines, 3 lines. The first and the last scenarios that depend solely on either points or lines have been studied a few decades earlier. However the mixed scenarios, which are more common in practice, have not been solved yet. In this paper we show that it is indeed possible to develop a general technique that can solve all four scenarios using the same approach and that the solutions involve computing the roots of either a 4th degree or an 8th degree equation. The centerpiece of our method is a simple and generic method that uses collinearity and coplanarity constraints for solving the pose. In addition to validating the performance of these algorithms in simulations, we also show a compelling application for geo-localization using image sequences and coarse (plane-based) 3D models of GPS-challenged urban canyons.