We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with a minimum of 2 line-line correspondences, while the second is solved up to 4 discrete solutions using 4 point-line correspondences. We use these algorithms to perform the extrinsic calibration between a pose tracking sensor and a 2D 3D ultrasound (US) curvilinear probe using a tracked needle as calibration target. The needle is tracked as a 3D line, and is scanned by the ultrasound as either a 3D line (3D US) or as a 2D point (2D US). Since the scale factor that converts US scan units to metric coordinates is unknown, the calibration is formulated as a similarity registration problem. We present results with both synthetic and real data and show that the minimum solutions outperform the correspondent non-minimal linear formulations.
The 2D US calibration problem is the similarity registration between a set of 3D lines and a set of co-planar points. This is a particular case of the pose and scale problem @cite_24 when the 3D points are co-planar, and therefore this method could be adapted to solve this problem. However, the co-planarity of points introduces further simplifications, and as we will show in this paper, this problem can be minimally solved with a much more compact set of equations.
@cite_24
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We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with a minimum of 2 line-line correspondences, while the second is solved up to 4 discrete solutions using 4 point-line correspondences. We use these algorithms to perform the extrinsic calibration between a pose tracking sensor and a 2D 3D ultrasound (US) curvilinear probe using a tracked needle as calibration target. The needle is tracked as a 3D line, and is scanned by the ultrasound as either a 3D line (3D US) or as a 2D point (2D US). Since the scale factor that converts US scan units to metric coordinates is unknown, the calibration is formulated as a similarity registration problem. We present results with both synthetic and real data and show that the minimum solutions outperform the correspondent non-minimal linear formulations. In this paper, we address the problem of extrinsic calibration of a camera and a 3D Light Detection and Ranging (LiDAR) sensor using a checkerboard. Unlike previous works which require at least three checkerboard poses, our algorithm reduces the minimal number of poses to one by combining 3D line and plane correspondences. Besides, we prove that parallel planar targets with parallel boundaries provide the same constraints in our algorithm. This allows us to place the checkerboard close to the LiDAR so that the laser points better approximate the target boundary without loss of generality. Moreover, we present an algorithm to estimate the similarity transformation between the LiDAR and the camera for the applications where only the correspondences between laser points and pixels are concerned. Using a similarity transformation can simplify the calibration process since the physical size of the checkerboard is not needed. Meanwhile, estimating the scale can yield a more accurate result due to the inevitable measurement errors of the checkerboard size and the LiDAR intrinsic scale factor that transforms the LiDAR measurement to the metric measurement. Our algorithm is validated through simulations and experiments. Compared to the plane-only algorithms, our algorithm can obtain more accurate result by fewer number of poses. This is beneficial to the large-scale commercial application. 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. We propose a novel solution for computing the relative pose between two generalized cameras that includes reconciling the internal scale of the generalized cameras. This approach can be used to compute a similarity transformation between two coordinate systems, making it useful for loop closure in visual odometry and registering multiple structure from motion reconstructions together. In contrast to alternative similarity transformation methods, our approach uses 2D-2D image correspondences thus is not subject to the depth uncertainty that often arises with 3D points. We utilize a known vertical direction (which may be easily obtained from IMU data or vertical vanishing point detection) of the generalized cameras to solve the generalized relative pose and scale problem as an efficient Quadratic Eigenvalue Problem. To our knowledge, this is the first method for computing similarity transformations that does not require any 3D information. Our experiments on synthetic and real data demonstrate that this leads to improved performance compared to methods that use 3D-3D or 2D-3D correspondences, especially as the depth of the scene increases.