Minimal Solutions to Relative Pose Estimation From Two Views Sharing a Common Direction With Unknown Focal Length
14 Jun 2020-pp 7045-7053
TL;DR: The proposed algorithms can cope with coplanar points, which is a degenerate configuration for these 6- and 7-point counterparts, and derive new 4- and 5-point algorithms for these two cases, respectively.
Abstract: We propose minimal solutions to relative pose estimation problem from two views sharing a common direction with unknown focal length. This is relevant for cameras equipped with an IMU (inertial measurement unit), e.g., smart phones, tablets. Similar to the 6-point algorithm for two cameras with unknown but equal focal lengths and 7-point algorithm for two cameras with different and unknown focal lengths, we derive new 4- and 5-point algorithms for these two cases, respectively. The proposed algorithms can cope with coplanar points, which is a degenerate configuration for these 6- and 7-point counterparts. We present a detailed analysis and comparisons with the state of the art. Experimental results on both synthetic data and real images from a smart phone demonstrate the usefulness of the proposed algorithms.
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01 Jan 2016
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290 citations
Posted Content•
TL;DR: This work proposes new minimal solutions to panoramic stitching of images taken by cameras with coinciding optical centers, i.e. undergoing pure rotation, and considers six practical camera configurations, from fully calibrated ones up to a camera with unknown fixed or varying focal length and with or without radial distortion.
Abstract: When capturing panoramas, people tend to align their cameras with the vertical axis, i.e., the direction of gravity. Moreover, modern devices, such as smartphones and tablets, are equipped with an IMU (Inertial Measurement Unit) that can measure the gravity vector accurately. Using this prior, the y-axes of the cameras can be aligned or assumed to be already aligned, reducing their relative orientation to 1-DOF (degree of freedom). Exploiting this assumption, we propose new minimal solutions to panoramic image stitching of images taken by cameras with coinciding optical centers, i.e., undergoing pure rotation. We consider four practical camera configurations, assuming unknown fixed or varying focal length with or without radial distortion. The solvers are tested both on synthetic scenes and on more than 500k real image pairs from the Sun360 dataset and from scenes captured by us using two smartphones equipped with IMUs. It is shown, that they outperform the state-of-the-art both in terms of accuracy and processing time.
10 citations
Posted Content•
TL;DR: This work proposes a novel globally optimal solver, minimizing the algebraic error in the least squares sense, to estimate the relative pose in the over-determined case, based on the epipolar constraint.
Abstract: Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the $y$-axes of the cameras can be aligned, reducing their relative orientation to a single degree-of-freedom. With this assumption, we propose a novel globally optimal solver, minimizing the algebraic error in the least-squares sense, to estimate the relative pose in the over-determined case. Based on the epipolar constraint, we convert the optimization problem into solving two polynomials with only two unknowns. Also, a fast solver is proposed using the first-order approximation of the rotation. The proposed solvers are compared with the state-of-the-art ones on four real-world datasets with approx. 50000 image pairs in total. Moreover, we collected a dataset, by a smartphone, consisting of 10933 image pairs, gravity directions, and ground truth 3D reconstructions.
9 citations
Cites background from "Minimal Solutions to Relative Pose ..."
...This parameterization introduces a degeneracy for a 180 rotation which can be ignored in real applications [29, 11]....
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TL;DR: Experimental results showed that the proposed method had better performance in terms of numerical stability, noise sensitivity, and computational speed than several state-of-the-art perspective-n-point solvers.
Abstract: In this paper, we proposed an accurate and robust method for absolute pose estimation with UAV (unmanned aerial vehicle) using RANSAC (random sample consensus). Because the artificial 3D control points with high accuracy are time-consuming and the small point set may lead low measuring accuracy, we designed a customized UAV to efficiently obtain mass 3D points. A light source was mounted on the UAV and used as a 3D point. The position of the 3D point was given by RTK (real-time kinematic) mounted on the UAV, and the position of the corresponding 2D point was given by feature extraction. The 2D–3D point correspondences exhibited some outliers because of the failure of feature extraction, the error of RTK, and wrong matches. Hence, RANSAC was used to remove the outliers and obtain the coarse pose. Then, we proposed a method to refine the coarse pose, whose procedure was formulated as the optimization of a cost function about the reprojection error based on the error transferring model and gradient descent to refine it. Before that, normalization was given for all the valid 2D–3D point correspondences to improve the estimation accuracy. In addition, we manufactured a prototype of a UAV with RTK and light source to obtain mass 2D–3D point correspondences for real images. Lastly, we provided a thorough test using synthetic data and real images, compared with several state-of-the-art perspective-n-point solvers. Experimental results showed that, even with a high outlier ratio, our proposed method had better performance in terms of numerical stability, noise sensitivity, and computational speed.
6 citations
01 Jun 2021
TL;DR: Yao et al. as mentioned in this paper proposed a novel globally optimal solver, minimizing the algebraic error in the least square sense, to estimate the relative pose in the over-determined case.
Abstract: Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the y-axes of the cameras can be aligned, reducing their relative orientation to a single degree-of-freedom. With this assumption, we propose a novel globally optimal solver, minimizing the algebraic error in the least squares sense, to estimate the relative pose in the over-determined case. Based on the epipolar constraint, we convert the optimization problem into solving two polynomials with only two unknowns. Also, a fast solver is proposed using the first-order approximation of the rotation. The proposed solvers are compared with the state-of-the-art ones on four real-world datasets with approx. 50000 image pairs in total. Moreover, we collected a dataset, by a smartphone, consisting of 10933 image pairs, gravity directions and ground truth 3D reconstructions. The source code and dataset are available at https://github.com/yaqding/opt_pose_gravity
4 citations
References
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TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.
Abstract: A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing
23,396 citations
"Minimal Solutions to Relative Pose ..." refers methods in this paper
...Since we only want to give a fair comparison, we use the standard RANSAC [10] without any optimizations to estimate the focal length and relative pose....
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...This case is quite unusual in practice and can be handled by robust estimators, such as RANSAC [10]....
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...algorithms can be used with RANSAC [10] in for example, SfM (structure-from-motion) pipelines....
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TL;DR: The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay and is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem.
Abstract: An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.
2,077 citations
"Minimal Solutions to Relative Pose ..." refers background or methods in this paper
...Similar to [28, 12, 29, 9], we focus on two important practical motions: sideways motion (parallel to the scene) and forward motion (along the zaxis)....
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...This measurement has been widely used in camera pose estimations [28, 4, 21, 29, 24, 9]....
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...For example, given internally calibrated cameras, it is well known that the relative pose can be estimated using the 5-point algorithm [16, 21, 28]....
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Book•
01 Jan 1987
TL;DR: This book discusses iterative projection methods for solving Eigenproblems, and some of the techniques used to solve these problems came from the literature on Hermitian Eigenvalue.
Abstract: List of symbols and acronyms List of iterative algorithm templates List of direct algorithms List of figures List of tables 1: Introduction 2: A brief tour of Eigenproblems 3: An introduction to iterative projection methods 4: Hermitian Eigenvalue problems 5: Generalized Hermitian Eigenvalue problems 6: Singular Value Decomposition 7: Non-Hermitian Eigenvalue problems 8: Generalized Non-Hermitian Eigenvalue problems 9: Nonlinear Eigenvalue problems 10: Common issues 11: Preconditioning techniques Appendix: of things not treated Bibliography Index .
1,418 citations
"Minimal Solutions to Relative Pose ..." refers background in this paper
...Based on [2], the solutions of s are the eigenvalues of the 24× 24 matrix:...
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...As shown in [2], polynomial eigenvalue problems are problems of the form...
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19 May 1992
TL;DR: A non-iterative algorithm is given for determining the focal lengths of the two cameras, as well as their relative placement, assuming all other internal camera parameters to be known.
Abstract: This paper considers, the determination of internal camera parameters from two views of a point set in three dimensions. A non-iterative algorithm is given for determining the focal lengths of the two cameras, as well as their relative placement, assuming all other internal camera parameters to be known. It is shown that this is all the information that may be deduced from a set of image correspondences.
663 citations
"Minimal Solutions to Relative Pose ..." refers background in this paper
...If the focal lengths of the two cameras are different and unknown, at least seven point correspondences are needed to recover the relative motion and focal lengths [3, 15]....
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01 Dec 2001
TL;DR: This paper shows how linear estimation of the fundamental matrix from two-view point correspondences may be augmented to include one term of radial lens distortion, by expressing fundamental matrix estimation as a quadratic eigenvalue problem (QEP), for which efficient algorithms are well known.
Abstract: A problem in uncalibrated stereo reconstruction is that cameras which deviate from the pinhole model have to be pre-calibrated in order to correct for nonlinear lens distortion. If they are not, and point correspondence is attempted using the uncorrected images, the matching constraints provided by the fundamental matrix must be set so loose that point matching is significantly hampered. This paper shows how linear estimation of the fundamental matrix from two-view point correspondences may be augmented to include one term of radial lens distortion. This is achieved by (1) changing from the standard radial-lens model to another which (as we show) has equivalent power, but which takes a simpler form in homogeneous coordinates, and (2) expressing fundamental matrix estimation as a quadratic eigenvalue problem (QEP), for which efficient algorithms are well known. I derive the new estimator, and compare its performance against bundle-adjusted calibration-grid data. The new estimator is fast enough to be included in a RANSAC-based matching loop, and we show cases of matching being rendered possible by its use. I show how the same lens can be calibrated in a natural scene where the lack of straight lines precludes most previous techniques. The modification when the multi-view relation is a planar homography or trifocal tensor is described.
595 citations