Estimating the relative pose between two cameras is a fundamental step in many applications such as Structure-from-Motion. The common approach to relative pose estimation is to apply a minimal solver inside a RANSAC loop. Highly efficient solvers exist for pinhole cameras. Yet, (nearly) all cameras exhibit radial distortion. Not modeling radial distortion leads to (significantly) worse results. However, minimal radial distortion solvers are significantly more complex than pinhole solvers, both in terms of run-time and implementation efforts. This paper compares radial distortion solvers with two simple-to-implement approaches that do not use minimal radial distortion solvers: The first approach combines an efficient pinhole solver with sampled radial undistortion parameters, where the sampled parameters are used for undistortion prior to applying the pinhole solver. The second approach uses a state-of-the-art neural network to estimate the distortion parameters rather than sampling them from a set of potential values. Extensive experiments on multiple datasets, and different camera setups, show that complex minimal radial distortion solvers are not necessary in practice. We discuss under which conditions a simple sampling of radial undistortion parameters is preferable over calibrating cameras using a learning-based prior approach. Code and newly created benchmark for relative pose estimation under radial distortion are available at https://github.com/kocurvik/rdnet.

In this paper, we propose a novel approach for recovering focal lengths from three-view homographies. By examining the consistency of normal vectors between two homographies, we derive new explicit constraints between the focal lengths and homographies using an elimination technique. We demonstrate that three-view homographies provide two additional constraints, enabling the recovery of one or two focal lengths. We discuss four possible cases, including three cameras having an unknown equal focal length, three cameras having two different unknown focal lengths, three cameras where one focal length is known, and the other two cameras have equal or different unknown focal lengths. All the problems can be converted into solving polynomials in one or two unknowns, which can be efficiently solved using Sturm sequence or hidden variable technique. Evaluation using both synthetic and real data shows that the proposed solvers are both faster and more accurate than methods relying on existing two-view solvers. The code and data are available on https://github.com/kocurvik/hf.

We study the challenging problem of estimating the relative pose of three calibrated cameras from four point correspondences. We propose novel efficient solutions to this problem that are based on the simple idea of using four correspondences to estimate an approximate geometry of the first two views. We model this geometry either as an affine or a fully perspective geometry estimated using one additional approximate correspondence. We generate such an approximate correspondence using a very simple and efficient strategy, where the new point is the mean point of three corresponding input points. The new solvers are efficient and easy to implement, since they are based on existing efficient minimal solvers, i.e., the 4-point affine fundamental matrix, the well-known 5-point relative pose solver, and the P3P solver. Extensive experiments on real data show that the proposed solvers, when properly coupled with local optimization, achieve state-of-the-art results, with the novel solver based on approximate mean-point correspondences being more robust and accurate than the affine-based solver.

The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the Bougnoux formula offers a means to compute the two unknown focal lengths. However, in many practical situations, the formula yields inaccurate results due to commonly occurring singularities. Moreover, the estimates are sensitive to noise in the com-puted fundamental matrix and to the assumed positions of the principal points. In this paper, we therefore propose an efficient and robust iterative method to estimate the focal lengths along with the principal points of the cameras given a fundamental matrix and priors for the estimated camera intrinsics. In addition, we study a computationally efficient check of models generated within RANSAC that improves the accuracy of the estimated models while reducing the to-tal computational time. Extensive experiments on real and synthetic data show that our iterative method brings signifi-cant improvements in terms of the accuracy of the estimated focal lengths over the Bougnoux formula and other state-of-the-art methods, even when relying on inaccurate priors. The code for the methods and experiments is available at https://github.com/kocurvik/robust.self.calibration