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.

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.

Determining the number of solutions of a multi-homogeneous polynomial system is a fundamental problem in algebraic geometry. The multi-homogeneous Bézout (m-Bézout) number bounds from above the number of non-singular solutions of a multi-homogeneous system, but its computation is a #P>-hard problem.