In this paper, we study the minimal problem of estimating the essential matrix between two cameras with constant but unknown focal length and radial distortion. This problem is of both theoretical and practical interest and it has not been solved previously. We have derived a fast and stable polynomial solver based on Grobner basis method. This solver enables simultaneous auto-calibration of focal length and radial distortion for cameras. For experiments, the numerical stability of the solver is demonstrated on synthetic data. We also evaluate on real images using either RANSAC or kernel voting. Compared with the standard minimal solver, which does not model the radial distortion, our proposed solver both finds a larger set of geometrically correct correspondences on distorted images and gives an accurate estimate of the radial distortion and focal length.
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