A minimal solution to the autocalibration of radial distortion

Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify the system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without computing complete Gröbner basis, which provides an efficient and robust solver. The quality of the solver is demonstrated on synthetic and real data. 1

Stereoscopic Cinema

International audienceStereoscopic cinema has seen a surge of activity in recent years, and for the first time all of the major Hollywood studios released 3-D movies in 2009. This is happening alongside the adoption of 3-D technology for sports broadcasting, and the arrival of 3-D TVs for the home. Two previous attempts to introduce 3-D cinema in the 1950s and the 1980s failed because the contemporary technology was immature and resulted in viewer discomfort. But current technologies – such as accurately-adjustable 3-D camera rigs with onboard computers to automatically inform a camera operator of inappropriate stereoscopic shots, digital processing for post-shooting rectification of the 3-D imagery, digital projectors for accurate positioning of the two stereo projections on the cinema screen, and polarized silver screens to reduce cross-talk between the viewers left- and right-eyes – mean that the viewer experience is at a much higher level of quality than in the past. Even so, creation of stereoscopic cinema is an open, active research area, and there are many challenges from acquisition to post-production to automatic adaptation for different-sized display. This chapter describes the current state-of-the-art in stereoscopic cinema, and directions of future work

Overconstrained linear estimation of radial distortion and multi-view geometry

Abstract. This paper introduces a new method for simultaneous estimation of lens distortion and multi-view geometry using only point correspondences. The new technique has significant advantages over the current state-of-the art in that it makes more effective use of correspondences arising from any number of views. Multi-view geometry in the presence of lens distortion can be expressed as a set of point correspondence constraints that are quadratic in the unknown distortion parameter. Previous work has demonstrated how the system can be solved efficiently as a quadratic eigenvalue problem by operating on the normal equations of the system. Although this approach is appropriate for situations in which only a minimal set of matchpoints are available, it does not take full advantage of extra correspondences in overconstrained situations, resulting in significant bias and many potential solutions. The new technique directly operates on the initial constraint equations and solves the quadratic eigenvalue problem in the case of rectangular matrices. The method is shown to contain significantly less bias on both controlled and real-world data and, in the case of a moving camera where additional views serve to constrain the number of solutions, an accurate estimate of both geometry and distortion is achieved. 2