Using vanishing points for camera calibration

In this article a new method for the calibration of a vision system which consists of two (or more) cameras is presented. The proposed method, which uses simple properties of vanishing points, is divided into two steps. In the first step, the intrinsic parameters of each camera, that is, the focal length and the location of the intersection between the optical axis and the image plane, are recovered from a single image of a cube. In the second step, the extrinsic parameters of a pair of cameras, that is, the rotation matrix and the translation vector which describe the rigid motion between the coordinate systems fixed in the two cameras are estimated from an image stereo pair of a suitable planar pattern. Firstly, by matching the corresponding vanishing points in the two images the rotation matrix can be computed, then the translation vector is estimated by means of a simple triangulation. The robustness of the method against noise is discussed, and the conditions for optimal estimation of the rotation matrix are derived. Extensive experimentation shows that the precision that can be achieved with the proposed method is sufficient to efficiently perform machine vision tasks that require camera calibration, like depth from stereo and motion from image sequence.