The projective equation of a circle and its application in camera calibration

In this article, we present the projective equation of a circle in a perspective view, which naturally encodes such important geometric entities as the projected circle center, the vanishing point of the normal direction of the circlepsilas supporting plane and the degenerate conic envelope spanned by the image of circular points (ICPs). Based on this projective equation, we propose an easy technique to calibrate the focal length and the extrinsic parameters of a camera merely by using one perspective view of two arbitrary coplanar circles. Unlike existing optimization algorithm, our method offers a closed form solution through simple matrix manipulation. Experimental results verify the correctness and efficiency of our proposed technique.