A new camera calibration method for robotic applications

In this paper, we present a camera calibration method using two views of three pairs of concentric circles with known sizes. A new invariant property for circle is introduced to determine the position of the center of the projected circle. Given two image ellipses and their corresponding centers, a cross-ratio based method estimates the center of projected circles using the new invariant property. The accurate center of projected concentric circles provides correct correspondences between ellipses in the image plane and circles in 3-D plane. We also demonstrate that two views of three pairs of coplanar concentric circles are enough to determine the intrinsic camera parameters, such as the focal length, the aspect ratio, and the principal point. We validate the performance of the method using both synthetic and real images. Our method shows a comparable performance with respect to similar calibration methods using planes. The use of concentric circles, however, provides correct correspondences between 3-D target points and their image points, and greatly simplifies the calibration problem.