Camera Calibration with Two Arbitrary Coplanar Circles

In this paper, we describe a novel camera calibration method to estimate the extrinsic parameters and the focal length of a camera by using only one single image of two coplanar circles with arbitrary radius. We consider that a method of simple operation to estimate the extrinsic parameters and the focal length of a camera is very important because in many vision based applications, the position, the pose and the zooming factor of a camera is adjusted frequently. An easy to use and convenient camera calibration method should have two characteristics: 1) the calibration object can be produced or prepared easily, and 2) the operation of a calibration job is simple and easy. Our new method satisfies this requirement, while most existing camera calibration methods do not because they need a specially designed calibration object, and require multi-view images. Because drawing beautiful circles with arbitrary radius is so easy that one can even draw it on the ground with only a rope and a stick, the calibration object used by our method can be prepared very easily. On the other hand, our method need only one image, and it allows that the centers of the circle and/or part of the circles to be occluded. Another useful feature of our method is that it can estimate the focal length as well as the extrinsic parameters of a camera simultaneously. This is because zoom lenses are used so widely, and the zooming factor is adjusted as frequently as the camera setting, the estimation of the focal length is almost a must whenever the camera setting is changed. The extensive experiments over simulated images and real images demonstrate the robustness and the effectiveness of our method.