Camera Calibration from the Quasi-affine Invariance of Two Parallel Circles

In this paper, a new camera calibration algorithm is proposed, which is from the quasi-affine invariance of two parallel circles. Two parallel circles here mean two circles in one plane, or in two parallel planes. They are quite common in our life. Between two parallel circles and their images under a perspective projection, we set up a quasi-affine invariance. Especially, if their images under a perspective projection are separate, we find out an interesting distribution of the images and the virtual intersections of the images, and prove that it is a quasi-affine invariance. The quasi-affine invariance is very useful which is applied to identify the images of circular points. After the images of the circular points are identified, linear equations on the intrinsic parameters are established, from which a camera calibration algorithm is proposed. We perform both simulated and real experiments to verify it. The results validate this method and show its accuracy and robustness. Compared with the methods in the past literatures, the advantages of this calibration method are: it is from parallel circles with minimal number; it is simple by virtue of the proposed quasi-affine invariance; it does not need any matching. Excepting its application on camera calibration, the proposed quasiaffine invariance can also be used to remove the ambiguity of recovering the geometry of single axis motions by conic fitting method in [8] and [9]. In the two literatures, three conics are needed to remove the ambiguity of their method. While, two conics are enough to remove it if the two conics are separate and the quasi-affine invariance proposed by us is taken into account.