Camera calibration based on the common pole-polar properties between two coplanar circles with various positions.

Computer vision camera calibration is widely performed using parallel circles. Various cases of two coplanar circles are algebraically explained, proving that the common pole is located at the line at infinity for all relative positions, and the corresponding polar passes through the centers of the two circles. The two common poles of the two coplanar circles are the points at infinity when concentric; one common pole of the two coplanar circles is a point at infinity when nonconcentric. Accordingly, the vanishing line can be obtained by using the common pole-polar properties of two groups of two coplanar circles, and the camera's intrinsic parameters are solved according to the constraints between the image of the circular points and the imaged absolute conic. The camera calibration can be solved using only three images of two coplanar circles. Simulation and experiments verify that the proposed algorithms are effective.