Coplanar circles, quasi-affine invariance and calibration

We define the lines associated with two coplanar circles, and give the distributions of any two coplanar circles and their associated lines. Further we prove that the distribution of two coplanar circles with no real intersection and their associated lines is a quasi-affine invariance. Then the results are applied to calibrating a camera. The calibration method has the advantages: (1) it is based on conic fitting; (2) it does not need any matching. Experiments with two separate circles validate our quasi-affine invariance and show that the estimated camera intrinsic parameters are as good as those obtained by Zhang's (2000) method.