Camera Calibration from a Translation + Planar Motion

This paper addresses the problem of camera calibration by exploiting image invariants under camera/object rotation. A novel translation + planar motion is studied here. The 3 × 3 homography mapping corresponding points before and after the motion is exploited to obtain image invariants under perspective projection. The homography is found to form a “rotation conic” under different rotation angles. Apart from the imaged circular points, this conic can also be exploited to find the vanishing point of the rotation axis and this provides extra constraints for camera calibration. A square calibration pattern, which is invariant under a rotation about its center by multiples of π/2 radians, is introduced as a special instantiation of the translation + planar motion. Experiments on synthetic and real data show good precisions in calibration results.