Camera Auto-calibration from the Steiner Conic of the Fundamental Matrix

Abstract

This paper addresses the problem of camera auto-calibration from the fundamental matrix under general motion. The fundamental matrix can be decomposed into a symmetric part (a Steiner conic) and a skew-symmetric part (a fixed point), which we find useful for fully calibrating camera parameters. We first obtain a fixed line from the image of the symmetric, skew-symmetric parts of the fundamental matrix and the image of the absolute conic. Then the properties of this fixed line are presented and proved, from which new constraints on general eigenvectors between the Steiner conic and the image of the absolute conic are derived. We thus propose a method to fully calibrate the camera. First, the three camera intrinsic parameters, i.e., the two focal lengths and the skew, can be solved from our new constraints on the imaged absolute conic obtained from at least three images. On this basis, we can initialize and then iteratively restore the optimal pair of projection centers of the Steiner conic, thereby obtaining the corresponding vanishing lines and images of circular points. Finally, all five camera parameters are fully calibrated using images of circular points obtained from at least three images. Experimental results on synthetic and real data demonstrate that our method achieves state-of-the-art performance in terms of accuracy.