A closed-form solution for a two-view self-calibration problem under fixation

It is well known that the epipolar geometry between two uncalibrated perspective views is completely encapsulated in the fundamental matrix. Since the fundamental matrix has seven degrees of freedom (DOF), self-calibration is possible if at most seven of the intrinsic or extrinsic camera parameters are unknown by extracting them from the fundamental matrix. This work presents a linear algorithm for self-calibrating a perspective camera which undergoes fixation, that is, a special motion in which the camera's optical axis is confined in a plane. Since this fixation has four degrees of freedom, which is one smaller than that of general motion, we can extract at most three intrinsic parameters from the fundamental matrix. We here assume that the focal length (1 DOF) and the principal point (2 DOF) are unknown but fixed for two views. It will be shown that these three parameters are obtained from the fundamental matrix in an analytical fashion and a closed-form solution is derived. We also characterize all the degenerate motions under which there exists an infinite set of solutions.

[1]  Peter Sturm,et al.  On focal length calibration from two views , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[2]  Jean Ponce,et al.  Analytical Methods for Uncalibrated Stereo and Motion Reconstruction , 1994, ECCV.

[3]  Kenichi Kanatani,et al.  Closed-Form Expression for Focal Lengths from the Fundamental Matrix , 2000 .

[4]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[5]  Rajiv Gupta,et al.  Stereo from uncalibrated cameras , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Richard I. Hartley,et al.  Estimation of Relative Camera Positions for Uncalibrated Cameras , 1992, ECCV.

[7]  Reinhard Koch,et al.  Self-Calibration and Metric Reconstruction Inspite of Varying and Unknown Intrinsic Camera Parameters , 1999, International Journal of Computer Vision.

[8]  Olivier D. Faugeras,et al.  The fundamental matrix: Theory, algorithms, and stability analysis , 2004, International Journal of Computer Vision.

[9]  S. Bougnoux,et al.  From projective to Euclidean space under any practical situation, a criticism of self-calibration , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[10]  Olivier Faugeras,et al.  Motion of an uncalibrated stereo rig: self-calibration and metric reconstruction , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[11]  M. Brooks,et al.  Recovering unknown focal lengths in self-calibration: an essentially linear algorithm and degenerate configurations , 1996 .

[12]  Du Q. Huynh,et al.  Towards robust metric reconstruction via a dynamic uncalibrated stereo head , 1998, Image Vis. Comput..

[13]  Olivier D. Faugeras,et al.  A theory of self-calibration of a moving camera , 1992, International Journal of Computer Vision.