A simple technique for self-calibration

This paper introduces an extension of Hartley's self-calibration technique based on properties of the essential matrix, allowing for the stable computation of varying focal lengths and principal point. It is well known that the three singular values of an essential must satisfy two conditions: one of them must be zero and the other two must be identical. An essential matrix is obtained from the fundamental matrix by a transformation involving the intrinsic parameters of the pair of cameras associated with the two views. Thus, constraints on the essential matrix can be translated into constraints on the intrinsic parameters of the pair of cameras. This allows for a search in the space of intrinsic parameters of the cameras in order to minimize a cost function related to the constraints. This approach is shown to be simpler than other methods, with comparable accuracy in the results. Another advantage of the technique is that it does not require as input a consistent set of weakly calibrated camera matrices (as defined by Harley) for the whole image sequence, i.e. a set of cameras consistent with the correspondences and known up to a projective transformation.

[1]  Reinhard Koch,et al.  Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

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

[3]  S. P. Mudur,et al.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[4]  Richard I. Hartley,et al.  Projective Reconstruction and Invariants from Multiple Images , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Roger Y. Tsai,et al.  Techniques for Calibration of the Scale Factor and Image Center for High Accuracy 3-D Machine Vision Metrology , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Bill Triggs,et al.  Autocalibration and the absolute quadric , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  Andrew Zisserman,et al.  Resolving ambiguities in auto–calibration , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Roger Y. Tsai,et al.  Techniques for calibration of the scale factor and image center for high accuracy 3D machine vision metrology , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[9]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[10]  R. Y. Tsai,et al.  An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision , 1986, CVPR 1986.

[11]  Andrew Zisserman,et al.  Self-Calibration from Image Triplets , 1996, ECCV.

[12]  Richard I. Hartley,et al.  Minimizing algebraic error in geometric estimation problems , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[13]  Peter F. Sturm,et al.  Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  Olivier D. Faugeras,et al.  What can two images tell us about a third one? , 1994, ECCV.

[15]  O. Faugeras,et al.  About the correspondences of points between N images , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[16]  Andrew Zisserman,et al.  Robust parameterization and computation of the trifocal tensor , 1997, Image Vis. Comput..

[17]  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).

[18]  Richard Szeliski,et al.  Geometrically Constrained Structure from Motion: Points on Planes , 1998, SMILE.

[19]  Olivier D. Faugeras,et al.  Some Properties of the E Matrix in Two-View Motion Estimation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..