Focal length calibration from two views: method and analysis of singular cases

We consider the problem of estimating the focal length of a camera from two views while the focal length is not varied during the motion of the camera. An approach based on Kruppa's equations is proposed. Specifically, we derive two linear and one quadratic equations to solve the problem. Although the three equations are interdependent in general, each one may be singular for different configurations. We study in detail the generic singularities of the problem and the actual singularities of the individual calibration equations. Results of our experiments using synthetic and real data underline the effect that singular configurations may have on self-calibration. However, these results are stable once the singularities are avoided.

[1]  Peter F. Sturm,et al.  A Case Against Kruppa's Equations for Camera Self-Calibration , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[3]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[4]  O. Faugeras,et al.  The Geometry of Multiple Images , 1999 .

[5]  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).

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

[7]  Bill Triggs,et al.  Critical motions in euclidean structure from motion , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[8]  Peter F. Sturm,et al.  Critical motion sequences for the self-calibration of cameras and stereo systems with variable focal length , 1999, Image Vis. Comput..

[9]  Anders Heyden,et al.  Euclidean reconstruction from image sequences with varying and unknown focal length and principal point , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Richard I. Hartley,et al.  In defence of the 8-point algorithm , 1995, Proceedings of IEEE International Conference on Computer Vision.

[11]  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).

[12]  O. Faugeras,et al.  Camera Self-Calibration from Video Sequences: the Kruppa Equations Revisited , 1996 .

[13]  Bill Triggs,et al.  Critical Motions for Auto-Calibration When Some Intrinsic Parameters Can Vary , 2000, Journal of Mathematical Imaging and Vision.

[14]  Richard I. Hartley,et al.  Kruppa's Equations Derived from the Fundamental Matrix , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Alexandru Tupan,et al.  Triangulation , 1997, Comput. Vis. Image Underst..

[16]  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.

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

[18]  Gene H. Golub,et al.  Matrix computations , 1983 .

[19]  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.

[20]  Rachid Deriche,et al.  A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry , 1995, Artif. Intell..

[21]  Andrew Zisserman,et al.  Multiple view geometry in computer visiond , 2001 .

[22]  R. Hartley.  Triangulation, Computer Vision and Image Understanding , 1997 .

[23]  O. D. Faugeras,et al.  Camera Self-Calibration: Theory and Experiments , 1992, ECCV.

[24]  Olivier D. Faugeras,et al.  The geometry of multiple images - the laws that govern the formation of multiple images of a scene and some of their applications , 2001 .

[25]  M. Pollefeys.  Self-calibration and metric 3d reconstruction from uncalibrated image sequences , 1999 .