A Bayesian Approach for Affine Auto-calibration

In this paper, we propose a Bayesian approach for affine auto-calibration. By the Bayesian approach, a posterior distribution for the affine camera parameters can be constructed, where also the prior knowledge can be taken into account. Moreover, due to the linearity of the affine camera model, the structure and translations can be analytically marginalised out from the posterior distribution, if certain prior distributions are assumed. The marginalisation reduces the dimensionality of the problem substantially that makes the MCMC methods better suitable for exploring the posterior of the intrinsic camera parameters. The experiments verify that the proposed approach is a versatile, statistically sound alternative for the existing affine auto-calibration methods.

[1]  Long Quan,et al.  Self-calibration of an affine camera from multiple views , 1996, International Journal of Computer Vision.

[2]  Takeo Kanade,et al.  A factorization method for affine structure from line correspondences , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[4]  J J Koenderink,et al.  Affine structure from motion. , 1991, Journal of the Optical Society of America. A, Optics and image science.

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

[6]  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 .

[7]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[8]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

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

[10]  Takeo Kanade,et al.  A Paraperspective Factorization Method for Shape and Motion Recovery , 1994, ECCV.

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

[12]  Marvin H. J. Guber Bayesian Spectrum Analysis and Parameter Estimation , 1988 .

[13]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[14]  Long Quan,et al.  A Unification of Autocalibration Methods , 2000 .

[15]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[16]  Jan-Olof Eklundh,et al.  Computer Vision — ECCV '94 , 1994, Lecture Notes in Computer Science.

[17]  Sami S. Brandt,et al.  Conditional solutions for the affine reconstruction of N-views , 2005, Image Vis. Comput..

[18]  Takeo Kanade,et al.  Shape and motion from image streams under orthography: a factorization method , 1992, International Journal of Computer Vision.

[19]  G. Sandini,et al.  Computer Vision — ECCV'92 , 1992, Lecture Notes in Computer Science.

[20]  Jerry Nedelman,et al.  Book review: “Bayesian Data Analysis,” Second Edition by A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Chapman & Hall/CRC, 2004 , 2005, Comput. Stat..

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

[22]  Tomás Pajdla,et al.  Autocalibration & 3D reconstruction with non-central catadioptric cameras , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[23]  Branislav Micus ´ ik Estimation of omnidirectional camera model from epipolar geometry , 2003 .