Robustness in Motion Averaging

The averaging of multiple pairwise relative motions in a sequence provides a fast and accurate method of camera motion estimation with a wide range of applications, including view registration, robotic path estimation, super-resolution. Since this approach involves averaging in the Lie-algebra of the underlying motion representation, it is non-robust and susceptible to contamination due to outliers in the individual relative motions. In this paper, we introduce a graph-based sampling scheme that efficiently remove such motion outliers. The resulting global motion solution is robust and also provides an empirical estimate of the inherent statistical uncertainty. Example results are provided to demonstrate the efficacy of our approach to incorporating robustness in motion averaging.

[1]  Philip N. Klein,et al.  A randomized linear-time algorithm for finding minimum spanning trees , 1994, STOC '94.

[2]  Philip H. S. Torr,et al.  The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix , 1997, International Journal of Computer Vision.

[3]  Venu Madhav Govindu,et al.  Lie-algebraic averaging for globally consistent motion estimation , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[4]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[5]  P. Thomas Fletcher,et al.  Statistics of shape via principal geodesic analysis on Lie groups , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

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

[7]  V. Varadarajan.  Lie groups, Lie algebras, and their representations , 1974 .

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

[9]  Venu Madhav Govindu,et al.  Combining two-view constraints for motion estimation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[10]  Michael Werman,et al.  The viewing graph , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[11]  Philip N. Klein,et al.  A randomized linear-time algorithm to find minimum spanning trees , 1995, JACM.

[12]  Paulo R. S. Mendonça,et al.  A simple technique for self-calibration , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[13]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[14]  P. Thomas Fletcher,et al.  Statistics of Shape via Principal Component Analysis on Lie Groups , 2003 .

[15]  Peter Meer,et al.  Balanced Recovery of 3D Structure and Camera Motion from Uncalibrated Image Sequences , 2002, ECCV.

[16]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

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