Two-View Motion Segmentation from Linear Programming Relaxation

This paper studies the problem of multibody motion segmentation, which is an important, but challenging problem due to its well-known chicken-and-egg-type recursive character. We propose a new mixture-of-fundamental-matrices model to describe the multibody motions from two views. Based on the maximum likelihood estimation, in conjunction with a random sampling scheme, we show that the problem can be naturally formulated as a linear programming (LP) problem. Consequently, the motion segmentation problem can be solved efficiently by linear program relaxation. Experiments demonstrate that: without assuming the actual number of motions our method produces accurate segmentation result. This LP formulation has also other advantages, such as easy to handle outliers and easy to enforce prior knowledge etc.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  R. Vidal,et al.  Motion segmentation with missing data using PowerFactorization and GPCA , 2004, CVPR 2004.

[3]  Nuno Vasconcelos,et al.  Empirical Bayesian EM-based motion segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  David B. Shmoys,et al.  Approximation algorithms for facility location problems , 2000, APPROX.

[5]  Ilan Shimshoni,et al.  Guided Sampling via Weak Motion Models and Outlier Sample Generation for Epipolar Geometry Estimation , 2005, CVPR.

[6]  Hongdong Li,et al.  Five-Point Motion Estimation Made Easy , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[7]  Yair Weiss,et al.  Incorporating Non-motion Cues into 3D Motion Segmentation , 2006, ECCV.

[8]  David W. Murray,et al.  Guided Sampling and Consensus for Motion Estimation , 2002, ECCV.

[9]  S. Shankar Sastry,et al.  Two-View Multibody Structure from Motion , 2005, International Journal of Computer Vision.

[10]  Lihi Zelnik-Manor,et al.  Multi-body Factorization with Uncertainty: Revisiting Motion Consistency , 2005, International Journal of Computer Vision.

[11]  Konrad Schindler,et al.  Perspective n-View Multibody Structure-and-Motion Through Model Selection , 2006, ECCV.

[12]  Lior Wolf,et al.  Two-body segmentation from two perspective views , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[13]  Marc Pollefeys,et al.  A Factorization-Based Approach to Articulated Motion Recovery , 2005, CVPR.

[14]  Kenichi Kanatani,et al.  Geometric Information Criterion for Model Selection , 1998, International Journal of Computer Vision.

[15]  An A Fabii,et al.  Improved Approximation Algorithms for Uncapacitated Facility Location , 1998 .

[16]  Ying Wu,et al.  Multibody motion segmentation based on simulated annealing , 2004, CVPR 2004.

[17]  David Suter,et al.  Two-View Multibody Structure-and-Motion with Outliers through Model Selection , 2006, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Hongdong Li.  A Simple Solution to the Six-Point Two-View Focal-Length Problem , 2006, ECCV.

[19]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[20]  Yi Ma,et al.  Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications , 2004, CVPR 2004.

[21]  Serge J. Belongie,et al.  What went where , 2003, CVPR 2003.

[22]  Kenichi Kanatani,et al.  Motion segmentation by subspace separation and model selection , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[23]  T. Kanade,et al.  A multi-body factorization method for motion analysis , 1995, ICCV 1995.

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

[25]  Jiri Matas,et al.  Epipolar geometry estimation via RANSAC benefits from the oriented epipolar constraint , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[26]  Jitendra Malik,et al.  Image and video segmentation: the normalized cut framework , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[27]  P. Torr.  Geometric motion segmentation and model selection , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.