Abstract
Motion segmentation is an old problem that is receiving renewed interest because of its role in video analysis. In this paper, we present a Semi-Nonnegative Matrix Factorization (SNMF)method that models dense point tracks in terms of their optical flow, and decomposes sets of point tracks into semantically meaningful motion components. We show that this formulation of SNMF with missing values outperforms the state-of-the-art algorithm of Brox and Malik in terms of accuracy on 10-frame video segments from the Berkeley test set, while being over 100 times faster. We then show how SNMF can be applied to longer videos using sliding windows. The result is competitive in terms of accuracy with Brox and Malik’s algorithm, while still being two orders of magnitude faster.
This work is supported by DARPA Contract W911NF-10-2-0066.
Chapter PDF
Similar content being viewed by others
References
Brox, T., Malik, J.: Object Segmentation by Long Term Analysis of Point Trajectories. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part V. LNCS, vol. 6315, pp. 282–295. Springer, Heidelberg (2010)
Vidal, R., Ma, Y.: A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 1–15. Springer, Heidelberg (2004)
Yan, J., Pollefeys, M.: A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3954, pp. 94–106. Springer, Heidelberg (2006)
Rao, S., Tron, R., Vidal, R., Ma, Y.: Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories. In: 2008 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2008)
Fan, Z., Zhou, J., Wu, Y.: Multibody grouping by inference of multiple subspaces from high-dimensional data using oriented-frames. IEEE Transactions on Pattern Analysis and Machine Intelligence 28, 91–105 (2006)
Elhamifar, E., Vidal, R.: Sparse subspace clustering. In: 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 2790–2797. IEEE (2009)
Cheriyadat, A., Radke, R.: Non-negative matrix factorization of partial track data for motion segmentation. In: 2009 IEEE 12th International Conference on Computer Vision, pp. 865–872. IEEE (2009)
Lee, D., Seung, H., et al.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Ding, C., Li, T., Jordan, M.: Convex and semi-nonnegative matrix factorizations. IEEE Transactions on Pattern Analysis and Machine Intelligence 32, 45–55 (2010)
Hoyer, P.: Non-negative matrix factorization with sparseness constraints. The Journal of Machine Learning Research 5, 1457–1469 (2004)
Hartley, R., Schaffalitzky, F.: Powerfactorization: 3d reconstruction with missing or uncertain data. In: Australia-Japan Advanced Workshop on Computer Vision, vol. 74, pp. 76–85 (2003)
Sundaram, N., Brox, T., Keutzer, K.: Dense point trajectories by gpu-accelerated large displacement optical flow. In: Proceedings of the 11th European Conference on Computer Vision, pp. 438–451 (2010)
Thurau, C.: PyMF: Python matrix factorization library (2010), http://code.google.com/p/pymf/
Tron, R., Vidal, R.: A benchmark for the comparison of 3-d motion segmentation algorithms. In: IEEE Conference on Computer Vision and Pattern Recognition 2007, pp. 1–8. IEEE (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mo, Q., Draper, B.A. (2012). Semi-Nonnegative Matrix Factorization for Motion Segmentation with Missing Data. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33786-4_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-33786-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33785-7
Online ISBN: 978-3-642-33786-4
eBook Packages: Computer ScienceComputer Science (R0)