Abstract
In this chapter we show how sparse constraints can be used to improve trajectories. We apply sparsity as a low rank constraint to trajectories via a robust coupling. We compute trajectories from an image sequence. Sparsity in trajectories is measured by matrix rank. We introduce a low rank constraint of linear complexity using random subsampling of the data and demonstrate that, by using a robust coupling with the low rank constraint, our approach outperforms baseline methods on general image sequences.
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References
MPI Sintel Flow Dataset. http://sintel.is.tue.mpg.de/, 2014
S. Baker, D. Scharstein, J.P. Lewis, S. Roth, M.J. Black, R. Szeliski, A database and evaluation methodology for optical flow. Int. J. Comput. Vis. 92(1), 1–31 (2011)
M. Black, Recursive non-linear estimation of discontinuous flow fields, in Computer Vision—ECCV’94, pp. 138–145 (1994)
M.J. Black, P. Anandan, Robust dynamic motion estimation over time, in Proceedings of Computer Vision and Pattern Recognition, CVPR-91, pp. 296–302 (1991)
T. Brox, J. Malik, Large Displacement optical flow: descriptor matching in variational motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011)
D.J. Butler, J. Wulff, G.B. Stanley, M.J. Black, A naturalistic open source movie for optical flow evaluation, in European Conference on Computer Vision (ECCV), pp. 611–625 (2012)
J. Cai, E. Candès, Z. Shen, A singular value thresholding algorithm for matrix completion. SIAM J. Optim. pp. 1–26 (2010)
L. Condat, A generic proximal algorithm for convex optimization—application to total variation minimization. Signal Process. Lett. IEEE 21(8), 985–989 (2014)
R. Garg, A. Roussos, L. Agapito, A variational approach to video registration with subspace constraints. Int. J. Comput. Vis. 104, 286–314 (2013)
J. Gibson, O. Marques, Sparse regularization of TV-L1 optical flow, in ICISP 2014, vol. LNCS, 8509 of Image and Signal Processing, ed. by A. Elmoataz, O. Lezoray, F. Nouboud, D. Mammass (Springer, Cherbourg, France, 2014), pp. 460–467
J. Gibson, O. Marques, Sparsity in optical flow and trajectories. Image Video Process. Signal, 1–8 (2015)
M. Irani, Multi-frame correspondence estimation using subspace constraints. Int. J. Comput. Vis. 48(153), 173–194 (2002)
R. Liu, Z. Lin, Z. Su, J. Gao, Linear time principal component pursuit and its extensions using \(\ell _1\) filtering. Neurocomputing 142, 529–541 (2014)
D. Murray, B.F. Buxton, Scene segmentation from visual motion using global optimization. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 9(March), 220–228 (1987)
H.H. Nagel. Extending the ‘oriented smoothness constraint’ into the temporal domain and the estimation of derivatives of optical flow, in Proceedings of the First European Conference on Computer Vision (Springer, New York, Inc., 1990), pp. 139–148
T. Nir, A.M. Bruckstein, R. Kimmel, Over-parameterized variational optical flow. Int. J. Comput. Vis. 76(2), 205–216 (2007)
D. Pizarro, A. Bartoli, Feature-based deformable surface detection with self-occlusion reasoning. Int. J. Comput. Vis. 97(1), 54–70 (2011)
S. Ricco, C. Tomasi. Dense lagrangian motion estimation with occlusions, in 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1800–1807 (2012)
S. Ricco, C. Tomasi, Video motion for every visible point, in International Conference on Computer Vision (ICCV), number i (2013)
P. Sand, S. Teller, Particle video: long-range motion estimation using point trajectories. Int. J. Comput. Vis. 80(1), 72–91 (2008)
S. Volz, A. Bruhn, L. Valgaerts, H. Zimmer, Modeling temporal coherence for optical flow, in 2011 International Conference on Computer Vision (ICCV), pp. 1116–1123 (2011)
A. Wedel, T. Pock, C. Zach, H. Bischof, D. Cremers, An improved algorithm for TV-L 1 optical flow, in Statistical and Geometrical Approaches to Visual Motion Analysis, pp. 23–45 (Springer Berlin, Heidelberg, 2009)
J. Weickert, C. Schnörr, Variational optic flow computation with a spatio-temporal smoothness constraint. J. Math. Imaging Vis. 245–255 (2001)
J. Wright, P. Yigang, Y. Ma, A. Ganesh, S. Rao, Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization, in NIPS, pp. 1–9 (2009)
X. Yuan, J. Yang, Sparse and low-rank matrix decomposition via alternating direction methods. Optimization (Online), 1–11 (2009)
H. Zimmer, A. Bruhn, J. Weickert, Optic flow in harmony. Int. J. Comput. Vis. 93(3), 368–388 (2011)
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Gibson, J., Marques, O. (2016). Robust Low Rank Trajectories. In: Optical Flow and Trajectory Estimation Methods. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44941-8_4
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DOI: https://doi.org/10.1007/978-3-319-44941-8_4
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