iccv iccv2013 iccv2013-301 iccv2013-301-reference knowledge-graph by maker-knowledge-mining
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Author: Etienne Huot, Giuseppe Papari, Isabelle Herlin
Abstract: This paper describes modeling and numerical computation of orthogonal bases, which are used to describe images and motion fields. Motion estimation from image data is then studied on subspaces spanned by these bases. A reduced model is obtained as the Galerkin projection on these subspaces of a physical model, based on Euler and optical flow equations. A data assimilation method is studied, which assimilates coefficients of image data in the reduced model in order to estimate motion coefficients. The approach is first quantified on synthetic data: it demonstrates the interest of model reduction as a compromise between results quality and computational cost. Results obtained on real data are then displayed so as to illustrate the method.
[1] D. B ´er ´eziat and I. Herlin. Solving ill-posed image processing problems using data assimilation. Numerical Algorithms, 52(2):219–252, 2011.
[2] R. H. Byrd, P. Lu, and J. Nocedal. A limited memory algorithm for bound constrained optimization. Journal on Scientific and Statistical Computing, 16(5): 1190–1208, 1995.
[3] T. Corpetti, E. M ´emin, and P. Prez. Dense estimation of fluid flows. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(3):365–380, Mar. 2002.
[4] P. Courtier, J.-N. Th´ epaut, and A. Hollingsworth. A strategy for operational implementation of 4d-var, using and incre33335570 Figure7.Resultof hetwinexp riment.Fromtop bot m: ground-truth, Horn et al. [11], Suter [19], Corpetti et al. [3], Sun et al. [18], and our estimation. mental approach. Quaterly Journal of the Royal Meteorological Society, 120(1367–1387), 1994.
[5] J. D’Adamo, N. Papadakis, E. M ´emin, and A. G. Variational assimilation of POD low-order dynamical systems. Journal of Turbulence, 8(9): 1–22, 2007. Figure8.Char cteristicpoints. Figure9.Char cteristcpointsonthelastobservation. Figure10.Resultonrealdta.Top:Sunetalmethod[18].Middle: using the full model. Bottom: our estimation.
[6] P. D ´erian, P. H e´as, C. Herzet, and E. M ´emin. Wavelets to reconstruct turbulence multifractals from experimental image sequences. In 7th International Symposium on Turbulence and Shear Flow Phenomena, TSFP-7, Ottawa, Canada, July 2011.
[7] P. D ´erian, P. H e´as, C. Herzet, and E. M ´emin. Wavelets and optical flow motion estimation. Numerical Mathematics: Theory, Methods and Applications, 2012.
[8] K. Drifi and I. Herlin. Coupling reduced models for opti33335581 Figure1 .Char cteristcpointsonthelastobservation. right.
[9]
[10]
[11]
[12]
[13] mal motion estimation. In Proceedings of International Conference on Pattern Recognition (ICPR), pages 265 1–2654, Tsukuba, Japan, November 2012. I. Herlin and K. Drifi. Learning reduced models for motion estimation on long temporal image sequences. In Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Munich, Germany, July 2012. C. Homescu, L. R. Petzold, and R. Serban. Error estimation for reduced-order models of dynamical systems. SIAM Journal of Numerical Analysis, 43(4): 1,693–1,714, 2005. B. Horn and B. Schunk. Determining optical flow. Artificial Intelligence, 17: 185–203, 1981. S. Kadri Harouna, P. D ´erian, P. H e´as, and E. M ´emin. Divergence-free wavelets and high order regularization. International Journal of Computer Vision, 2012. S. Kadri Harouna and V. Perrier. Effective construction of divergence-free wavelets on the square. Journal of Computational and Applied Mathematics, 240:74–86, March 2012.
[14] F. Le Dimet and O. Talagrand. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects., pages 97–1 10. Tellus, 1986.
[15] J.-L. Lions. Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, 1971 .
[16] N. Papadakis, T. Corpetti, and E. M ´emin. Dynamically consistent optical flow estimation. In Proceedings of In- Figure 13. Results of motion estimation. Middle: full model. Bottom: our method.
[17]
[18]
[19]
[20]
[21] Top: Sun et al. [18]. ternational Conference on Computer Vision (ICCV), Rio de Janeiro, Brazil, Oct. 2007. M. Restelli, L. Bonaventura, and R. Sacco. A semiLagrangian discontinuous Galerkin method for scalar advection by incompressible flows. Journal of Computational Physics, 216(1): 195–215, 2006. D. Sun, S. Roth, and M. Black. Secrets of optical flow estimation and their principles. In Proceedings of European Conference on Computer Vision (ECCV), pages 2432–2439, 2010. D. Suter. Motion estimation and vector splines. In Proceedings of International Conference on Computer Vision and Pattern Recognition (CVPR), pages 939–942, 1994. O. Titaud, A. Vidard, I. Souopgui, and F.-X. Le Dimet. Assimilation of image sequences in numerical models. Tellus A, 62:30–47, 2010. E. Valur H o´lm. Lectures notes on assimilation algo- rithms. Technical report, European Centre for MediumRange Weather Forecasts Reading, U.K, Apr. 2008. 33335592