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A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination
Diane Gilliocq-Hirtz1; Zakaria Belhachmi1
1 LMIA, 6 rue des Frères Lumière, 68093 Mulhouse, France
The SMAI Journal of computational mathematics, Volume 2 (2016), pp. 121-140.

We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To reduce the complexity of the estimation for high resolution images and the time of computations, we implement a multi-level parallel approach based on the domain decomposition with the Schwarz overlapping method. The second level of parallelism uses the massively parallel solver MUMPS. We perform some numerical simulations to show the efficiency of our approach and to validate it on classical and real-world image sequences.

Published online:
DOI: 10.5802/smai-jcm.11
Keywords: optical flow, varying illumination, domain decomposition, adaptive control, finite element method, variational method, multi-level parallelism.

Diane Gilliocq-Hirtz 1; Zakaria Belhachmi 1

1 LMIA, 6 rue des Frères Lumière, 68093 Mulhouse, France 
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     title = {A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination},
     journal = {The SMAI Journal of computational mathematics},
     pages = {121--140},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {2},
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Diane Gilliocq-Hirtz; Zakaria Belhachmi. A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination. The SMAI Journal of computational mathematics, Volume 2 (2016), pp. 121-140. doi : 10.5802/smai-jcm.11. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.11/

[1] P.R. Amestoy; I.S. Duff; J.-Y. L’Excellent; J. Koster MUMPS: A General Purpose Distributed Memory Sparse Solver, Applied Parallel Computing. New Paradigms for HPC in Industry and Academia: 5th International Workshop, PARA 2000 Bergen, Norway, June 18–20, 2000 Proceedings, Springer Berlin Heidelberg (2001) | DOI

[2] G. Aubert; R. Deriche; P. Kornprobst Computing Optical Flow via Variational Techniques, SIAM Journal on Applied Mathematics, Volume 60 (1999), pp. 156-182 | DOI | MR | Zbl

[3] J.L. Barron; D.J. Fleet; S.S. Beauchemin Performance of optical flow techniques, International Journal of Computer Vision, Volume 12 (1994), pp. 43-77 | DOI

[4] Z. Belhachmi; D. Gilliocq-Hirtz, Computer Vision and Image Analysis Applications (ICCVIA), 2015 International Conference on (2015), pp. 1-6

[5] Z. Belhachmi; F. Hecht Control of the Effects of Regularization on Variational Optic Flow Computations, Journal of Mathematical Imaging and Vision, Volume 40 (2011), pp. 1-19 | DOI | MR | Zbl

[6] Z. Belhachmi; F. Hecht An adaptive approach for segmentation and TV denoising in the optic flow estimation (2014) (Working paper or preprint)

[7] T. Brox; A. Bruhn; N. Papenberg; J. Weickert High Accuracy Optical Flow Estimation Based on a Theory for Warping, Computer Vision - ECCV 2004 (T. Pajdla; J. Matas, eds.), Springer Berlin Heidelberg, 2004, pp. 25-36 | DOI | Zbl

[8] A. Bruhn Variational optic flow computation: Accurate modelling and efficient numerics, University of Saarland (2006) (Ph. D. Thesis)

[9] A. Bruhn; J. Weickert; C. Schnorr Lucas/Kanade meets Horn/Schunck: Combining Local and Global Optic Flow Methods, International Journal of Computer Vision, Volume 61 (2005), pp. 211-231 | DOI

[10] M.A. Gennert; S. Negahdaripour Relaxing the Brightness Constancy Assumption in Computing Optical Flow, Technical Report, Massachusetts Institute of Technology Cambridge, MA, USA (1987)

[11] F. Hecht New development in FreeFem++, J. Numer. Math., Volume 20 (2012), pp. 251-265 | DOI | MR | Zbl

[12] B. Horn; B. Schunck Determining optical flow, Artificial Intelligence, Volume 17 (1981), pp. 185 -203 | DOI

[13] P.-L. Lions, Third internationnal symposium on domain decomposition methods for partial differential equations, Volume 6 (1990), pp. 202-223 | Zbl

[14] B.D. Lucas; T. Kanade, Proceedings of the 7th International Joint Conference on Artificial Intelligence - Volume 2 (IJCAI’81) (1981), pp. 674-679 http://dl.acm.org/citation.cfm?id=1623264.1623280

[15] E. Mémin; P. Pérez, Proc. Int. Conf. on Computer Vision, ICCV’98 (1998), pp. 933-938 | DOI

[16] Y. Mileva; A. Bruhn; J. Weickert Illumination-Robust Variational Optical Flow with Photometric Invariants, Pattern Recognition (F. Hamprecht; C. Schnorr; B. Jähne, eds.), Springer Berlin Heidelberg, 2007, pp. 152-162

[17] P. Ruhnau; T. Kohlberger; C. Schnorr; H. Nobach Variational optical flow estimation for particle image velocimetry, Experiments in Fluids, Volume 38 (2005), pp. 21-32 | DOI

[18] J. Weickert; A. Bruhn; N. Papenberg; T. Brox, International Workshop on Computer Vision and Image Analysis (ed. L. Alvarez), IWCVIA-03, Las Palmas de Gran Canaria (2003)

[19] J. Weickert; C. Schnorr Variational Optic Flow Computation with a Spatio-Temporal Smoothness Constraint, Journal of Mathematical Imaging and Vision, Volume 14 (2001), pp. 245-255 | DOI | Zbl

[20] H. Zimmer; A. Bruhn; J. Weickert; L. Valgaerts; A. Salgado; B. Rosenhahn; H.-P. Seidel Complementary Optic Flow, Energy Minimization Methods in Computer Vision and Pattern Recognition (D. Cremers; Y. Boykov; A. Blake; Schmidt F., eds.), Springer, 2009, pp. 207-220 | DOI

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