A framework for estimating potential fluid flow from digital imagery

Chaos

Volumn 23, Issue 3, 2013, Pages

  Luttman, Aaron ^a   Bollt, Erik M ^a   Basnayake, Ranil ^a   Kramer, Sean ^a   Tufillaro, Nicholas B ^b  

^a CLARKSON UNIVERSITY   (United States)

^b OREGON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84884961419     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4821188     Document Type: Article

References (43)

1. Horn B.K. P. Schunck B.G. Determining optical flow. Artif. Intell. 1981, 17:185-203. 10.1016/0004-3702(81)90024-2.
2. Bresky W. Daniels J. The feasibility of an optical flow algorithm for estimating atmospheric motion. Proceedings of the Eighth Int. Winds Workshop, Beijing, China 2006, 24-28. in
3. Brox T. Malik J. Large displacement optical flow: Descriptor matching in variational motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 2011, 33:500-513. 10.1109/TPAMI.2010.143.
4. Bruhn A. Weickert J. Feddern C. Kohlberger T. Schnorr C. Real-time optic flow computation with variational methods. CAIP 2003 2003, 222-229. in (Springer)
5. Gupta S. Gupta E.N. Prince J.L. On div-curl regularization for motion estimation in 3-d volumetric imaging. In Proc. International Conf. on Image Proc. (ICIP96) 1996, 929-932. in
6. Haussecker H.W. Fleet D.J. Computing optical flow with physical models of brightness variation. IEEE Trans. Pattern Anal. Mach. Intell. 2002, 23:661-673. 10.1109/34.927465.
7. Kim Y.H. Martínez A.M. Kak A.C. A local approach for robust optical flow estimation under varying illumination. Proc. British Machine Vision Conf 2004, in.
8. Marzat J. Dumortier Y. Ducrot A. Real-time dense and accurate parallel optical flow using cuda. Symposium on Advances in Image and Video Technology 2009, in.
9. Werlberger M. Trobin W. Pock T. Wedel A. Cremers D. Bischof H. Anisotropic Huber-L1 optical flow. Proceedings of the British Machine Vision Conference 2009, in.
10. Quénot G.M. Pakleza J. Kowalewski T.A. Particle image velocimetry with optical flow. Exp. Fluids 1998, 25:177-189. 10.1007/s003480050222.
11. Corpetti T. Heitz D. Arroyo G. Mémin E. Santa-Cruz A. Fluid experimental flow estimation based on an optical-flow scheme. Exp. Fluids 2006, 40:80-97. 10.1007/s00348-005-0048-y.
12. Auroux D. Extraction of velocity fields for geophysical fluids from a sequence of images. Acoustics, Speech, and Signal Processing, IEEE Proceedings on (ICASSP) 2009, 961-964. in
13. Auroux D. Fehrenbach J. Identification of velocity fields for geophysical fluids from a sequence of images. Exp. Fluids 2011, 50:313-328. 10.1007/s00348-010-0926-9.
14. Cassisa C. Prinet V. Shao L. Simoens S. Liu C.L. Optical flow robust estimation in a hybrid multi-resolution MRF framework. Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on 2008, 793-796. in
15. Heitz D. Mémin E. Schnorr C. Variational fluid flow measurements from image sequences: Synopsis and perspectives. Exp. Fluids 2010, 48:369-393. 10.1007/s00348-009-0778-3.
16. Luttman A. Bollt E. Holloway J. An optical flow approach to analyzing species density dynamics and transport. J. Comput. Math. 2012, 30:249-261. 10.4208/jcm.1111-m3714.
17. Luttman A. Bollt E. Basnayake R. Kramer S. A stream function approach to optical flow with applications to fluid transport dynamics. Proc. Appl. Math. Mechanic 2011, 11:855-856. in Vol.
18. Corpetti T. Mémin E. Pérez P. Adaptation of standard optic flow methods to fluid motion. 9th Int. Symp. Flow Visualisation 2000, 1-10. in
19. Corpetti T. Mémin E. Pérez P. Estimating fluid optical flow. ICPR 2000, 7045-7048. in
20. Corpetti T. Mémin E. Pérez P. Dense estimation of fluid flows. IEEE Trans. Pattern Anal. Mach. Intell. 2002, 24:365-380. 10.1109/34.990137.
21. Corpetti T. Mémin E. Pérez P. Dense motion analysis in fluid imagery. in Proc. 7th Eur. Conf. Computer Vision 2002, 676-691. A. Heyden, edited by
22. Mémin E. Corpetti T. 2000, "Dense fluid flow estimation," Tech. Rep. (INRIA).
23. Suter D. Motion estimation and vector splines. Proc. Conf. Comp. Vision Pattern Rec 1994, 939-942. in (IEEE)
24. Kohlberger T. Mémin E. Schnorr C. Variational dense motion estimation using the helmholtz decomposition. Scale Space '03 2003, 432-448. L. D. Griffin, M. Lillholm, in edited by and (Isle of Skye, UK), Vol. 2695
25. Schmidt M. Fung G. Rosales R. Fast optimization methods for l1 regularization: A comparative study and two new approaches. Mach. Learn. 2007, 4701:286. 10.1007/978-3-540-74958-5_28.
26. Koppel D. Tsai C.-M. Wang Y.-F. Regularizing optical-flow computation using tensor theory and complex analysis. Computer Vision and Pattern Recognition Workshops, 2008. CVPRW'08. IEEE Computer Society Conference on 2008, 1-6. in
27. Weickert J. Bruhn A. Papenberg N. Brox T. Variational optic flow computation: From continuous models to algorithms. International Workshop on Computer Vision and Image Analysis, IWCVIA03, Las Palmas de Gran Canaria 2003, in edited by L. Alvarez.
28. Basnayake R. Luttman A. Bollt E. A lagged diffusivity method for computing total variation regularized fluid flow. Contemp. Math. 2013, 586:57-64. 10.1090/conm/586/11632.
29. Hansen P.C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 1992, 34:561-580. 10.1137/1034115.
30. Hansen P.C. The L-curve and its use in the numerical treatment of inverse problems. Computational Inverse Problems in Electrocardiology, Advances in Computational Bioengineering 2000, 119-142. P. Johnston, in edited by (WIT Press)
31. Krawczyk-Stado D. Rudnicki M. Regularization parameter selection in discrete ill-posed problems-the use of the U-curve. Int. J. Appl. Math. Comput. Sci. 2007, 17:157-164. 10.2478/v10006-007-0014-3.
32. Krawczyk-Stado D. Rudnicki M. The use of L-curve and U-curve in inverse electromagnetic modelling. Intell. Comput. Tech. Appl. Electromagn. 2008, 119:73-82. 10.1007/978-3-540-78490-6_9.
33. Golub G. Heath M. Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 1979, 21:215-223. 10.1080/00401706.1979.10489751.
34. Lukas M.A. Strong robust generalized cross-validation for choosing the regularization parameter. Inverse Probl. 2008, 24:034006. 10.1088/0266-5611/24/3/034006.
35. Vogel C.R. Non-convergence of the L-curve regularization parameter selection method. Inverse Probl. 1996, 12:535-548. 10.1088/0266-5611/12/4/013.
36. Hanke M. Limitations of the L-curve method in ill-posed problems. BIT 1996, 36:287-301. 10.1007/BF01731984.
37. McCane B. Novins K. Crannitch D. Galvin B. On benchmarking optical flow. Comput. Vis. Image Underst. 2001, 84:126-143. 10.1006/cviu.2001.0930.
38. Osborne J.J. Kurapov A.L. Egbert G.D. Kosro P.M. Spatial and temporal variability of the m2 internal tide generation and propagation on the oregon shelf. J. Phys. Oceanogr. 2011, 41:2037-2062. 10.1175/JPO-D-11-02.1.
39. Vallis G.K. Atmospheric and Oceanic Fluid Dynamics 2006, 745. (Cambridge University Press, Cambridge, U.K.)
40. Allen J. Holm D.D. Extended-geostrophic hamiltonian models for rotating shallow water motion. Physica D 1996, 98:229-248. 10.1016/0167-2789(96)00120-0.
41. Holm D.D. Zeitlin V. Hamilton's principle for quasigeostrophic motion. Phys. Fluids 1998, 10:800-806. 10.1063/1.869623.
42. Marshall D.P. Maddison J.R. Berloff P.S. A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr. 2012, 42:539-557. 10.1175/JPO-D-11-048.1.
43. Bollt E.M. Luttman A. Kramer S. Basnayake R. Measurable dynamics analysis of transport in the Gulf of Mexico during the oil spill. Int. J. Bifurcation Chaos 2012, 22:1230012. 10.1142/S0218127412300121.