The infinitesimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: Vector fields and transport barriers from movies

Chaos

Volumn 17, Issue 2, 2007, Pages

  Santitissadeekorn, N ^a   Bollt, E M ^a  

^a CLARKSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547311975     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2742932     Document Type: Article

References (44)

1. E. Bollt, L. Billings, and I. Schwartz, " A manifold independent approach to understanding transport in stochastic dynamical systems., " Physica D 173, 153 (2002).
2. L. Billings, E. Bollt, and I. B. Schwartz, " Phase-space transport of stochastic chaos in population dynamics of virus spread., " Phys. Rev. Lett. 88, 234101 (2002).
3. G. Froyland, " Extracting dynamical behaviour via Markov models., " in Proceedings, Nonlinear Dynamics and Statistics (Birkhauser, Boston, 2001), pp. 283-324.
4. B. K. P. Horn and B. G. Schunck, " Determining optical flow., " Artif. Intell. 17, 185 (1981).
5. T. Corpetti, E. Měmin, and P. Pěrez, " Dense estimation of fluid flows., " IEEE Trans. Pattern Anal. Mach. Intell. 24, 365 (2002).
6. T. Corpetti, D. Heitz, G. Arroyo, E. Memin, and A. Sant-Cruz, " Fluid experimental flow estimation based on an optical-flow scheme., " Exp. Fluids 40, 80 (2006).
7. D. Bereziat and J.-P. Berroir, " Motion estimation on meteorological infrared data using a total brightness invariance hypothesis., " Environ. Modell. Software 15 (2000).
8. J. J. Simpson and J. I. Gobat, " Robust velocity estimates, stream functions, and simulated Lagrangian drifters from sequential spacecraft data., " IEEE Trans. Geosci. Remote Sens. GE-32, 479 (1994).
9. P. Heas, E. Memin, and N. Papadakis, " Dense estimation of layer motions in the atmosphere., " in Int. Conf. Pattern Recognition (ICPR' 06), Hong-Kong, China (2006).
10. S. Gutierrez and D. G. Long, " Optical flow and scale-space theory applied to sea-ice motion estimation in Antarctica., " in Proceedings of the Geoscience and Remote Sensing Symposium (2003), Vol. 4, pp. 2805-2807.
11. A. Suvichakorn and A. Tatnall, " The application of cloud texture and motion derived from geostationary satellite images in rain estimation-A study on mid-latitude depression., " in Proceedings of the Geoscience and Remote Sensing Symposium (2005), Vol. 3.
12. R. P. Wildes, M. J. Ambabile, A. M. Lanzillotto, and T. S. Leu, " Recovering estimate of fluid flow from image sequence data., " Comput. Vis. Image Underst. 80, 246 (2000).
13. A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise, Stochastic Aspects of Dynamics, 2nd ed. (Springer, New York, 1994).
14. M. E. J. Newman and M. Girvan, " Finding and evaluating community structure to networks., " Phys. Rev. E 69, 026113 (2004).
15. M. E. J. Newman and M. Girvan, Statistical Mechanics of Complex Networks (Springer, Berlin, 2004).
16. M. E. J. Newman, " Fast algorithm for detecting community structure in networks., " Phys. Rev. E 69, 066133 (2004).
17. A. Clauset, M. E. J. Newman, and C. Moore, " Finding community structure in very large networks., " Phys. Rev. E 70, 066111 (2004).
18. M. Dellnitz and O. Junge, " On the approximation of complicated dynamical behavior., " SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 36, 491 (1999).
19. R. Pries and M. Dellnitz, " Congestion and almost invariant sets in dynamical systems., " Proceedings of Symbolic and Numerical Scientific Computation (SNSC'01) (Springer, Berlin, 2003).
20. R. Pries, M. Dellnitz, M. Hessel, Ch. Schutte, and E. Meerbach, " Dominant paths between almost invariant sets of dynamical systems., " Preprint 154 of the DFG Schwerpunktprogramm 1095 (2004).
21. K. Padberg, R. Preis, and M. Dellnitz, " Integrating multilevel graph partitioning with hierarchical set oriented methods for the analysis of dynamical systems., " Preprint 152 of the DFG Schwerpunktprogramm 1095 (2004).
22. G. Haller, " Lagrangian coherent structures from approximate velocity data., " Phys. Fluids 14, 1851 (2002).
23. S. C. Shadden, F. Lekien, and J. E. Marsden, " Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows., " Physica D 212, 271 (2005).
24. S. C. Shadden, J. O. Dabiriand, and J. E. Marsden, " Lagrangian analysis of fluid transport in empirical vortex ring flows., " Phys. Fluids 18, 271 (2006).
25. S. M. Ulam, Problems in Modern Mathematics, Science ed. (Wiley, New York, 1970).
26. T. Y. Li, " Finite approximation for the Frobenius-Perron operator: A solution to Ulam's conjecture., " J. Approx. Theory 17, 177 (1976).
27. C. Chui, Q. Du, and T. Li, " Error estimates of the Markov finite approximation of the Frobenius-Perron operator., " Nonlinear Anal. Theory, Methods Appl. 19, 291 (1992).
28. J. Ding and A. Zhou, " The projection method for computing multidimensional absolutely continuous invariant measures., " J. Stat. Phys. 77, 899 (2004).
29. G. Froyland, " Finite approximation of Sinai-Bowen-Ruelle measure for Anosov systems in two dimensions., " Random Comput. Dyn. 3, 251 (1995).
30. G. Froyland, " Estimating physical invariant measures and space averages of dynamical systems indicators., " Ph.D. thesis, University of Western Australia (1996).
31. F. Hunt, " Approximating the invariant measures of randomly perturbed dissipative maps., " J. Math. Anal. Appl. 198, 534 (1996).
32. B. D. Lucas and T. Kanade, " An iterative image registration technique with an application to stereo vision., " in IJCAI81 (1981), pp. 674-679.
33. J. Bign, G. H. Granlund, and J. Wiklund, " Multidimensional orientation estimation with applications to texture analysis and optical flow., " IEEE Trans. Pattern Anal. Mach. Intell. 13, 775 (1991).
34. J. L. Barron, D. J. Fleet, and D. J. Beauchemin, " Performance of optical flow techniques., " Int. J. Comput. Vis. 12, 43 (1994).
35. B. Galvin, B. McCane, K. Novins, D. Mason, and S. Mills, " Recovering motion fields: An evaluation of eight optical flow algorithms., " In Proceedings of the Ninth British Machine Vision Conference (BMVC'98) (1998), Vol. 1, pp. 195-204.
36. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-posed Problem (Winston, Washington, DC, 1977).
37. D. Suter, " Motion estimation and vector splines., " in Proceedings of CVPR'94 (IEEE, Piscataway, NJ, 1994), pp. 939-942.
38. M. W. Hirchh and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, Orlando, FL, 1974).
39. J. P. Bagrow and E. M. Bollt, " A local method for detecting communities., " Phys. Rev. E 72, 046108 (2005).
40. B. Fronberg, A Practical Guide to Pseudospectral Methods (Cambridge University Press, Cambridge, UK, 1996).
41. L. N. Trefethen, Spectral Methods in MATLAB (SIAM, Philadelphia, 2000).
42. A. Jameson, " Analysis and design of numerical schemes for gas dynamics. 1: Artificial diffusion, upwind biasing limiters, and their effect on accuracy and multigrid convergence., " Int. J. Comput. Fluid Dyn., 4, 171 (1995).
43. J. D. Skufca and E. M. Bollt, " Mostly conjugate: Relating dynamical systems-Beyond homeomorphism., " SIAM J. Appl. Dyn. Syst. (submitted for publication).
44. E. P. Simoncelli, " Design of multi-dimensional derivative filters., " IEEE Trans. Image Process. 1, 790 (1994).