The variational particle-mesh method for matching curves

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 34, 2008, Pages

  Cotter, C J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52349121017     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/34/344003     Document Type: Article

References (28)

1. Bertsekas D P 1982 Constrained Optimization and Lagrange Multiplier Methods (New York: Academic)
2. Beg M F, Miller M I, Trouvé A and Younes L 2005 Computing large deformation metric mappings via geodesics flows of diffeomorphisms Int. J. Comput. Vision 61 139-57
3. Cotter C J and Holm D D 2008 Continuous and discrete Clebsch variational principles Found. Comput. Mech. at press
4. Camassa R and Holm D D 1993 An integrable shallow water equation with peaked solitons Phys. Rev. Lett. 71 1661-4
5. Cotter C J and Holm D D 2008 Discrete momentum maps for lattice EPDiff Handb. Numer. Anal. at press
6. Cotter C J, Holm D D and Hydon P E 2007 Multisymplectic formulation of fluid dynamics using the inverse map Proc. R. Soc. A 463 2671-87
7. Cotter C J 2005 A general approach for producing Hamiltonian numerical schemes for fluid equations Preprint math.NA/0501468
8. Camion V and Younes L 2001 Geodesic interpolating splines EMMCVPR 2001 (Lecture Notes in Computer Sciences vol 2134) ed M Figueiredo, J Zerubia and A K Jain (Berlin: Springer)
9. Frank J, Gottwald G and Reich S 2002 A Hamiltonian particle-mesh method for the rotating shallow-water equations (Lecture Notes in Computational Science and Engineering vol 26) (Berlin: Springer) pp 131-42
10. Grenander U and Miller M I 1998 Computational anatomy: an emerging discipline Q. Appl. Math. LVI 617-94
11. Greengard L and Strain J 1991 The fast Gauss transform SIAM J. Sci. Stat. Comput. 12 79-94
12. Glaunes J, Trouvé A and Younes L 2004 Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching In IEEE Computer Society Conf. Computer Vision and Pattern Recognition vol 2 pp 712-8
13. Glaunes J, Trouve A and Younes L 2006 Modeling planar shape variation via Hamiltonian flows of curves Statistics and Analysis of Shapes ed H Krim and A Yezzi Jr (Basle: Birkhäuser)
14. Gunzburger M D 2003 Advances in design and control Perspectives in Flow Control and Optimization (Philadelphia, PA: SIAM)
15. Holm D D and Marsden J E 2004 Momentum maps and measure valued solutions of the Euler-Poincaré equations for the diffeomorphism group Progr. Math. 232 203-35 http://arxiv.org/ abs/nlin.CD/0312048
16. Holm D D, Marsden J E and Ratiu T S 1998 The Euler-Poincaré equations and semidirect products with applications to continuum theories Adv. Math. 137 1-81 http://xxx.lanl.gov/abs/chao-dyn/9801015
17. Junge O, Marsden J and Ober-Blobaum S 2005 Discrete mechanics and optimal control Proc. 16th IFAC World Congress
18. Jones Eric, Oliphant Travis and Peterson Pearu et al 2001 SciPy: open source scientific tools for Python http://www.scipy.org/
19. Lew A, Marsden J E, Ortiz M and West M 2003 An overview of variational integrators Finite Element Methods: 1970s and Beyond ed L P Franca (Spain: CIMNE) pp 85-146
20. Leimkuhler B and Reich S 2005 Simulating Hamiltonian Dynamics (Cambridge: Cambridge University Press)
21. McLachlan R and Marsland S 2007 Discrete mechanics and optimal control for image registration ANZIAM J. 48 C1-C16
22. McLachlan R I and Marsland S 2006 The Kelvin-Helmholtz instability of momentum sheets in the Euler equations for planar diffeomorphisms SIAM J. Appl. Dyn. Syst. 5 726-58
23. Mills A, Marsland S and Shardlow T 2006 Computing the geodesic interpolating spline Biomedical Image Registration (Berlin: Springer) pp 169-77
24. Miller M I, Trouvé A and Younes L 2003 Geodesic shooting in computational anatomy Technical Report Center for Imaging Science, Johns Hopkins University
25. Miller M I and Younes L 2001 Group action, diffeomorphism and matching: a general framework Int. J. Comp. Vis. 41 61-84
26. Twinings C, Marsland S and Taylor C 2002 Measuring geodesic distances on the space of bounded diffeomorphisms Proc. Conf. British Machine Vision (BMVC) (Cardiff, Sept. 2002) eds P L Rosin and D Marshall 2 847-56
27. Trouvé A and Younes L 2004 Metamorphoses through lie group action Technical Report Center for Imaging Science, Johns Hopkins University
28. Vaillant Marc and Glaunes Joan 2005 Surface matching via currents Proc. Conf. IPMI pp 381-92