A reparameterisation based approach to geodesic constrained solvers for curve matching

International Journal of Computer Vision

Volumn 99, Issue 1, 2012, Pages 103-121

  Cotter, Colin J ^a   Clark, Allan ^a   Peiró, Joaquim ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Computational anatomy; Curve registration; Geodesic shooting

Indexed keywords

COMPUTATIONAL ANATOMY; CONJUGATE MOMENTUM; CURVE MATCHING; CURVE REGISTRATION; DIFFEOMORPHISMS; DISCRETISATION; HAMILTONIAN EQUATIONS; LARGE DEFORMATIONS; MATCHING CONDITION; NONLINEAR OPTIMISATION; NUMERICAL ALGORITHMS; NUMERICAL CONVERGENCE; PARTICLE-MESH METHOD; ROBUST REGISTRATION; SHAPE SPACE;

ALGORITHMS; DEFORMATION; EQUATIONS OF MOTION; GEODESY; HAMILTONIANS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 84860505493     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-012-0520-0     Document Type: Article

References (51)

1. Allassonnière, S., Kuhn, E., & Trouvé, A. (2008). Map estimation of statistical deformable template via nonlinear mixed effect models: Deterministic and stochastic approaches. In Proc. of mathematical foundations of computational anatomy.
2. S. Allassonnière E. Kuhn A. Trouvé 2010 Construction of Bayesian deformable models via stochastic approximation algorithm: A convergence study Bernoulli 16 3 641 678 2730643 1220.62101 10.3150/09-BEJ229
3. Bauer, M., Harms, P., & Michor, P. W. (2010). Sobolev metrics on shape space of surfaces. Preprint.
4. M. Bauer P. Harms P. W. Michor 2012 Curvature weighted metrics on shape space of hypersurfaces in n-space Differential Geometry and Its Applications 30 1 33 41 06013276 10.1016/j.difgeo.2011.10.002
5. M. Beg M. Miller A. Trouvé L. Younes 2005 Computing large deformation metric mappings via geodesic flows of diffeomorphisms International Journal of Computer Vision 61 2 139 157 10.1023/B:VISI.0000043755.93987.aa 10.1023/B:VISI.0000043755.93987.aa
6. P. Besl N. McKay 1992 A method for registration of 3D shapes IEEE Transactions on Pattern Analysis and Machine Intelligence 14 239 256 10.1109/34.121791
7. G. Charpiat O. Faugeras R. Keriven 2005 Approximations of shape metrics and application to shape warping and empirical shape statistics Foundations of Computational Mathematics 1 1 58 2125690 10.1007/s10208-003-0094-x (Pubitemid 41310096)
8. Chetverikov, D., Svirko, D., Stepanov, D., & Krsek, P. (2002). The trimmed iterative closest point algorithm. In International conference on pattern recognition (pp. 545-548). (Pubitemid 44844547)
9. Cootes, T., Marsland, S., Twining, C., Smith, K., & Taylor, C. (2004). Groupwise diffeomorphic non-rigid registration for automatic model building. In T. Pajdla & J. Matas (Eds.), Lecture notes in computer science: Vol. 3024. Computer vision-ECCV 2004 (pp. 316-327). Berlin: Springer.
10. C. J. Cotter 2008 The variational particle-mesh method for matching curves Journal of Physics A: Mathematical and Theoretical 41 34 344,003 2456340 10.1088/1751-8113/41/34/344003 URL http://stacks.iop.org/1751-8121/41/i=34/a= 344003
11. C. Cotter D. Holm 2010 Geodesic boundary value problems with symmetry Journal of Geometric Mechanics 2 1 51 68 2646535 05762845 10.3934/jgm.2010.2.51
12. S. Cotter M. Dashti J. Robinson A. Stuart 2009 Bayesian inverse problems for functions and applications to fluid mechanics Inverse Problems 25 115,008 2558668 10.1088/0266-5611/25/11/115008
13. Davies, R., Twining, C., Cootes, T., Waterton, J., & Taylor, C. (2002). 3D statistical shape models using direct optimisation of description length. In A. Heyden, G. Sparr, M. Nielsen, & P. Johansen (Eds.), Lecture notes in computer science: Vol. 2352. Computer vision: ECCV 2002 (pp. 1-17). Berlin: Springer.
14. Durrleman, S., Pennec, X., Trouvé, A., Gerig, G., & Ayache, N. (2009). Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In Lecture notes in computer science: Vol. 5761. Medical image computing and computer-assisted intervention MICCAI 2009 (pp. 297-304).
15. J. Feldmar N. Ayache 1996 Rigid, affine and locally affine registration of free-form surfaces International Journal of Computer Vision 18 99 119 10.1007/BF00054998 (Pubitemid 126713871)
16. Fishbaugh, J., Durrleman, S., & Gerig, G. (2011). Estimation of smooth growth trajectories with controlled acceleration from time series shape data. In Proc. of medical image computing and computer assisted intervention (MICCAI'11).
17. Fletcher, P. T. (2004). Statistical variability in nonlinear spaces: Application to shape analysis and DT-MRI. Ph.D. thesis, Department of Computer Science, University of North Carolina.
18. P. T. Fletcher C. Lu M. Pizer S. Joshi 2004 Principal geodesic analysis for the study of nonlinear statistics of shape IEEE Transactions on Medical Imaging 23 995 1005 10.1109/TMI.2004.831793
19. Fletcher, P. T., Venkatasubramanian, S., & Joshi, S. (2008). Robust statistics on Riemannian manifolds via the geometric median. In Computer vision and pattern recognition (pp. 1-8).
20. J. Frank S. Reich 2004 The hamiltonian particle-mesh method for the spherical shallow water equations Atmospheric Science Letters 5 5 89 95 10.1002/asl.70
21. Gambaruto, A. M., Taylor, D. J., & Doorly, D. J. (2008). Modelling nasal airflow using a Fourier descriptor representation of geometry. International Journal for Numerical Methods in Fluids, 2071-2091. doi: 10.1002/fld.1866.
22. F. Gay-Balmaz T. S. Ratiu 2011 Clebsch optimal control formulation in mechanics Journal of Geometric Mechanics 3 1 41 79 2794295 1233.49005 10.3934/jgm.2011.3.41
23. Glaunes, J., Trouve, A., & Younes, L. (2006). Modeling planar shape variation via hamiltonian flows of curves. In H. Krim Jr. & Y. A. (Eds.), Statistics and analysis of shapes. Basel: Birkhäuser.
24. J. Glaunès A. Qiu M. I. Miller L. Younes 2008 Large deformation diffeomorphic metric curve mapping International Journal of Computer Vision 80 3 317 336 10.1007/s11263-008-0141-9 10.1007/s11263-008-0141-9
25. Granger, S., & Pennec, X. (2006). Multi-scale em-icp: A fast and robust approach for surface registration. In A. Heyden, G. Sparr, M. Nielsen, & P. Johansen (Eds.), Lecture notes in computer science: Vol. 2353. Computer vision ECCV 2002 (pp. 69-73). Berlin: Springer.
26. L. Greengard J. Strain 1991 The fast Gauss transform SIAM Journal of Scientific Statistical Computing 12 79 94 1078797 0721.65089 10.1137/0912004
27. U. Grenander M. Miller 1998 Computational anatomy: an emerging discipline Quarterly of Applied Mathematics LVI 4 617 694 1668732 (Pubitemid 128597100)
28. Khesin, B., & Wendt, R. (2008). Ergebnisse der Mathematik und Grenzgebiete 3. Folge: Vol. 51. Geometry of infinite-dimensional groups. Berlin: Springer. Chap. 1
29. Kilian, M., Mitra, N. J., & Pottmann, H. (2007). Geometric modeling in shape space. ACM Transactions on Graphics, 26.
30. Kurtek, S., Klassen, E., Ding, Z., & Srivastava, A. (2010). A novel riemannian framework for shape analysis of 3d objects. In IEEE computer vision and pattern recognition (pp. 1625-1632).
31. Kurtek, S., Klassen, E., Ding, Z., Avison, M. J., & Srivastava, A. (2011a). Parameterization-invariant shape statistics and probabilistic classification of anatomical surfaces. In Lecture notes in computer science: Vol. 6801. Information processing in medical imaging (pp. 147-158). Berlin: Springer.
32. S. Kurtek E. Klassen Z. Ding S. Jacobson J. Jacobson M. Avison A. Srivastava 2011 Parameterization-invariant shape comparisons of anatomical surfaces IEEE Transactions on Medical Imaging 30 3 849 858 10.1109/TMI.2010. 2099130
33. R. McLachlan S. Marsland 2007 Discrete mechanics and optimal control for image registration ANZIAM Journal 48 C 1 16 2318548
34. P. W. Michor D. Mumford 2006 Riemannian geometries on spaces of plane curves Journal of the European Mathematical Society 8 1 1 48 2201275 1101.58005 10.4171/JEMS/37 (Pubitemid 43169774)
35. P. W. Michor D. Mumford 2007 An overview of the riemannian metrics on spaces of curves using the hamiltonian approach Applied and Computational Harmonic Analysis 23 1 74 113 2333829 1116.58007 10.1016/j.acha.2006.07.004 (Pubitemid 46856884)
36. M. Miller L. Younes 2001 Group actions, homeomorphisms, and matching: A general framework International Journal of Computer Vision 41 61 84 1012.68714 10.1023/A:1011161132514 (Pubitemid 32512206)
37. Nocedal, J., & Wright, S. (2006). Practical methods of optimization (2nd edn.). New York: Wiley.
38. T. Oliphant 2007 Python for scientific computing Computing in Science & Engineering 9 3 10 20 10.1109/MCSE.2007.58 (Pubitemid 46646860)
39. Powell, M. (1995). A thin plate spline method for mapping curves into curves in two dimensions. In Computational techniques and applications (pp. 43-57).
40. E. Sharon D. Mumford 2006 2d-shape analysis using conformal mapping International Journal of Computer Vision 70 1 55 75 10.1007/s11263-006-6121-z 10.1007/s11263-006-6121-z (Pubitemid 43855867)
41. A. Srivastava E. Klassen S. H. Joshi I. H. Jermyn 2011 Shape analysis of elastic curves in Euclidean spaces IEEE Transactions on Pattern Analysis and Machine Intelligence 33 1415 1428 10.1109/TPAMI.2010.184
42. G. Sundaramoorthi A. Mennucci S. Soatto A. Yezzil 2011 A new geometric metric in the space of curves with applications to tracking deforming objects by filtering and prediction SIAM Journal on Imaging Sciences 4 109 145 2792407 1214.93033 10.1137/090781139
43. Taylor, D., Doorly, D., & Shroter, R. (2009). Airflow in the human nasal cavity: an inter-subject comparison. In ASME summer bioengineering conference (pp. 1071-1072). Amer. Soc. Mechanical Engineers.
44. Trouvé, A., & Vialard, F. X. (2010, to appear). Shape splines and stochastic shape evolution: a second order point of view. Quarterly of Applied Mathematics.
45. A. Trouve L. Younes 2005 Local geometry of deformable templates SIAM Journal on Mathematical Analysis 37 1 17 59 10.1137/S0036141002404838 2176922 1090.58008 10.1137/S0036141002404838 (Pubitemid 43265726)
46. Vaillant, M., & Glaunes, J. (2005). Surface matching via currents. In Lecture notes in computer science:Vol. 3565. IPMI (pp. 381-392). Berlin: Springer.
47. Vialard, F. X. (2009). Hamiltonian approach to shape spaces in a diffeomorphic framework: From the discontinuous image matching problem to a stochastic growth model. Ph.D. thesis, ENS Cachan.
48. F. X. Vialard L. Risser D. Rueckert C. Cotter 2012 Diffeomorphic 3d image registration via geodesic shooting using an efficient adjoint calculation International Journal of Computer Vision 10.1007/s11263-011-0481-8
49. L. Younes 2007 Jacobi fields in groups of diffeomorphisms and applications Quarterly of Applied Mathematics 65 113 134 2313151 1128.53040
50. L. Younes P. Michor J. Shah D. Mumford 2008 A metric on shape spaces with explicit geodesics Rendiconti Lincei - Math. e Appl. 19 1 25 57 2383560 1142.58013 10.4171/RLM/506
51. Z. Zhang 1994 Iterative point matching for registration of free-form curves and surfaces International Journal of Computer Vision 13 119 152 10.1007/BF01427149