Flexible shape matching with finite element based LDDMM

International Journal of Computer Vision

Volumn 105, Issue 2, 2013, Pages 128-143

  Günther, Andreas ^a   Lamecker, Hans ^a   Weiser, Martin ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Adaptive finite elements; Currents; Diffeomorphic registration; Large deformation; Matching

Indexed keywords

ADAPTIVE FINITE ELEMENT; CLASSICAL APPROACH; DIFFEOMORPHIC REGISTRATIONS; INDIVIDUAL PARTICLES; LARGE DEFORMATION DIFFEOMORPHIC METRIC MAPPINGS; MATCHING; NUMERICAL EXPERIMENTS; NUMERICAL TREATMENTS;

MEDICAL IMAGING; OCEAN CURRENTS;

DEFORMATION;

EID: 84883192007     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-012-0599-3     Document Type: Article

References (28)

1. Adams, R. (1975). Sobolev spaces. New York: Academic Press.
2. Beg, M. F.; Miller, M. I.; Trouvé, A.; Younes, L. (2005). Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision, 61(2), 139-157. doi: 10.1023/B:VISI.0000043755.93987.aa.
3. Burger, M.; Ruthotto, L.; Modersitzki, J. (2011). A hyperelastic regularization energy for image registration. Münster: WWU Münster.
4. Camion, V.; Younes, L. (2001). Geodesic interpolating splines energy minimization methods in computer vision and pattern recognition. Berlin: Springer.
5. Cao, Y.; Miller, M. I.; Winslow, R. L.; Younes, L. (2005). Large deformation diffeomorphic metric mapping of vector fields. IEEE Transactions on Medical Imaging, 24(9), 1216-1230. (Pubitemid 41337161)
6. Ciarlet, P. (1987). The finite element method for elliptic problems. Amsterdam: North-Holland.
7. Cotter, C. (2008). The variational particle-mesh method for matching curves. Journal of Physics A: Mathematical and Theoretical, 41(34): 344003.
8. Deuflhard, P.; Weiser, M. (2012). Adaptive numerical solution of PDEs. Berlin: de Gruyter.
9. Dupuis, P.; Grenander, U.; Miller, M. I. (1998). Variational problems on flows of diffeomorphisms for image matching. Quarterly of Applied Mathematics, 56(3), 587-600.
10. Durrleman, S. (2010). Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution. Thèse de sciences (phd thesis), Université de Nice-Sophia Antipolis, Cedex.
11. Durrleman, S.; Pennec, X.; Trouvé, A.; Ayache, N. (2009). Statistical models of sets of curves and surfaces based on currents. Medical Image Analysis, 13(5), 793-808. doi: 10.1016/j.media.2009.07.007; includes special section on the 12th international conference on medical imaging and computer assisted intervention.
12. Federer, H. (1969). Geometric measure theory. Report of the 1969. Berlin: Springer-Verlag.
13. Glaunès, J. (2005). Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique. PhD thesis, Université Paris, Paris.
14. Glaunès. J.; Trouvé A.; Younes, L. (2004). Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching. In Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2 (pp. 712-718). Washington, DC: CVPR. doi: 10.1109/CVPR.2004.1315234.
15. Glaunès, J.; Qiu, A.; Miller, M. I.; Younes, L. (2008). Large deformation diffeomorphic metric curve mapping. International Journal of Computer Vision, 80(3), 317-336. doi: 10.1007/s11263-008-0141-9.
16. Günther, A.; Lamecker H.; Weiser, M.; (2011). Direct lddmm of discrete currents with adaptive finite elements. In X. Pennec, S. Joshi, & M. Nielsen (Eds.), Proceedings of 3rd MICCAI Workshop on Mathematical Foundations of Computational Anatomy (pp. 1-15). Beijing: MICCAI.
17. Haber, E.; Heldmann, S.; Modersitzki, J. (2008). Adaptive mesh refinement for nonparametric image registration. SIAM Journal on Scientific Computing, 30(6), 3012-3027. doi: 10.1137/070687724.
18. Joshi, S. C.; Miller, M. I. (2000). Landmark matching via large deformation diffeomorphisms. IEEE Transactions on Image Processing, 9(8), 1357-1370. doi: 10.1109/83.855431.
19. Kirk, B. S.; Peterson, J. W.; Stogner, R. H.; Carey, G. F. (2006). libMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulation. Engineering with Computers, 22(3-4), 237-254.
20. Marsland, S.; Twining, C. (2004). Constructing diffeomorphic representations for the groupwise analysis of non-rigid registrations of medical images. IEEE Transactions on Medical Imaging, 23(8), 1006-1020.
21. Mattheij, R. M.; Molenaar, J. (2002). Ordinary differential equations in theory and practice. Reprint of (1996) original. In Classics in applied mathematics. Philadelphia: SIAM.
22. Morgan, F. (2009). Geometric measure theory: A beginner's guide (4th ed.). New York: Elsevier.
23. Morita, S. (2001). Geometry of differential forms. New York: American Mathematical Society.
24. Risser, L.; Vialard, F. X.; Wolz, R.; Holm, D. D.; Rueckert, D. (2010). Simultaneous fine and coarse diffeomorphic registration: Application to atrophy measurement in Alzheimer's disease. In T. Jiang, N. Navab, J. Pluim, M. Viergever (Eds.), Medical image computing and computer-assisted intervention. Lecture notes in computer science, Vol. 6362 (pp. 610-617). Berlin/Heidelberg: Springer. doi: 10.1007/978-3-642-15745-5-75.
25. Sommer, S. H.; Nielsen, M.; Lauze, F. B.; Pennec, X. (2011). A multi-scale kernel bundle for LDDMM: Towards sparse deformation description across space and scales. In G. Szkely & H. Hahn (Eds.), Information processing in medical imaging. Lecture notes in computer science, Vol. 6801 (pp. 624-635). Berlin/Heidelberg: Springer. doi: 10.1007/978-3-642-22092-0-51.
26. Trouvé, A. (1995). An infinite dimensional group approach for physics based models in pattern recognition. Technical report. Baltimore: Johns Hopkins University.
27. Vaillant, M.; Glaunès, J. (2005). Surface matching via currents. In G. Christensen & M. Sonka (Eds.), Information processing in medical imaging. Lecture notes in computer science, Vol. 3565 (pp. 1-5). Berlin/Heidelberg: Springer. doi: 10.1007/11505730-32.
28. Younes, L. (2010). Shapes and diffeomorphisms. In Applied mathematical sciences, Vol. 171. Berlin: Springer. doi: 10.1007/978-3-642-12055-8.