Diffeomorphic Matching and Dynamic Deformable Surfaces in 3d Medical Imaging

Computational Methods in Applied Mathematics

Volumn 10, Issue 3, 2010, Pages 235-274

  Azencott, R ^a,b   Glowinski, R ^a   He, J ^a   Jajoo, A ^a   Li, Y ^a   Martynenko, A ^a   Hoppe, R H W ^a,c   Benzekry, S ^d   Little, S H ^e   Zoghbi, W A ^e  

^a University of Houston   (United States)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c UNIVERSITY OF AUGSBURG   (Germany)

^d Medical Office   (United States)

^e HOUSTON METHODIST RESEARCH INSTITUTE   (United States)

Author keywords

deformable surfaces; diffeomorphic image matching; Dirac measures; gradient method; medical image analysis; reproducing kernel Hilbert spaces

Indexed keywords

EID: 84989315530     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2010-0014     Document Type: Article

References (38)

1. N. Arad, N. Dyn, D. Reisfeld, and Y. Yeshurun, Image warping: application to facial expressions, CVGIP: Graphical Models and Image Proc, 56 (1994), pp. 161-172.
2. L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J. Math., 16 (1966), pp. 1-3.
3. V.I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à, l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble), 1 (1966), pp. 319-361.
4. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68, 337-404, 1950.
5. R. Azencott, Elastic deformations of soft 3D-shapes, IBIS Colloquium on Medical image analysis. The Methodist Hospital, Kiawah Island, 2006.
6. R. Azencott, R. Glowinski, and A. Ramos, A controllability approach to shape identification, Applied Math. Letters 21 (2008), pp. 861-865.
7. R. Azencott, S. Alexander, A. Aggarwaal, A. Jajoo, S. Jain, Y. Li, S. BenZekry (MD), S.H. Little (MD), W. Zoghbi (MD), New parameters to compare Mitral Annulus shapes extracted from 3D-echocardiography, submitted, 2010.
8. R. Azencott, A. Jajoo, S. Jain, Y. Li, A. Martynenko, S. BenZekry (MD), S.H. Little (MD), W. Zoghbi (MD), 3D-echocardiographic movies analysis: dynamic deformable models for Mitral Valve, in preparation, 2010.
9. M.F. Beg, M.I. Miller, A. Trouve, and L. Younes, Computing large deformations metric mappings via geodesic flows of diffeomorphisms, Int. J. Comp. Vis., 61(2005), pp 139-157.
10. L. G. Brown, A survey on image registration techniques, ACM Computing Surveys, 24 (1992), pp. 326-376.
11. Y. Cao, M. I. Miller, R. Winslow, and L. Younes, Large deformation metric mapping of vector fields, IEEE Trans. Med. Imaging, 24 (2005), pp. 1216-1230.
12. A. Chinchuluun, P. M. Pardalos, A. Migdalas, and L. Pitsoulis (eds.), Pareto Optimality, Game Theory and Equilibria, Springer, Berlin-Heidelberg-New York, 2008.
13. H. Chui and A. Rangarajan, A new point matching algorithm for non-rigid registration, Computer Vision and Understanding, 89 (2003), pp. 114-141.
14. M.Chupin, D. Hasboun, S. Baillet, and altri, Competitive segmentation of the hippocampus and volumetry in Alzheimer disease, In: 10th meeting of the Organization for Human Brain Mapping, 2004.
15. J.M. Coron, Control and Nonlinearity, Math. Surveys and Monographs, Vol. 136, American Mathematical Society, Providence, 2007.
16. P. Dupuis, U. Grenander, and M. I. Miller, Variational problems on flows of diffeomorphisms for image matching, Quart. Appl. Math, 56 (1998), pp. 587-600.
17. H. Drury, D.V. Essen, M. Corbetta, and A. Snyder, Surface based analysis of human cerebral cortex, In: Brain Warping, 337-363, Academic Press, 1999.
18. L. Greengard, and J Strain, Fast Gauss transform, SIAM Jour. Sci. Stat. Comp., 12 (1991), pp. 79-94.
19. J. Glaunes, Transport par difféomorphismes de points, de mesures et de courants pour la comparaison des formes et l'anatomie numérique, PhD Thesis, Universite Paris 13, 2005.
20. J. Glaunes, A. Qiu, M.I. Miller, and L. Younes, Large deformation diffeomorphic metric curve mapping, Int. J. Comp. Vision, 80 (2008), pp. 317-336.
21. J. Glaunes, A. Trouve, and L. Younes, Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching, in: 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognizion (CVPR'04), Vol. 2, IEEE Computer Society, Washington, DC, 2004, pp. 712-718.
22. J. Glaunes, M. Vaillant, and M. I. Miller, Landmark matching via large deformation diffeomorphisms on the sphere, J. Math. Imaging Vis, 20 (2003), pp. 179-200.
23. R. Glowinski, J.L. Lions, and J. He; Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach, Cambridge University Press, Cambridge, 2008.
24. H. Guo, A. Rangarajan, S. Joshi, and L. Younes, Non-rigid registration of shapes via diffeomorphic point matching, in: Proceedings of the 2004 Int. Symposium on Biomedical Imaging: From Nano to Macro, IEEE Computer Society, Washington, DC, 2004, pp. 924-927.
25. H. Guo, A. Rangarajan, and S. Joshi, Diffeomorphic point matching, in: Handbook of Mathematical Models in Computer Vision, Springer, Berlin-Heidelberg-New York, 2006, pp. 205-219.
26. U. Grenander, and M. I. Miller, Computational anatomy: an emerging discipline, Quart. App. Math, 56 (1998), pp. 617-694.
27. H. Guo, Diffeomorphic point matching with applications in medical image analysis, Ph.D. thesis, Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 2005.
28. S. Joshi and M. Miller, Landmark matching via, large deformation diffeomorphisms, IEEE Trans. Image Processing, 9 (2000), pp. 1357-1370.
29. E. Klassen, A. Srivastava, W. Mio, and S. Joshi, Analysis of planar shapes using geodesic paths on shape spaces, IEEE Trans. Pattern Analysis and Machine Intelligence, 26 (2004), pp. 372-383.
30. J.L. Lions, Controlabilite exacte, perturbation et stabilisation des syst'emes distribu.es, Masson, Paris, 1988.
31. I. Miller, A. Trouve, and L. Younes, On the metrics and Euler-Lagrange equations of computational anatomy, Ann. Review of Biomedical Engineering, 4 (2002), pp. 375-405.
32. M. I. Miller and L. Younes, Group action, diffeomorphism and matching: A general framework, Int. J. Comp. Vis, 41 (2001), pp. 61-84.
33. S. Saitoh, Theory of Reproducing Kernels and its Applications, Pitman Research Notes in Mathematics, Vol. 189, Longman, 1988.
34. L. Tartar, Introduction to Sobolev Spaces and Interpolation Theory, Springer, Berlin-Heidelberg-New York, 2007.
35. A. Trouve, Diffeomorphisms groups and pattern matching in image analysis, Int. J. of Comp. Vis., 28 (1998), pp. 213-221.
36. L. Younes, Computable elastic distances between shapes, SIAM J. Appl. Math. 58 (1998), pp. 565-586.
37. B. Zitova and J. Flusser, Image registration methods: A survey, Image and Vision Computing, 21 (2003), pp. 977-1000.
38. E. Zuazua, Controllability and observability of partial differential equations, Chapter 7 in Handbook of Differential Equations, Vol. 3, Evolutionary Equations, Elsevier, Amsterdam, 527-621, (2007).