Landmark and intensity-based registration with large deformations via quasi-conformal maps∗

SIAM Journal on Imaging Sciences

Volumn 7, Issue 4, 2014, Pages 2364-2392

  Lam, Ka Chun ^a   Lui, Lok Ming ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Beltrami coefficient; Intensity matching; Landmark matching; Large deformations; Quasi conformal mapping; Registration

Indexed keywords

ALGORITHMS; CURVE FITTING; DEFORMATION; IMAGE MATCHING;

BELTRAMI; INTENSITY MATCHING; LANDMARK MATCHING; QUASI-CONFORMAL MAPPINGS; REGISTRATION;

CONFORMAL MAPPING;

EID: 84919667764     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/130943406     Document Type: Article

References (61)

1. F. L. Bookstein, Principal warps: Thin-plate splines and the decomposition of deformations, IEEE Trans. Pattern Anal. Mach. Intell., 11 (1989), pp. 567-585.
2. T. Chanwimaluang and G. Fan, Hybrid retinal image registration, IEEE Trans. Inform. Tech. Biomed., 10 (2006), pp. 129-142.
3. P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces, SIAM J. Imaging Sci., to appear.
4. B. Fischl, M. Sereno, R. Tootell, and A. Dale, High-resolution intersubject averaging and a coordinate system for the cortical surface, Hum. Brain Mapp., 8 (1999), pp. 272-284.
5. F. Gardiner and N. Lakic, Quasiconformal Teichmüller Theory, American Mathematical Society, Providence, RI, 2000.
6. B. Glocker and N. Komodakis, DROP: Deformable Image Registration Using Discrete Optimization; Software available online from http://www.mrf-registration.net/.
7. B. Glocker, N. Komodakis, N. Paragios, and N. Navab, Approximated curvature penalty in nonrigid registration using pairwise MRFs, in Proceedings of the 5th International Symposium on Visual Computing (ISVC), Las Vegas, NV, 2009.
8. B. Glocker, N. Komodakis, N. Paragios, G. Tziritas, and N. Navab, Inter and intra-modal deformable registration: Continuous deformations meet efficient optimal linear programming, in Proceedings of the 20th International Conference on Information Processing in Medical Imaging, Kerkrade, The Netherlands, 2007.
9. B. Glocker, N. Komodakis, G. Tziritas, N. Navab, and N. Paragios, Dense image registration through MRFs and efficient linear programming, Med. Image Anal., 12 (2008), pp. 731-741.
10. J. Glaunès, A. Qiu, M. Miller, and L. Younes, Large deformation diffeomorphic metric curve mapping, Int. J. Comput. Vis., 80 (2008), pp. 317-336.
11. J. Glaunès, A. Qiu, M. Miller, and L. Younes, Surface matching via currents, in Proceedings of the 19th International Conference on Information Processing in Medical Imaging (IPMI’05), Lecture Notes in Comput. Sci. 3565, Springer, Berlin, 2005, pp. 381-392.
12. B. Glocker, A. Sotiras, N. Komodakis, and N. Paragios, Deformable medical image registration: Setting the state of the art with discrete methods, Annu. Rev. Biomed. Eng., 12 (2011), pp. 219-244.
13. J. Glaunès, M. Vaillant, and M. I. Miller, Landmark matching via large deformation diffeomorphisms on the sphere, J. Math. Imaging Vision, 20 (2004), pp. 179-200.
14. J. Glaunès, L. Younes, and A. Trouve, Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’04), Vol. 2, 2004, pp. 712-718.
15. X. F. Gu, Y. Wang, T. F. Chan, P. M. Thompson, and S.-T. Yau, Genus zero surface conformal mapping and its application to brain surface mapping, IEEE Trans. Med. Imag., 23 (2004), pp. 949-958.
16. X. F. Gu and S. Yau, Computing conformal structures of surfaces, Commun. Inf. Syst., 2 (2002), pp. 121-146.
17. S. Haker, S. Angenent, A. Tannenbaum, R. Kikinis, G. Sapiro, and M. Halle, Conformal surface parameterization for texture mapping, IEEE Trans. Visual Comput. Graph., 6 (2000), pp. 181-189.
18. X. Huang, Y. Sun, D. Metaxas, F. Sauer, and C. Xu, Hybrid image registration based on configural matching of scale-invariant salient region features, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshop (CVPRW’04), Vol. 11, 2004, pp. 167-174.
19. M. K. Hurdal and K. Stephenson, Discrete conformal methods for cortical brain flattening, NeuroImage, 45 (2009), pp. 86-98.
20. A. Jacobson and O. Sorkine, A cotangent Laplacian for images as surfaces, ACM Trans. Graph., 25 (2012), pp. 646-653.
21. M. Jin, J. Kim, F. Luo, and X. F. Gu, Discrete surface Ricci flow, IEEE Trans. Visual. Comput. Graph., 14 (2008), pp. 1030-1043.
22. H. J. Johnson and G. E. Christensen, Consistent landmark and intensity-based image registration, IEEE Trans. Med. Imag., 21 (2002), pp. 450-461.
23. S. Joshi and M. Miller, Landmark matching via large deformation diffeomorphisms, IEEE Trans. Image Process., 9 (2000), pp. 1357-1370.
24. O. Lehto and K. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlag, New York, 1973.
25. T. Lin, C. L. Guyader, I. Dinov, P. Thompson, A. Toga, and L. Vese, Gene expression data to mouse atlas registration using a nonlinear elasticity smoother and landmark points constraints, J. Sci. Comput., 50 (2012), pp. 586-609.
26. N. A. Lord, J. Ho, B. C. Vemuri, and S. Eisenschenk, Simultaneous registration and parcellation of bilateral hippocampal surface pairs for local asymmetry quantification, IEEE Trans. Med. Imag., 26 (2007), pp. 471-478.
27. L. M. Lui, S. Thiruvenkadam, Y. Wang, T. Chan, and P. Thompson, Optimized conformal parameterization of cortical surfaces using shape based matching of landmark curves, in Proceedings in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2005, 2008, pp. 494-502.
28. L. M. Lui, S. Thiruvenkadam, Y. Wang, P. M. Thompson, and T. F. Chan, Optimized conformal surface registration with shape-based landmark matching, SIAM J. Imaging Sci., 3 (2010), pp. 52-78.
29. L. M. Lui, Y. Wang, T. Chan, and P. Thompson, Landmark constrained genus zero surface conformal mapping and its application to brain mapping research, Appl. Numer. Math., 57 (2007), pp. 847-858.
30. L. M. Lui, T. W. Wong, W. Zeng, X. F. Gu, P. M. Thompson, T. F. Chan, and S. T. Yau, Optimization of surface registrations using Beltrami holomorphic flow, J. Sci. Comput., 50 (2012), pp. 557-585.
31. L. M. Lui, T. W. Wong, X. F. Gu, P. M. Thompson, T. F. Chan, and S. T. Yau, Hippocampal shape registration using Beltrami holomorphic flow, in Medical Image Computing and Computer Assisted Intervention (MICCAI), Part II, Lecture Notes in Comput. Sci. 6362, Springer-Verlag, Berlin, 2010, pp. 323-330.
32. L. M. Lui, K. C. Lam, T. W. Wong, and X. Gu, Texture map and video compression using Beltrami representation, SIAM J. Imaging Sci., 6 (2013), pp. 1880-1902.
33. L. M. Lui and T. C. Ng, A splitting method for diffeomorphism optimization problem using Beltrami
34. L. M. Lui, X. F. Gu, and S. T. Yau, Convergence analysis of an iterative algorithm for Teichmuller maps via harmonic energy optimization, Math. Comp., to appear.
35. L. M. Lui, K. C. Lam, S.-T. Yau, and X. Gu, Teichmüller mapping (T-Map) and its applications to landmark matching registrations, SIAM J. Imaging Sci., 7 (2014), pp. 391-426.
36. T. C. Ng, X. F. Gu, and L. M. Lui, Teichmuller extremal map of multiply-connected domains using Beltrami holomorphic flow, J. Sci. Comput., 60 (2013), pp. 249-275.
37. L. M. Lui and C. Wen, Geometric registration of high-genus surfaces, SIAM J. Imaging Sci., 7 (2014), pp. 337-365.
38. P. T. Choi and L. M. Lui, Fast Disk Conformal Parameterization for Simply-Connected Open Surfaces, Preprint, arXiv:1408.6974, 2014.
39. K. T. Ho and L. M. Lui, QCMC: Quasi-conformal Parameterization for Multiply-Connected Domains, preprint, arXiv:1403.6614, 2014.
40. K. C. Lam, X. F. Gu, and L. M. Lui, Genus-one surface registration via Teichmüller extremal mapping, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2014, Springer, Berlin, 2014, pp. 25-32.
41. O. Lyttelton, M. Boucher, S. Robbins, and A. Evans, An unbiased iterative group registration template for cortical surface analysis, NeuroImage, 34 (2007), pp. 1535-1544.
42. D. Paquin, D. Levy, and L. Xing, Hybrid multiscale landmark and deformable image registration, Math. Biosci. Eng., 4 (2007), pp. 711-737.
43. J. P. Thirion, Image matching as a diffusion process an analogy with Maxwell’s demons, Med. Image Anal., 15 (1996), pp. 112-115.
44. D. Tosun, M. Rettmann, and J. Prince, Mapping techniques for aligning sulci across multiple brains, Med. Image Anal., 8 (2004), pp. 295-309.
45. T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache, Diffeomorphic demons: Efficient nonparametric image registration, NeuroImage, 45 (2009), pp. S61-S72.
46. H. Wang, L. Dong, J. O’Daniel, R. Mohan, A. S. Garden, K. K. Ang, and R. Cheung, Validation of an accelerated "demons" algorithm for deformable image registration in radiation therapy, Phys. Med. Biol., 50 (2005), pp. 2887-2905.
47. Y. Wang, L. M. Lui, X. F. Gu, K. M. Hayashi, T. F. Chan, A. W. Toga, P. M. Thompson, and S.-T. Yau, Brain surface conformal parameterization using Riemann surface structure, IEEE Trans. Med. Imag., 26 (2007), pp. 853-865.
48. Y. L. Yang, J. Kim, F. Luo, S. Hu, and X. F. Gu, Optimal surface parameterization using inverse curvature map, IEEE Trans. Visual. Comput. Graph., 14 (2008), pp. 1054-1066.
49. B. T. Yeo, M. R. Sabuncu, T. Vercauteren, N. Ayache, B. Fischl, and P. Golland, Spherical demons: Fast diffeomorphic landmark-free surface registration, IEEE Trans. Med. Imag., 29 (2010), pp. 650-668.
50. W. Zeng and X. F. Gu, Registration for 3D surfaces with large deformations using quasi-conformal curvature flow, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’11), Colorado Springs, CO, 2011.
51. W. Zeng, L. M. Lui, F. Luo, T. F. Chan, S. T. Yau, and X. F. Gu, Computing quasiconformal maps using an auxiliary metric and discrete curvature flow, Numer. Math., 121 (2012), pp. 671-703.
52. W. Zeng, L. M. Lui, L. Shi, D. Wang, W. C. Chu, J. C. Cheng, J. Hua, S. T. Yau, and X. F. Gu, Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra, Med. Image Comput. Comput. Assist. Interv., 13 (2010), pp. 538-546.
53. B. Zitova and J. Flusser, Image registration methods: A survey, Image Vis. Comput., 21 (2003), pp. 977-1000.
54. C. R. Vogel, Computational Methods for Inverse Problems, Frontiers Appl. Math. 23, SIAM, Philadelphia, 2002.
55. T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache, Symmetric log-domain diffeomorphic registration: A demons-based approach, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2008, Springer, Berlin, Heidelberg, 2008, pp. 754-761.
56. S. Klein, M. Staring, K. Murphy, M. A. Viergever, and J. P. W. Pluim, Elastix: A toolbox for intensity based medical image registration, IEEE Trans. Med. Imag., 29 (2010), pp. 196-205.
57. D. P. Shamonin, E. E. Bron, B. P. F. Lelieveldt, M. Smits, S. Klein, and M. Staring, Fast parallel image registration on CPU and GPU for diagnostic classification of Alzheimer’s disease, Front. Neuroinform., 7 (2014), pp. 1-15.
58. J. Nocedal and S. Wright, Numerical Optimization, 2nd ed., Springer Ser. Oper. Res. Financ. Eng., Springer, New York, 2006.
59. M. J. D. Powell, On search directions for minimization algorithms, Math. Programming, 4 (1973), pp. 193-201.
60. A. Sotiras, C. Davatzikos, and N. Paragios, Deformable medical image registration: A survey, IEEE Trans. Med. Imag., 32 (2013), pp. 1153-1190.
61. J. B. Maintz and M. A. Viergever, A survey of medical image registration, Med. Image Anal., 2 (1998), pp. 1-36.