Skip to main content
SpringerLink
Log in

A Review of Deformation Models in Medical Image Registration

  • Review Article
  • Published:
Journal of Medical and Biological Engineering Aims and scope Submit manuscript

Abstract

The main task of medical image registration is to match different modal images or the same modal images of different periods to provide the doctor with richer diagnostic information. Image registration has been widely used in image diagnostics, image-guided surgical planning and real-time interventional surgical navigation. The deformation model is a key part of the image registration process and can drive the image deformation to achieve a perfect match of the same organization in the two images. In practical application, it is important to establish a reasonable registration deformation model according to the research object, which directly affects the registration results. This paper presents a review of the deformation models used in medical image registration. The deformation model is summarized with respect to four aspects: the elastic image model, the viscoelastic image model, the optical flow model and the prior knowledge model. We primarily summarize the deformation models with good registration results in recent years and analyze their adaptability and existing defects. The purpose of this paper is to provide a reference for the selection of a deformation model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Brown, L. G. (1992). A survey of image registration techniques. ACM Computing Surveys, 24(4), 325–376.

    Google Scholar 

  2. Maintz, J. B. A., & Viergever, M. A. (1998). A survey of medical image registration. Medical Image Analysis, 33(1), 1–36.

    Google Scholar 

  3. Mäkelä, T., Clarysse, P., Sipilä, O., Pauna, N., Pham, Q. C., Katila, T., et al. (2002). A review of cardiac image registration methods. IEEE Transactions on Medical Imaging, 21(9), 1011–1021.

    Google Scholar 

  4. Holden, M. (2008). A review of geometric transformations for nonrigid body registration. IEEE Transactions on Medical Imaging, 27(1), 111–128.

    Google Scholar 

  5. Ryan, N., Heneghan, C., & Chazal, P. D. (2004). Registration of digital retinal images using landmark correspondence by expectation maximization. Image and Vision Computing, 22(11), 883–898.

    Google Scholar 

  6. Ramirez, L., Durdle, N. G., & Raso, V. J. (2006). A parameters selection scheme for medical image registration. In Nafips 2006–2006 Meeting of the North American Fuzzy Information Processing Society (Vol. 1, pp. 505–510).

  7. Fei, B., Wheaton, A., Lee, Z., Duerk, J. L., & Wilson, D. L. (2002). Automatic MR volume registration and its evaluation for the pelvis and prostate. Physics in Medicine & Biology, 47(5), 823–838.

    Google Scholar 

  8. Holden, M., Hill, D. L., Denton, E. R., Jarosz, J. M., Cox, T. C., Rohlfing, T., et al. (2000). Voxel similarity measures for 3-d serial mr brain image registration. IEEE Transactions on Medical Imaging, 19(2), 94.

    Google Scholar 

  9. Sotiras, A., Davatzikos, C., & Paragios, N. (2013). Deformable medical image registration: A survey. IEEE Transactions on Medical Imaging, 32(7), 1153.

    Google Scholar 

  10. Rohr, K. (2000). Elastic registration of multimodal medical images: A survey. Künstliche Intelligenz, 14, 11–17.

    Google Scholar 

  11. Broit, C. (1981). Optimal registration of deformed images. Philadelphia, PA: University of Pennsylvania.

    Google Scholar 

  12. Modersitzki, J. (2004). Numerical methods for image registration. Oxford: Oxford University Press.

    MATH  Google Scholar 

  13. Rueckert, D., Sonoda, L. I., Hayes, C., Hill, D. L. G., Leach, M. O., & Hawkes, D. J. (1999). Nonrigid registration using free-form deformations: Application to breast MR images. IEEE Transactions on Medical Imaging, 18(8), 712.

    Google Scholar 

  14. Rueckert, D., Aljabar, P., Heckemann, R. A., Hajnal, J. V., & Hammers, A. (2006). Diffeomorphic registration using b-splines. In Lecture notes in computer science (Vol. 9, pp. 702–709).

  15. Craene, M. D., Camara, O., Bijnens, B. H., & Frangi, A. F. (2009). Large diffeomorphic FFD registration for motion and strain quantification from 3D-US sequences. In International Conference on Functional Imaging and Modeling of the Heart (Vol. 5528, pp. 437–446).

  16. Christensen, G. E., & Johnson, H. J. (2001). Consistent image registration. IEEE Transactions on Medical Imaging, 20(7), 568–582.

    Google Scholar 

  17. Leow, A., Huang, S. C., Geng, A., Becker, J., Davis, S., Toga, A., et al. (2005). Inverse consistent mapping in 3D deformable image registration: Its construction and statistical properties. Information processing in medical imaging. Berlin: Springer.

    Google Scholar 

  18. Cachier, P., & Ayache, N. (2004). Isotropic energies, filters and splines for vectorial regularization. Journal of Mathematical Imaging & Vision, 20(3), 251–265.

    MathSciNet  Google Scholar 

  19. Mansi, T., Peyrat, J. M., Sermesant, M., Delingette, H., Blanc, J., Boudjemline, Y., et al. (2009). Physically-constrained diffeomorphic demons for the estimation of 3D myocardium strain from cine MRI. functional imaging and modeling of the heart. Berlin: Springer.

    Google Scholar 

  20. He, J., & Christensen, G. E. (2003). Large deformation inverse consistent elastic image registration. Information Processing in Medical Imaging, 18, 438–449.

    Google Scholar 

  21. Papademetris, X., Sinusas, A. J., Dione, D. P., Constable, R. T., & Duncan, J. S. (2000). Estimating 3D strain from 4D cine-MRI and echocardiography: In-vivo validation. Medical image computing and computer assisted intervention C MICCAI 2000. Berlin: Springer.

    Google Scholar 

  22. Sinusas, A. J., Papademetris, X., Constable, R. T., Dione, D. P., Slade, M. D., Shi, P., et al. (2001). Quantification of 3-d regional myocardial deformation: Shape-based analysis of magnetic resonance images. American Journal of Physiology Heart & Circulatory Physiology, 281(2), 698–714.

    Google Scholar 

  23. Veress, A. I., Gullberg, G. T., & Weiss, J. A. (2005). Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration. Journal of Biomechanical Engineering, 127(7), 1195.

    Google Scholar 

  24. Phatak, N. S., Maas, S. A., Veress, A. I., Pack, N. A., Bella, E. V. R. D., & Weiss, J. A. (2007). Strain measurement in the left ventricle during systole with deformable image registration. In International Conference on Functional Imaging and Modeling of the Heart (Vol. 13, pp. 32–40).

  25. Sundar, H., Davatzikos, C., & Biros, G. (2009). BiomechanicallyConstrained 4D Estimation of Myocardial Motion. In International Conference on Medical Image Computing & Computer-assisted Intervention (Vol. 12, p. 257).

  26. Ferrant, M., Nabavi, A., Macq, B., & Jolesz, F. A. (2000). Registration of 3-d intraoperative MR images of the brain using a finite-element biomechanical model. IEEE Transactions on Medical Imaging, 20(12), 1384–1397.

    Google Scholar 

  27. Clatz, O., Delingette, H., Talos, I. F., Golby, A. J., Kikinis, R., Jolesz, F. A., et al. (2005). Robust non-rigid registration to capture brain shift from intra-operative mri. IEEE Transactions on Medical Imaging, 24(11), 1417–1427.

    Google Scholar 

  28. Christensen, G. E. (1995). Mapping of hyperelastic deformable templates using the finite element method. Proceedings of SPIE, 2573, 252–265.

    Google Scholar 

  29. Pennec, X., Stefanescu, R., Arsigny, V., Fillard, P., & Ayache, N. (2005). Riemannian elasticity: A statistical regularization framework for nonlinear registration. Medical Image Computing & Computer-Assisted Intervention-MICCAI, 8, 943.

    Google Scholar 

  30. Yanovsky, I., Guyader, C. L., Leow, A., Thompson, P., & Vese, L. (2008). Unbiased volumetric registration via nonlinear elastic regularization. Miccai Workshop on Mathematical Foundations of Computational Anatomy.

  31. Ahmad, S., & Khan, M. F. (2015). Deformable image registration based on elastodynamics. Machine Vision and Applications, 26(5), 689–710.

    Google Scholar 

  32. Zhang, J., Wang, J., Wang, X., & Feng, D. (2014). The adaptive fem elastic model for medical image registration. Physics in Medicine & Biology, 59(1), 97.

    Google Scholar 

  33. Amit, Y. (1994). A nonlinear variational problem for image matching. SIAM Journal on Scientific Computing, 15(1), 207–224.

    MathSciNet  MATH  Google Scholar 

  34. Ashburner, J., & Friston, K. J. (1999). Nonlinear spatial normalization using basis functions. Human Brain Mapping, 7(4), 254.

    Google Scholar 

  35. Little, J. A., Hill, D. L. G., & Hawkes, D. J. (1996). Deformations incorporating rigid structures medical imaging. Computer Vision and Image Understanding, 66(2), 223–232.

    Google Scholar 

  36. Buhmann, M. (2000). Radial basis functions. Acta Numerica, 5(5), 1–38.

    MathSciNet  MATH  Google Scholar 

  37. Eric, T., & Jean-Yves, B. (2000). Elastic registration of MRI scans using fast DCT. Engineering in medicine and biology society, 2000. Proceedings of the International Conference of the IEEE, 4, 2854–2856.

    Google Scholar 

  38. Rohr, K., Fornefett, M., & Stiehl, H. S. (2003). Spline-based elastic image registration: Integration of landmark errors and orientation attributes. Computer Vision and Image Understanding, 90(2), 153–168.

    Google Scholar 

  39. Siddiqui, A. M., Masood, A., & Saleem, M. (2009). A locally constrained radial basis function for registration and warping of images. Pattern Recognition Letters, 30(4), 377–390.

    Google Scholar 

  40. Kohlrausch, J. (2005). A new class of elastic body splines for nonrigid registration of medical images. Journal of Mathematical Imaging and Vision, 23(3), 253–280.

    MathSciNet  Google Scholar 

  41. Cavoretto, R., & Rossi, A. D. (2008). A local IDW transformation algorithm for medical image registration. American Institute of Physics, 1048, 970–973.

    MATH  Google Scholar 

  42. Cavoretto, R., De Rossi, A., & Quatember, B. (2010). Landmark-based registration using a local radial basis function transformation. Journal of Numerical Analysis Industrial & Applied Mathematics, 5(5), 141–152.

    MathSciNet  MATH  Google Scholar 

  43. Allasia, G., Cavoretto, R., Rossi, A. D., Quatember, B., Recheis, W., Mayr, M., et al. (2010). Radial basis functions and splines for landmark based registration of medical images. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 1281(1), 716–719.

    Google Scholar 

  44. Fornefett, M., Rohr, K., & Stiehl, H. S. (2001). Radial basis functions with compact support for elastic registration of medical images. Image & Vision Computing, 19(1–2), 87–96.

    Google Scholar 

  45. Cavoretto, R., & Rossi, A. D. (2013). Analysis of compactly supported transformations for landmark-based image registration. Applied Mathematics & Information Sciences, 7(6), 2113–2121.

    MathSciNet  Google Scholar 

  46. Liu, J. X., Chen, Y. S., & Chen, L. F. (2010). Fast and accurate registration techniques for affine and nonrigid alignment of mr brain images. Annals of Biomedical Engineering, 38(1), 138.

    Google Scholar 

  47. Shusharina, N., & Sharp, G. (2012). Analytic regularization for landmark-based image registration. Physics in Medicine & Biology, 57(6), 1477–1498.

    Google Scholar 

  48. Bookstein, F. L. (1989). Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(6), 567–585.

    MATH  Google Scholar 

  49. Bookstein, F. L. (1991). Thin-plate splines and the atlas problem for biomedical images. In International Conference on Information Processing in Medical Imaging (Vol. 511, pp. 326–342).

  50. Rohr, K., Stiehl, H. S., Sprengel, R., Buzug, T. M., Weese, J., & Kuhn, M. H. (2001). Landmark-based elastic registration using approximating thin-plate splines. IEEE Transactions on Medical Imaging, 20(6), 526–534.

    Google Scholar 

  51. Wirth, M. A., & Gray, D. W. S. (2002). Nonrigid mammogram registration using mutual information. Proceedings of SPIE: The International Society for Optical Engineering, 4684, 562–573.

    Google Scholar 

  52. Quatember, B., Mayr, M., Recheis, W., Demertzis, S., Allasia, G., Rossi, A. D., et al. (2010). Geometric modelling and motion analysis of the epicardial surface of the heart. Mathematics and Computers in Simulation, 81(3), 608–622.

    MathSciNet  MATH  Google Scholar 

  53. Quatember, B., Recheis, W., Mayr, M., Demertzis, S., Allasia, G., Cavoretto, R., et al. (2010). Methods for accurate motion tracking and motion analysis of the beating heart wall. CMMSE, 12, 218–219.

    MATH  Google Scholar 

  54. Zhang, Z., & Yang, X. (2008). Elastic image warping using a new radial basic function with compact support. In International Conference on Biomedical Electronics and Devices (Vol. 28(31), pp. 216–219).

  55. Allasia, G., Cavoretto, R., & Rossi, A. D. (2012). A class of spline functions for landmark-based image registration. Mathematical Methods in the Applied Sciences, 35(8), 923–934.

    MathSciNet  MATH  Google Scholar 

  56. Wörz, S., & Rohr, K. (2014). Spline-based hybrid image registration using landmark and intensity information based on matrix-valued non-radial basis functions. International Journal of Computer Vision, 106(1), 76–92.

    MATH  Google Scholar 

  57. Wörz, S., Winz, M. L., & Rohr, K. (2008). Geometric alignment of 2D gel electrophoresis images using physics-based elastic registration. IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 48, 1135–1138.

    Google Scholar 

  58. Unser, M. (1999). Splines: A perfect fit for signal and image processing. Signal Processing Magazine IEEE, 16(6), 22–38.

    Google Scholar 

  59. Klein, S., Staring, M., & Pluim, J. P. (2007). Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines. IEEE Transactions on Image Processing, 16(12), 2879–2890.

    MathSciNet  Google Scholar 

  60. Ledesma Carbayo, M. J., Mahia, C. P. A., Perez, D. E., Garcia Fernandez, M. A., & Desco, M. (2006). Cardiac motion analysis from ultrasound sequences using nonrigid registration: Validation against doppler tissue velocity. Ultrasound in Medicine and Biology, 32(4), 483–490.

    Google Scholar 

  61. Prümmer, M., Hornegger, J., Lauritsch, G., Wigström, L., GirardHughes, E., & Fahrig, R. (2009). Cardiac c-arm CT: A unified framework for motion estimation and dynamic CT. IEEE Transactions on Medical Imaging, 28(11), 1836–1849.

    Google Scholar 

  62. Kybic, J., & Unser, M. (2003). Fast parametric elastic image registration. IEEE Transactions on Image Processing, 12(11), 1427–1442.

    Google Scholar 

  63. Sorzano, C. O. S., Thevenaz, P., & Unser, M. (2005). Elastic registration of biological images using vector-spline regularization. IEEE Transactions on Biomedical Engineering, 52(4), 652–663.

    Google Scholar 

  64. Cao, K., Du, K., Ding, K., Reinhardt, J. M., & Christensen, G. E. (2010). Regularized nonrigid registration of lung CT images by preserving tissue volume and vesselness measure. In Medical image analysis for the clinic—A grand challenge (pp. 43–54).

  65. Loeckx, D., Smeets, D., Keustermans, J., Hermans, J., Maes, F., & Vandermeulen, D., et al. (2010). 3D lung registration using splineMIRIT and robust tree registration (RTR). In Medical image analysis for the clinic: A grand challenge (pp. 109–117).

  66. Isola, A. A., Grass, M., & Niessen, W. J. (2010). Fully automatic nonrigid registration-based local motion estimation for motion-corrected iterative cardiac ct reconstruction. Medical Physics, 37(3), 1093–1109.

    Google Scholar 

  67. Nielsen, T., Manzke, R., Proksa, R., & Grass, M. (2005). Cardiac conebeam ct volume reconstruction using art. Medical Physics, 32(4), 851–860.

    Google Scholar 

  68. Klein, A., Andersson, J., Ardekani, B. A., Ashburner, J., Avants, B., Chiang, M. C., et al. (2009). Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. Neuroimage, 46(3), 786–802.

    Google Scholar 

  69. Sdika, Michaë. (2008). A fast nonrigid image registration with constraints on the jacobian using large scale constrained optimization. IEEE Transactions on Medical Imaging, 27(2), 271.

    Google Scholar 

  70. Ansorge, R. E., Sawiak, S. J., & Williams, G. B. (2009). Exceptionally fast non-linear 3D image registration using GPUs. In Nuclear Science Symposium Conference Record (pp. 4088–4094).

  71. Modat, M., Ridgway, G. R., Taylor, Z. A., Lehmann, M., Barnes, J., Hawkes, D. J., et al. (2010). Fast free-form deformation using graphics processing units. Computer Methods and Programs in Biomedicine, 98(3), 278–284.

    Google Scholar 

  72. Gruslys, A., Acosta-Cabronero, J., Nestor, P. J., Williams, G. B., & Ansorge, R. E. (2014). A new fast accurate nonlinear medical image registration program including surface preserving regularization. Medical Imaging IEEE Transactions on, 33(11), 2118–2127.

    Google Scholar 

  73. Christensen, G. E., et al. (1996). Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing, 5, 1435–1447.

    Google Scholar 

  74. Christensen, G. E., Joshi, S. C., & Miller, M. I. (1997). Volumetric transformation of brain anatomy. Medical Imaging IEEE Transactions on, 16(6), 864.

    Google Scholar 

  75. Dawant, B. M. (2002). Non-rigid registration of medical images: Purpose and methods, a short survey. In IEEE International Symposium on Biomedical Imaging (pp. 465–468).

  76. Christensen, G. E., Rabbitt, R. D., & Miller, M. I. (1996). Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing a Publication of the IEEE Signal Processing Society, 5(10), 1435–1447.

    Google Scholar 

  77. Bronielsen, M., & Gramkow, C. (1996). Fast fluid registration of medical images. Microscopy and Microanalysis, 28(12), 680–681.

    Google Scholar 

  78. Lester, H., & Arridge, S. R. (1999). A survey of hierarchical non-linear medical image registration. Pattern Recognition, 32(1), 129–149.

    Google Scholar 

  79. Wang, Y., & Staib, L. H. (2000). Physical model-based non-rigid registration incorporating statistical shape information. Medical Image Analysis, 4(1), 7.

    Google Scholar 

  80. D’Agostino, E., Maes, F., Vandermeulen, D., & Suetens, P. (2003). A viscous fluid model for multimodal non-rigid image registration using mutual information. Medical Image Analysis, 7(4), 565–575.

    MATH  Google Scholar 

  81. Crum, W. R., Tanner, C., & Hawkes, D. J. (2005). Anisotropic multiscale fluid registration: Evaluation in magnetic resonance breast imaging. Physics in Medicine & Biology, 50(21), 5153.

    Google Scholar 

  82. Chiang, M. C., Leow, A. D., Klunder, A. D., Dutton, R. A., Barysheva, M., Rose, S. E., et al. (2008). Fluid registration of diffusion tensor images using information theory. IEEE Transactions on Medical Imaging, 27(4), 442–456.

    Google Scholar 

  83. Hellier, P., & Barillot, C. (2001). Cooperation between local and global approaches to register brain images. In Proceedings of IPMI (pp. 315–328).

  84. Horn, B. K. P., & Schunck, B. G. (1981). Determining optical flow. In Artificial intelligence.

  85. Lucas, B. D., & Kanade, T. (1981). An iterative image registration technique with an application to stereo vision. In International Joint Conference on Artificial Intelligence (Vol. 73, pp. 674–679).

  86. Uras, S., Girosi, F., Verri, A., & Torre, V. (1988). A computational approach to motion perception. Biological Cybernetics, 60(2), 79–87.

    Google Scholar 

  87. Brox, T., Bruhn, A., Papenberg, N., & Weickert, J. (2004). High accuracy optical flow estimation based on a theory for warping. In Computer vision—ECCV 2004, lecture notes in computer science (Vol. 2034, pp. 25–36).

  88. Brox, T., & Malik, J. (2011). Large displacement optical flow: Descriptor matching in variational motion estimation. IEEE Transactions on Software Engineering, 33(3), 500–513.

    Google Scholar 

  89. Cuzol, A., Hellier, P., & Min, E. (2007). A low dimensional fluid motion estimator. International Journal of Computer Vision, 75(3), 329–349.

    Google Scholar 

  90. Saddi, K. A., Chefd’Hotel, C., & Cheriet, F. (2007). Large deformation registration of contrast-enhanced images with volume-preserving constraint. In Medical imaging (Vol. 6512). Bellingham: International Society for Optics and Photonics.

  91. Thirion, J. P. (1998). Image matching as a diffusion process: An analogy with Maxwells demons. Medical Image Analysis, 2(3), 243–260.

    Google Scholar 

  92. Wang, H., Dong, L., O’Daniel, J., Mohan, R., Garden, A. S., Ang, K. K., et al. (2005). Validation of an accelerated demons algorithm for deformable image registration in radiation therapy. Physics in Medicine & Biology, 50(50), 2887–2905.

    Google Scholar 

  93. Rogelj, P., & Kovacic, S. (2006). Symmetric image registration. Medical Image Analysis, 10(3), 484–493.

    Google Scholar 

  94. Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N. (2007). Nonparametric diffeomorphic image registration with the demons algorithm. Medical Image Computing and Computer Assisted Intervention, 10(2), 319–326.

    Google Scholar 

  95. Peyrat, J. M., Delingette, H., Sermesant, M., Pennec, X., Xu, C., & Ayache, N. (2008). Registration of 4D time-series of cardiac images with multichannel diffeomorphic demons. In International Conference on Medical Image Computing and Computer-Assisted Intervention (Vol. 11, pp. 972–979).

  96. Yeo, B. T. T., Vercauteren, T., Fillard, P., Peyrat, J. M., Pennec, X., Golland, P., et al. (2009). Dt-refind: Diffusion tensor registration with exact finite-strain differential. IEEE Transactions on Medical Imaging, 28(12), 1914–1928.

    Google Scholar 

  97. Yeo, B. T. T., Sabuncu, M. R., Vercauteren, T., Ayache, N., Fischl, B., & Golland, P. (2010). Spherical demons: Fast diffeomorphic landmark-free surface registration. IEEE Transactions on Medical Imaging, 29(3), 650.

    Google Scholar 

  98. Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N. (2008). Symmetric log-domain diffeomorphic registration: A demons-based approach. In Lecture notes in computer science (Vol. 5241, pp. 754–761). Berlin: Springer.

  99. Mansi, T., Pennec, X., Sermesant, M., Delingette, H., & Ayache, N. (2011). Ilogdemons: A demons-based registration algorithm for tracking incompressible elastic biological tissues. International Journal of Computer Vision, 92(1), 92–111.

    Google Scholar 

  100. Glocker, B., Komodakis, N., Paragios, N., & Navab, N. (2009). Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs. In International Symposium on Advances in Visual Computing (Vol. 5875, pp. 1101–1109). Berlin: Springer.

  101. Beuthien, B., Kamen, A., & Fischer, B. (2010). Recursive Green’s function registration. In International Conference on Medical Image Computing and Computer-Assisted Intervention (Vol. 13, pp. 546–553). Berlin: Springer.

  102. Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N. (2007). Nonparametric diffeomorphic image registration with the demons algorithm. Medical Image Computing Computer-Assisted Intervention, 10(2), 319–326.

    Google Scholar 

  103. Lombaert, H., Grady, L., Pennec, X., Peyrat, J. M., Ayache, N., & Cheriet, F. (2012). Groupwise spectral log-demons framework for atlas construction. In International Conference on Medical Computer Vision: Recognition Techniques and Applications in Medical Imaging (Vol. 7766, pp. 11–19). Berlin: Springer.

  104. Lorenzi, M., Ayache, N., Frisoni, G. B., & Pennec, X. (2013). Lcc-demons: A robust and accurate symmetric diffeomorphic registration algorithm. Neuroimage, 81(6), 470–483.

    Google Scholar 

  105. Arsigny, V., Commowick, O., Pennec, X., & Ayache, N. (2006). A logeuclidean framework for statistics on diffeomorphisms. In Lecture notes in computer science (Vol. 4190, pp. 924–931).

  106. Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N. (2009). Diffeomorphic demons: Efficient non-parametric image registration. Neuroimage, 45(1), 61–72.

    Google Scholar 

  107. Lombaert, H., Grady, L., Pennec, X., Ayache, N., & Cheriet, F. (2014). Spectral log-demons: Diffeomorphic image registration with very large deformations. International Journal of Computer Vision, 107(3), 254–271.

    Google Scholar 

  108. Bhatia, K. K., Rao, A., Price, A. N., Wolz, R., Hajnal, J. V., & Rueckert, D. (2014). Hierarchical manifold learning for regional image analysis. IEEE Transactions on Medical Imaging, 33(2), 444–461.

    Google Scholar 

  109. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323.

    Google Scholar 

  110. Tenenbaum, J. B., De, S. V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319.

    Google Scholar 

  111. Wu, Y., Ma, W., Gong, M., Su, L., & Jiao, L. (2015). A novel pointmatching algorithm based on fast sample consensus for image registration. IEEE Geoscience and Remote Sensing Letters, 12(1), 43–47.

    Google Scholar 

  112. Jia, Y., Zhang, Y., & Rabczuk, T. (2015). A novel dynamic multilevel technique for image registration. Computers and Mathematics with Applications, 69(9), 909–925.

    MathSciNet  Google Scholar 

  113. Saxena, S., & Singh, R. K. (2014). A survey of recent and classical image registration methods. International Journal of Signal Processing Image Processing & Pattern Recognition, 7(4), 167–176.

    Google Scholar 

  114. Liu, X., Yuan, Z., Zhu, J., & Xu, D. (2013). Medical image registration by combining global and local information: A chain-type diffeomorphic demons algorithm. Physics in Medicine & Biology, 58(23), 8359–8378.

    Google Scholar 

  115. Zhou, L., Zhou, L., Zhang, S., Zhen, X., Yu, H., Zhang, G., et al. (2014). Validation of an improved’ diffeomorphic demons’ algorithm for deformable image registration in image-guided radiation therapy. Biomedical Material Engineering, 23(1), 373–382.

    Google Scholar 

  116. Linger, M. E., & Goshtasby, A. A. (2015). Aerial image registration for tracking. IEEE Transactions on Geoscience & Remote Sensing, 53(4), 2137–2145.

    Google Scholar 

  117. Arnold, V. I. (1989). Mathematical method of classical mechanics. Graduate Texts in Mathematics, 20(1), x+207.

    Google Scholar 

  118. Miller, M. I., Trouv, A., & Younes, L. (2012). On the metrics and eulerlagrange equations of computational anatomy. Annual Review of Biomedical Engineering, 4(4), 375–405.

    Google Scholar 

  119. 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, 610(2), 139–157.

    Google Scholar 

  120. Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504.

    MathSciNet  MATH  Google Scholar 

  121. Zell, Andreas. (1994). Simulation neuronaler netze. Unknown, 45(3), 151–181.

    MATH  Google Scholar 

  122. Karniely, H., & Siegelmann, H. T. (2000). Sensor registration using neural networks. IEEE Transactions on Aerospace and Electronic Systems, 36(1), 85–101.

    Google Scholar 

  123. Li, X., & Wang, D. (2009). A sensor registration method using improved bayesian regularization algorithm. In International Joint Conference on Computational Sciences and Optimization (Vol. 2, pp. 195–199).

  124. Kramer, K. A., Stubberud, S. C., & Geremia, J. A. (2010). Target registration correction using the neural extended kalman filter. IEEE Transactions on Instrumentation and Measurement, 59(7), 1964–1971.

    Google Scholar 

  125. Fischer, P., Dosovitskiy, A., & Brox, T. (2014). Descriptor matching with convolutional neural networks: A comparison to sift. Computer Science.

  126. Mahapatra, D., & Sun, Y. (2012). Integrating segmentation information for improved MRF-based elastic image registration. IEEE Transactions on Image Processing, 21(1), 170–183.

    MathSciNet  MATH  Google Scholar 

  127. Kim, M., Wu, G., Yap, P. T., & Shen, D. (2012). A general fast registration framework by learning deformation appearance correlation. IEEE Transactions on Image Processing a Publication of the IEEE Signal Processing Society, 21(4), 1823–1833.

    MathSciNet  MATH  Google Scholar 

  128. Zhou, Y., & Bai, J. (2007). Multiple abdominal organ segmentation: An atlas-based fuzzy connectedness approach. IEEE Transactions on Information Technology in Biomedicine, 11(3), 348–352.

    Google Scholar 

  129. Okada, T., Yokota, K., Hori, M., Nakamoto, M., Nakamura, H., & Sato, Y. (2008). Construction of hierarchical multi-organ statistical atlases and their application to multi-organ segmentation from CT images. In International Conference on Medical Image Computing and ComputerAssisted Intervention (Vol. 11, pp. 502–509).

  130. Isgum, I., Staring, M., Rutten, A., Prokop, M., Viergever, M. A., & Van, G. B. (2009). Multi-atlas-based segmentation with local decision fusion—Application to cardiac and aortic segmentation in CT scans. IEEE Transactions on Medical Imaging, 28(7), 1000–1010.

    Google Scholar 

  131. Wolz, R., Chu, C., Misawa, K., Mori, K., & Rueckert, D. (2012). Multiorgan abdominal CT segmentation using hierarchically weighted subject specific atlases. In International Conference on Medical Image Computing & Computer-Assisted Intervention (Vol. 15, p. 10).

  132. Seghers, D., D’Agostino, E., Maes, F., Vandermeulen, D., & Suetens, P. (2004). Construction of a brain template from mr images using state-ofthe-art registration and segmentation techniques. In Lecture Notes in Computer Science (Vol. 3216, pp. 696–703).

  133. Joshi, S., Davis, B., & Jomier, M. G. (2004). Unbiased diffeomorphic atlas construction for computational anatomy. Neuroimage, 23(Suppl 1), 151.

    Google Scholar 

  134. Davis, B. C., Fletcher, P. T., Bullitt, E., & Joshi, S. (2007). Population shape regression from random design data. In IEEE, International Conference on Computer Vision (Vol. 90, pp. 1–7).

  135. Geng, X., Christensen, G. E., Gu, H., Ross, T. J., & Yang, Y. (2009). Implicit reference-based group-wise image registration and its application to structural and functional mri. Neuroimage, 47(4), 1341.

    Google Scholar 

  136. Marsland, S., Twining, C. J., & Taylor, C. J. (2008). A minimum description length objective function for groupwise non-rigid image registration. Image and Vision Computing, 26(3), 333–346.

    Google Scholar 

  137. Wu, G., Wang, Q., Jia, H., & Shen, D. (2012). Feature-based groupwise registration by hierarchical anatomical correspondence detection. Human Brain Mapping, 33(2), 253–271.

    Google Scholar 

  138. Sun, K., Udupa, J. K., Odhner, D., Tong, Y., Zhao, L., & Torigian, D. A. (2016). Automatic thoracic anatomy segmentation on CT images using hierarchical fuzzy models and registration. Medical Physics, 43(34), 1487–1655.

    Google Scholar 

  139. Zitová, B., & Flusser, J. (2003). Image registration methods: A survey. Image and Vision Computing, 21(11), 977–1000.

    Google Scholar 

  140. Salvado, O., & Wilson, D. L. (2007). Removal of local and biased global maxima in intensity-based registration. Medical Image Analysis, 11(2), 183–196.

    Google Scholar 

  141. Souza, A., Udupa, J. K., & Madabhushi, A. (2008). Image filtering via generalized scale. Medical Image Analysis, 12(2), 87–98.

    Google Scholar 

  142. Vovk, Uroš, Pernuš, Franjo, & Likar, Boštjan. (2007). A review of methods for correction of intensity inhomogeneity in MRI. IEEE Transactions on Medical Imaging, 26(3), 405–421.

    Google Scholar 

  143. Knops, Z. F., Maintz, J. B. A., Viergever, M. A., & Pluim, J. P. W. (2006). Normalized mutual information based pet-mr registration using k-means clustering and shading correction. Medical Image Analysis, 10(3), 432–439.

    MATH  Google Scholar 

  144. Erlandsson, K., Buvat, I., Pretorius, P. H., Thomas, B. A., & Hutton, B. F. (2012). A review of partial volume correction techniques for emission tomography and their applications in neurology, cardiology and oncology. Physics in Medicine & Biology, 57(21), 119–159.

    Google Scholar 

  145. Isaac, J. S., & Kulkarni, R. (2015). Super resolution techniques for medical image processing. In International Conference on Technologies for Sustainable Development (pp. 1–6). IEEE.

  146. Townsend, D. W. (2008). Dual-modality imaging: Combining anatomy and function. Journal of Nuclear Medicine Official Publication Society of Nuclear Medicine, 49(6), 938–955.

    Google Scholar 

  147. Janssens, G., Jacques, L., Xivry, J. O. D., Geets, X., & Macq, B. (2010). Diffeomorphic registration of images with variable contrast enhancement. International Journal of Biomedical Imaging, 2011(1687–4188), 891585.

    Google Scholar 

  148. Lötjönen, J., Wolz, R., Koikkalainen, J., Julkunen, V., Thurfjell, L., Lundqvist, R., et al. (2011). Fast and robust extraction of hippocampus from mr images for diagnostics of Alzheimer’s disease. Neuroimage, 56(1), 185.

    Google Scholar 

  149. Wu, G., Yap, P. T., Kim, M., & Shen, D. (2010). Tps-hammer: Improving hammer registration algorithm by soft correspondence matching and thin-plate splines based deformation interpolation. Neuroimage, 49(3), 2225–2233.

    Google Scholar 

  150. Xie, Z. (2004). Image registration using hierarchical b-splines. IEEE Transactions on Visualization and Computer Graphics, 10(1), 85–94.

    Google Scholar 

  151. Reinertsen, I., Lindseth, F., Unsgaard, G., & Collins, D. L. (2007). Clinical validation of vessel-based registration for correction of brain-shift. Medical Image Analysis, 11(4), 374–388.

    Google Scholar 

  152. Rivest-Henault, D., Sundar, H., & Cheriet, M. (2012). Nonrigid 2d/3d registration of coronary artery models with live fluoroscopy for guidance of cardiac interventions. IEEE Transactions on Medical Imaging, 31(8), 1557.

    Google Scholar 

  153. Kim, H. R., Kang, M. S., & Kim, M. H. (2014). Non-rigid registration of vascular structures for aligning 2D X-ray angiography with 3D CT angiography. In Advances in visual computing. New York: Springer.

  154. Yin, Y., Hoffman, E. A., & Lin, C. L. (2009). Mass preserving nonrigid registration of CT lung images using cubic b-spline. Medical Physics, 36(9), 4213–4222.

    Google Scholar 

  155. Lu, X., Yu, H., Zhao, Y., Hou, H., & Li, Y. (2015). Three-dimensional lung medical image registration based on improved demons algorithm. Optik, 127(4), 1893–1899.

    Google Scholar 

  156. Ehrhardt, J., Werner, R., Schmidt-Richberg, A., & Handels, H. (2011). Statistical modeling of 4d respiratory lung motion using diffeomorphic image registration. IEEE Transactions on Medical Imaging, 30(2), 251–265.

    Google Scholar 

  157. Murphy, K., Van, G. B., Reinhardt, J. M., Kabus, S., Ding, K., Deng, X., et al. (2011). Evaluation of registration methods on thoracic CT: The empire 10 challenge. IEEE Transactions on Medical Imaging, 30(11), 1901.

    Google Scholar 

  158. Wang, X., & Feng, D. D. (2004). Automatic hybrid registration for 2-dimensional CT abdominal images. In International Conference on Image and Graphics (pp. 208–211).

  159. Zhao, Q., Chou, C. R., Mageras, G., & Pizer, S. (2014). Local metric learning in 2d/3d deformable registration with application in the abdomen. IEEE Transactions on Medical Imaging, 33(8), 1592–1600.

    Google Scholar 

  160. Xu, Z., Lee, C. P., Heinrich, M. P., Modat, M., Rueckert, D., Ourselin, S., et al. (2016). Evaluation of six registration methods for the human abdomen on clinically acquired CT. IEEE Transactions on Biomedical Engineering, 63(8), 1563–1572.

    Google Scholar 

  161. Iglesias, J. E., & Sabuncu, M. R. (2014). Multi-atlas segmentation of biomedical images: A survey. Medical Image Analysis, 24(1), 205.

    Google Scholar 

  162. Wolz, R., Chu, C., Misawa, K., Fujiwara, M., Mori, K., & Rueckert, D. (2013). Automated abdominal multi-organ segmentation with subject-specific atlas generation. IEEE Transactions on Medical Imaging, 32(9), 1723.

    Google Scholar 

  163. Lu, C., Chelikani, S., Papademetris, X., Knisely, J. P., Milosevic, M. F., Chen, Z., et al. (2011). An integrated approach to segmentation and nonrigid registration for application in image-guided pelvic radiotherapy. Medical Image Analysis, 15(5), 772.

    Google Scholar 

  164. Rodriguez-Vila, B., Garcia-Vicente, F., & Gomez, E. J. (2012). Methodology for registration of distended rectums in pelvic ct studies. Medical Physics, 39(10), 6351–6359.

    Google Scholar 

  165. Dréan, G., et al. (2011). Evaluation of inter-individual pelvic CT-scans registration. IRBM, 32(5), 288–292.

    Google Scholar 

  166. Ghosal, S., & Ray, N. (2017). Deep deformable registration: Enhancing accuracy by fully convolutional neural net. Pattern Recognition Letters, 94, 81–84.

    Google Scholar 

  167. Chen, J., Liao, I. Y., Belaton, B., & Zaman, M. (2015). A neural network based point registration method for 3d rigid face image. World Wide Web-Internet & Web Information Systems, 18(2), 197–214.

    Google Scholar 

  168. Bai, W., Shi, W., Ledig, C., & Rueckert, D. (2015). Multi-atlas segmentation with augmented features for cardiac mr images. Medical Image Analysis, 19(1), 98.

    Google Scholar 

  169. Rikxoort, V. E. E., et al. (2010). Adaptive local multi-atlas segmentation: Application to the heart and the caudate nucleus. Medical Image Analysis, 14(1), 39–49.

    Google Scholar 

  170. Pearlman, P. C., Adams, A., Elias, S. G., Mali, W. P., Viergever, M. A., & Pluim, J. P. (2012). Mono- and multimodal registration of optical breast images. Journal of Biomedical Optics, 17(8), 080901-1.

    Google Scholar 

  171. Ireland, R. H., Dyker, K. E., Barber, D. C., Wood, S. M., Hanney, M. B., Tindale, W. B., et al. (2007). Nonrigid image registration for head and neck cancer radiotherapy treatment planning with PET/CT. International Journal of Radiation Oncology Biology Physics, 68(3), 952–957.

    Google Scholar 

  172. Gong, L., Pathak, S., Alessio, A., & Kinahan, P. (2006). Automatic arm removal in PET and CT images for deformable registration. Computerized Medical Imaging and Graphics, 30(8), 469–477.

    Google Scholar 

  173. Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K., & Eubank, W. (2003). PET-CT image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging, 22(1), 120.

    Google Scholar 

  174. Rubio-Guivernau, J. L., Ledesma-Carbayo, M. J., Lamare, F., Ortuno, J. E., Guerra, P., & Visvikis, D., et al. (2007). Respiratory motion correction in PET with super-resolution techniques and non-rigid registration. In Nuclear Science Symposium Conference Record, 2007. NSS’07. IEEE (Vol. 5, pp. 3560–3563). IEEE Xplore.

  175. Santos, J., Chaudhari, A. J., Joshi, A. A., Ferrero, A., Yang, K., Boone, J. M., et al. (2014). Non-rigid registration of serial dedicated breast CT, longitudinal dedicated breast ct and pet/ct images using the diffeomorphic demons method. Physica Medica, 30(6), 713.

    Google Scholar 

  176. Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., & Suetens, P. (1997). Multimodality image registration by maximization of mutual information. IEEE Transactions on Medical Imaging, 16(2), 187–198.

    Google Scholar 

  177. Studholme, C., Hill, D. L. G., & Hawkes, D. J. (1999). An overlap invariant entropy measure of 3d medical image alignment. Pattern Recognition, 32(1), 71–86.

    Google Scholar 

  178. Thevenaz, P., & Unser, M. (2000). Optimization of mutual information for multiresolution image registration. IEEE Transactions on Image Processing, 9, 2083–2099.

    MATH  Google Scholar 

  179. Rivaz, H., & Collins, D. L. (2012). Self-similarity weighted mutual information: A new nonrigid image registration metric. In Medical image computing and computer-assisted intervention—MICCAI 2012. Berlin: Springer.

  180. Tustison, N. J., Awate, S. P., Song, G., Cook, T. S., & Gee, J. C. (2011). Point set registration using Havrda–Charvat–Tsallis entropy measures. IEEE Transactions on Medical Imaging, 30(2), 451.

    Google Scholar 

  181. Wu, W. K. H., Chung, A. C. S., & Lam, H. H. N. (2013). Multi-resolution LC-MS images alignment using dynamic time warping and Kullback–Leibler distance. In IEEE International Conference on Image Processing (pp. 1681–1684). IEEE.

Download references

Acknowledgements

This research was supported by NSFC (No. 61572159), NCET (NCET-13-0756) and Distinguished Young Scientists Funds of Heilongjang Province (JC201302).

Author information

Authors and Affiliations

  1. Mechanical & Power Engineering College, Harbin University of Science and Technology, Xue Fu Road No. 52, Nangang District, Harbin, Heilongjiang, 150080, People’s Republic of China

    Monan Wang & Pengcheng Li

Authors
  1. Monan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pengcheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Monan Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, M., Li, P. A Review of Deformation Models in Medical Image Registration. J. Med. Biol. Eng. 39, 1–17 (2019). https://doi.org/10.1007/s40846-018-0390-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40846-018-0390-1

Keywords

Search

Navigation