Diffeomorphic Registration Using B-Splines

  • Daniel Rueckert
  • Paul Aljabar
  • Rolf A. Heckemann
  • Joseph V. Hajnal
  • Alexander Hammers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4191)


In this paper we propose a diffeomorphic non-rigid registration algorithm based on free-form deformations (FFDs) which are modelled by B-splines. In contrast to existing non-rigid registration methods based on FFDs the proposed diffeomorphic non-rigid registration algorithm based on free-form deformations (FFDs) which are modelled by B-splines. To construct a diffeomorphic transformation we compose a sequence of free-form deformations while ensuring that individual FFDs are one-to-one transformations. We have evaluated the algorithm on 20 normal brain MR images which have been manually segmented into 67 anatomical structures. Using the agreement between manual segmentation and segmentation propagation as a measure of registration quality we have compared the algorithm to an existing FFD registration algorithm and a modified FFD registration algorithm which penalises non-diffeomorphic transformations. The results show that the proposed algorithm generates diffeomorphic transformations while providing similar levels of performance as the existing FFD registration algorithm in terms of registration accuracy.


Control Point Manual Segmentation Registration Algorithm Segmentation Propagation Diffeomorphic Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics 56(4), 617–694 (1998)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Bajcsy, R., Kovačič, S.: Multiresolution elastic matching. Computer Vision, Graphics and Image Processing 46, 1–21 (1989)CrossRefGoogle Scholar
  3. 3.
    Gee, J.C.: On matching brain volumes. Pattern Recognition 32(1), 99–111 (1999)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Christensen, G.E., Rabbitt, R.D., Miller, M.I., Joshi, S.C., Grenander, U., Coogan, T.A., van Essen, D.C.: Topological properties of smooth anatomic maps. In: Information Processing in Medical Imaging: Proc. 14th International Conference (IPMI 1995), pp. 101–112 (1995)Google Scholar
  5. 5.
    Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing 5(10), 1435–1447 (1996)CrossRefGoogle Scholar
  6. 6.
    Bro-Nielsen, M., Gramkow, C.: Fast fluid registration of medical images. In: Höhne, K.H., Kikinis, R. (eds.) VBC 1996. LNCS, vol. 1131, pp. 267–276. Springer, Heidelberg (1996)Google Scholar
  7. 7.
    Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision 61(2), 139–157 (2005)CrossRefGoogle Scholar
  8. 8.
    Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J.: Non-rigid registration using free-form deformations: Application to breast MR images. IEEE Transactions on Medical Imaging 18(8), 712–721 (1999)CrossRefGoogle Scholar
  9. 9.
    Davatzikos, C.: Spatial transformation and registration of brain images using elastically deformable models. Computer Vision and Image Understanding 66(2), 207–222 (1997)CrossRefGoogle Scholar
  10. 10.
    Hellier, P., Barillot, C., Mémin, É., Perex, P.: Hierarchical estimation of a dense deformation field for 3d robust registration. IEEE Transactions on Medical Imaging 20(5), 388–402 (2001)CrossRefGoogle Scholar
  11. 11.
    Shen, D., Davatzikos, C.: Hammer: Hierarchical attribute matching mechanism for elastic registration. IEEE Transactions on Medical Imaging 21(11), 1421–1439 (2002)CrossRefGoogle Scholar
  12. 12.
    Thirion, J.P.: Image matching as a diffusion process: An analogy with Maxwell’s demons. Medical Image Analysis 2(3), 243–260 (1998)CrossRefGoogle Scholar
  13. 13.
    Ashburner, J., Hutton, C., Frackowiak, R., Johnsrude, I., Price, C., Friston, K.: Identifying global anatomical differences: Deformation-based morphometry. Human Brain Mapping 6, 638–657 (1998)CrossRefGoogle Scholar
  14. 14.
    Chung, M.K., Worsley, K.J., Paus, T., Cherif, C., Collins, D.L., Giedd, J.N., Rapoport, J.L., Evans, A.C.: A unified statistical approach to deformation-based morphometry. NeuroImage 14(3), 595–606 (2001)CrossRefGoogle Scholar
  15. 15.
    Cootes, T.F., Marsland, S., Twining, C.J., Smith, K., Taylor, C.J.: Groupwise diffeomorphic non-rigid registration for automatic model building. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 316–327. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Crum, W.R., Rueckert, D., Jenkinson, M., Kennedy, D., Smith, S.M.: A framework for detailed objective comparison of non-rigid registration algorithms in neuroimaging. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 679–686. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Kybic, J., Unser, M.: Fast parametric elastic image registration. IEEE Transactions on Image Processing 12(11), 1427–1442 (2003)CrossRefGoogle Scholar
  18. 18.
    Studholme, C., Hill, D.L.G., Hawkes, D.J.: An overlap invariant entropy measure of 3D medical image alignment. Pattern Recognition 32(1), 71–86 (1998)CrossRefGoogle Scholar
  19. 19.
    Lee, S., Wolberg, G., Chwa, K.Y., Shin, S.Y.: Image metamorphosis with scattered feature constraints. IEEE Transactions on Visualization and Computer Graphics 2(4), 337–354 (1996)CrossRefGoogle Scholar
  20. 20.
    Edwards, P.J., Hill, D.L.G., Little, J.A., Hawkes, D.J.: A three-component deformation model for image-guided surgery. Medical Image Analysis 2(4), 355–367 (1998)CrossRefGoogle Scholar
  21. 21.
    Choi, Y., Lee, S.: Injectivity conditions of 2D and 3D uniform cubic b-spline functions. Graphical Models 62(6), 411–427 (2000)zbMATHCrossRefGoogle Scholar
  22. 22.
    Hagenlocker, M., Fujimura, K.: CFFD: a tool for designing flexible shapes. The Visual Computer 14(5/6), 271–287 (1998)CrossRefGoogle Scholar
  23. 23.
    Hammers, A., Allom, R., Koepp, M.J., Free, S.L., Myers, R., Lemieux, L., Mitchell, T.N., Brooks, D.J., Duncan, J.S.: Three-dimensional maximum probability atlas of the human brain, with particular reference to the temporal lobe. Human Brain Mapping 19(4), 224–247 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Daniel Rueckert
    • 1
  • Paul Aljabar
    • 1
  • Rolf A. Heckemann
    • 2
  • Joseph V. Hajnal
    • 2
  • Alexander Hammers
    • 3
  1. 1.Department of ComputingImperial College LondonUK
  2. 2.Imaging Sciences Department, MRC Clinical Sciences CentreImperial College LondonUK
  3. 3.Division of Neuroscience and Mental Health, MRC Clinical Sciences CentreImperial College LondonUK

Personalised recommendations