Piecewise Affine Registration of Biological Images

  • Alain Pitiot
  • Grégoire Malandain
  • Eric Bardinet
  • Paul M. Thompson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2717)


his manuscript tackles the registration of 2D biological images (histological sections or autoradiographs) to 2D images from the same or different modalities (e.g., histology or MRI). The process of acquiring these images typically induces composite transformations that can be modeled as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. A hierarchical clustering algorithm then automatically partitions this field into a number of classes from which we extract independent pairs of sub-images. Finally, the pairs of sub-images are, independently, affinely registered and a hybrid affine/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach under a variety of conditions, and discuss examples using real biomedical images, including MRI, histology and cryosection data.


Input Image Reference Image Geodesic Distance Local Transformation Biological Image 
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.


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  1. 1.
    Collins, D.L., Zijdenbos, A.P., Paus, T., Evans, A.C.: Use of registration for cohort studies. In: Hajnal, J., Hawkes, D., Hill, D. (eds.) Medical Image Registration (2003)Google Scholar
  2. 2.
    Thompson, P.M., Woods, R.P., Mega, M.S., Toga, A.W.: Mathematical/ computational challenges in creating deformable and probabilistic atlases of the human brain. Human Brain Mapping 9, 81–92 (2000)CrossRefGoogle Scholar
  3. 3.
    Maintz, J.B.A., Viergever, M.A.: A survey of medical image registration. Medical Image Analysis 2, 1–36 (1998)CrossRefGoogle Scholar
  4. 4.
    Roche, A., Malandain, G., Ayache, N.: Unifying Maximum Likelihood Approaches in Medical Image Registration. International Journal of Imaging Systems and Technology: Special Issue on 3D Imaging 11, 71–80 (2000)Google Scholar
  5. 5.
    Woods, R.P., Grafton, S.T., Holmes, C.J., Cherry, S.R., Mazziotta, J.C.: Automated image registration: I. General methods and intrasubject, intramodality validation. J. Comput. Assist. Tomogr. 22, 141–154 (1998)Google Scholar
  6. 6.
    Davatzikos, C.: Spatial transformation and registration of brain images using elastically deformable models. CVIU 66, 207–222 (1997)Google Scholar
  7. 7.
    Gee, J.C., Reivich, M., Bajcsy, R.: Elastically Deforming 3D Atlas to Match Anatomical Brain Images. J. Comput. Assist. Tomogr. 17, 225–236 (1993)CrossRefGoogle Scholar
  8. 8.
    Christensen, G.E.: Consistent linear-elastic transformations for image matching. In: Kuba, A., Sámal, M., Todd-Pokropek, A. (eds.) IPMI 1999. LNCS, vol. 1613, pp. 224–237. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Likar, B., Pernus, F.: Registration of Serial Transverse Sections of Muscular Fibers. Cytometry 37, 93–106 (1999)CrossRefGoogle Scholar
  10. 10.
    Little, J.A., Hill, D.L.G., Hawkes, D.J.: Deformations Incorporating Rigid Structures. Computer Vision and Image Understanding 66, 223–232 (1997)CrossRefGoogle Scholar
  11. 11.
    Ourselin, S., Roche, A., Subsol, G., Pennec, X., Ayache, N.: Reconstructing a 3D Structure from Serial Histological Sections. Image and Vision Computing 19, 25–31 (2001)CrossRefGoogle Scholar
  12. 12.
    Dengler, J.: Estimation of discontinuous displacement vector fields with the minimum description length criterion. In: Proc. of CVPR, pp. 276–282. IEEE, Los Alamitos (1991)Google Scholar
  13. 13.
    Penney, G.P., Weese, J.W., Little, J.A., Desmedt, P., Hill, D.L.G., Hawkes, D.J.: A comparison of similarity measures for use in 2D-3D medical image registration. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 1153–1161. Springer, Heidelberg (1998)Google Scholar
  14. 14.
    Backer, E.: Computer-assisted reasoning in cluster analysis. Prentice-Hall, Englewood Cliffs (1995)Google Scholar
  15. 15.
    Johnson, S.C.: Hierarchical Clustering Schemes. Psychometrika 2, 241–254 (1967)CrossRefGoogle Scholar
  16. 16.
    Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. PAMI 1, 224–227 (1979)Google Scholar
  17. 17.
    Rubner, Y., Tomasi, C., Guibas, L.: A metric for distributions with applications to image databases. In: Proc. of ICCV, Bombay, India. IEEE, Los Alamitos (1998)Google Scholar
  18. 18.
    Haker, S., Angenent, S., Tannenbaum, A.: Minimizing Flows for the Monge- Kantorovich Problem. SIAM Journal of Math Analysis (2003) (to appear )Google Scholar
  19. 19.
    Horn, B.K.P.: Closed-form solution of absolute orientation using unit quaternions. Journal of the Optical Society of America A 4, 629–642 (1987)CrossRefGoogle Scholar
  20. 20.
    Kjems, U., Hansen, L.K., Chen, C.T.: A non-linear 3d brain co-registration method. In: Hansen, P.C. (ed.) Proceedings of the Interdisciplinary Inversion Workshop 4, Lyngby, Denmark, IMM, Technical University of Denmark (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alain Pitiot
    • 1
    • 2
  • Grégoire Malandain
    • 1
  • Eric Bardinet
    • 1
    • 3
  • Paul M. Thompson
    • 2
  1. 1.Epidaure, INRIASophia-AntipolisFrance
  2. 2.LONI, UCLA School of MedicineLos AngelesUSA
  3. 3.CNRS UPR640-LENAParisFrance

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