Non-rigid Free-Form 2D-3D Registration Using Statistical Deformation Model

  • Guoyan ZhengEmail author
  • Weimin Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9352)


This paper presents a non-rigid free-from 2D-3D registration approach using statistical deformation model (SDM). In our approach the SDM is first constructed from a set of training data using a non-rigid registration algorithm based on b-spline free-form deformation to encode a priori information about the underlying anatomy. A novel intensity-based non-rigid 2D-3D registration algorithm is then presented to iteratively fit the 3D b-spline-based SDM to the 2D X-ray images of an unseen subject, which requires a computationally expensive inversion of the instantiated deformation in each iteration. In this paper, we propose to solve this challenge with a fast B-spline pseudo-inversion algorithm that is implemented on graphics processing unit (GPU). Experiments conducted on C-arm and X-ray images of cadaveric femurs demonstrate the efficacy of the present approach.


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  1. 1.
    Sadowsky, O., Chintalapani, G., Taylor, R.H.: Deformable 2D-3D registration of the pelvis with a limited field of view, using shape statistics. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 519–526. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  2. 2.
    Ahmad, O., Ramamurthi, K., et al.: Volumetric DXA (VXA) - A new method to extract 3D information from multiple in vivo DXA images. J. Bone Miner. Res. 25, 2468–2475 (2010)CrossRefGoogle Scholar
  3. 3.
    Zheng, G.: Personalized x-ray reconstruction of the proximal femur via intensity-based non-rigid 2D-3D registration. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 598–606. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  4. 4.
    Whitmarsh, T., Humbert, L., et al.: Reconstructing the 3D shape and bone mineral density distribution of the proximal femur from dual-energy X-ray absorptiometry. IEEE T. Med. Imaging 30, 2101–2114 (2011)CrossRefGoogle Scholar
  5. 5.
    Lucas, B.C., Otake, Y., Armand, M., Taylor, R.H.: An active contour method for bone cement reconstruction from C-arm X-ray images. IEEE T. Med. Imaging 31, 860–869 (2012)CrossRefGoogle Scholar
  6. 6.
    Markelj, P., Tomazevic, D., et al.: A review of 3D/2D registration methods for image-guided interventions. Med. Image Anal. 16, 642–661 (2012)CrossRefGoogle Scholar
  7. 7.
    Yu, W., Zheng, G.: Personalized x-ray reconstruction of the proximal femur via a new control point-based 2D–3D registration and residual complexity minimization. In: VCBM 2014, pp. 155–162 (2014)Google Scholar
  8. 8.
    Rueckert, D., Frangi, A.F., Schnabel, J.A.: Automatic construction of 3D statistical deformation models using non-rigid registration. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 77–84. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  9. 9.
    Loeckx, D., et al.: Temporal subtraction of thorax CR images using a statistical deformation model. IEEE T. Med. Imaging 22, 1490–1504 (2003)CrossRefGoogle Scholar
  10. 10.
    Barratt, D.C., et al.: Instantiation and registration of statistical shape models of the femur and pelvis using 3D ultrasound imaging. Med. Image Anal. 12, 358–374 (2008)CrossRefGoogle Scholar
  11. 11.
    Onofrey J., Papademetris X., Staib L.: Low-Dimensional Non-rigid Image Registration Using Statistical Deformation Models from Semi-Supervised Training Data. IEEE T. Med. Imaging (2015) (in press)Google Scholar
  12. 12.
    Pszczolkowski, S., Pizarro, L., Guerrero, R., Rueckert, D.: Nonrigid free-form registration using landmark-based statistical deformation models. In: Proc. SPIE, Medical Imaging, vol. 8314 (2012). doi:10.1117/12.911441Google Scholar
  13. 13.
    Klein, S., Staring, M., et al.: Elastix: a toolox for intensity-based medical image registration. IEEE T. Med. Imaging 29, 196–205 (2010)CrossRefGoogle Scholar
  14. 14.
    Rueckert, D., Sonoda, L.I., et al.: Nonrigid registration using free-form deformations: Application to breast MR images. IEEE T. Med. Imaging 18, 712–721 (1999)CrossRefGoogle Scholar
  15. 15.
    Tristán, A., Arribas, J.I.: A fast B-spline pseudo-inversion algorithm for consistent image registration. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 768–775. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  16. 16.
    Zheng, G.: Effective incorporating spatial information in a mutual information based 3D–2D registration of a CT volume to X-ray images. Comput. Med. Imag. Grap. 34, 553–562 (2010)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Institute for Surgical Technology and BiomechanicsUniversity of BernBernSwitzerland

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