High Accuracy Optical Flow for 3D Medical Image Registration Using the Census Cost Function

  • Simon Hermann
  • René Werner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8333)


In 2004, Brox et al. described how to minimize an energy functional for dense 2D optical flow estimation that enforces both intensity and gradient constancy.

This paper presents a novel variant of their method, in which the census cost function is utilized in the data term instead of absolute intensity differences. The algorithm is applied to the task of pulmonary motion estimation in 3D computed tomography (CT) image sequences. The performance evaluation is based on DIR-lab benchmark data for lung CT registration. Results show that the presented algorithm can compete with current state-of-the-art methods in regards to both registration accuracy and run-time.


Medical image registration census cost function pulmonary motion estimation 4D CT gradient constancy 


  1. 1.
    Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High Accuracy Optical Flow Estimation Based on a Theory for Warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Brox, T.: From Pixels to Regions: Partial Differential Equations in Image Analysis. PhD thesis, Saarland University (2005)Google Scholar
  3. 3.
    Castillo, R., Castillo, E., Guerra, R., Johnson, V.E., McPhail, T., et al.: A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Phys. Med. Biol. 54, 1849–1870 (2009)CrossRefGoogle Scholar
  4. 4.
    Castillo, R., Castillo, E., Martinez, J., Guerrero, T.: Ventilation from four-dimensional computed tomography: density versus Jacobian methods. Phys. Med. Biol. 55, 4661–4685 (2010)CrossRefGoogle Scholar
  5. 5.
    Castillo, E., Castillo, R., White, B., Rojo, J., Guerrero, T.: Least median of squares filtering of locally optimal point matches for compressible flow image registration. Phys. Med. Biol. 57, 4827–4833 (2012)CrossRefGoogle Scholar
  6. 6.
    Gwosdek, P., Bruhn, A., Weickert, J.: High Performance Parallel Optical Flow Algorithms on the Sony Playstation 3. In: Proc. Vision, Modeling, and Visualization - VMV, pp. 253–262 (2008)Google Scholar
  7. 7.
    Heinrich, M.P., Jenkinson, M., Brady, M., Schnabel, J.A.: Discontinuity preserving regularisation for variational optical-flow registration using the modified Lp norm. In: Med. Image Anal. Clinic: A Grand Challenge, pp. 185–194 (2010)Google Scholar
  8. 8.
    Heinrich, M.P., Jenkinson, M., Gleeson, F.V., Brady, M., Schnabel, J.A.: Deformable multimodal registration with gradient orientation based on structure tensors. Annals of the BMVA, 1–11 (2011)Google Scholar
  9. 9.
    Heinrich, M.P., Jenkinson, M., Brady, M., Schnabel, J.A.: MRF-based deformable registration and ventilation estimation of lung CT. IEEE Trans. Medical Imaging 32, 1239–1248 (2013)CrossRefGoogle Scholar
  10. 10.
    Hermann, S., Werner, R.: TV-L1-based 3D Medical Image Registration with the Census Cost Function. In: Klette, R., Rivera, M., Satoh, S. (eds.) PSIVT 2013. LNCS, vol. 8333, pp. 149–161. Springer, Heidelberg (2014)Google Scholar
  11. 11.
    Hoog, A.C.B., Singh, T., Singla, P., Podgorsak, M.: Evaluation of advanced Lukas-Kanade optical flow on thoracic 4D-CT. J. Clin. Monit. Comput. 27, 433–441 (2013)CrossRefGoogle Scholar
  12. 12.
    Kabus, S., Lorenz, C.: Fast Elastic Image Registration. Medical Image Analysis for the Clinic: A Grand Challenge, 81–89 (2010)Google Scholar
  13. 13.
    Müller, T., Rabe, C., Rannacher, J., Franke, U., Mester, R.: Illumination-Robust Dense Optical Flow Using Census Signatures. In: Mester, R., Felsberg, M. (eds.) DAGM 2011. LNCS, vol. 6835, pp. 236–245. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Negahdar, N., Amini, A.A.: A 3D Optical Flow Technique based on Mass Conservation for Deformable Motion Estimation from 4-D CT Images of the Lung. In: SPIE Medical Imaging 2012: Biomedical Applications in Molecular, Structural, and Functional Imaging. SPIE, vol. 8317, p. 83171F (2012)Google Scholar
  15. 15.
    Rühaak, J., Heldmann, S., Kipshagen, T., Fischer, B.: Highly Accurate Fast Lung CT Registration. In: SPIE Medical Imaging: Image Processing. SPIE, vol. 8669, p. 86690Y (2013)Google Scholar
  16. 16.
    Schmidt-Richberg, A., Werner, R., Handels, H., Ehrhardt, J.: Estimation of slipping organ motion by registration with direction-dependent regularization. Med. Image Anal. 16, 150–159 (2012)CrossRefGoogle Scholar
  17. 17.
    Sundaram, N., Brox, T., Keutzer, K.: Dense Point Trajectories by GPU-Accelerated Large Displacement Optical Flow. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part I. LNCS, vol. 6311, pp. 438–451. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Warren, H.S.: Hacker’s Delight, pp. 65–72. Addison-Wesley Longman, Amsterdam (2002)Google Scholar
  19. 19.
    Werner, R., Ehrhardt, J., Schmidt-Richberg, A., Albers, D., Frenzel, T., et al.: Towards accurate dose accumulation for Step-&-Shoot IMRT: Impact of weighting schemes and temporal image resolution on the estimation of dosimetric motion Eeffects. Z. Med. Phys. 22, 109–122 (2012)CrossRefGoogle Scholar
  20. 20.
    Zabih, R., Woodfill, J.: Non-parametric Local Transforms for Computing Visual Correspondence. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 801, pp. 151–158. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  21. 21.
    Zach, C., Pock, T., Bischof, H.: A Duality Based Approach for Realtime TV-L1 Optical Flow. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 214–223. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Simon Hermann
    • 1
    • 2
  • René Werner
    • 3
  1. 1.Department of Computer ScienceThe University of AucklandNew Zealand
  2. 2.Department of Computer ScienceHumboldt University of BerlinGermany
  3. 3.Department of Computational NeuroscienceUniversity Medical Center Hamburg-EppendorfGermany

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