Numerical Investigation of an Axis-based Approach to Rigid Registration

  • Michele ConconiEmail author
  • Nicola Sancisi
  • Vincenzo Parenti-Castelli
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The term rigid registration identifies the process that optimally aligns different data sets whose information has to be merged, as in the case of robot calibration, image-guided surgery or patient-specific gait analysis.

One of the most common approaches to rigid registration relies on the identification of a set of fiducial points in each data set to be registered to compute the rototranslational matrix that optimally aligns them. Both measurement and human errors directly affect the final accuracy of the process. Increasing the number of fiducials may improve registration accuracy but it will also increase the time and complexity of the whole procedure, since correspondence must be established between fiducials in different data sets.

The aim of this paper is to present a new approach that resorts to axes instead of points as fiducial features. The fundamental advantage is that any axis can be easily identified in each data set by least-square linear fitting of multiple, unsorted measured data. This provides a way to filtering the measurement error within each data set, improving the registration accuracy with a reduced effort. In this work, a closed-form solution for the optimal axis-based rigid registration is presented. The accuracy of the method is compared with standard point-based rigid registration through a numerical test. Axis-based registration results one order of magnitude more accurate than point-based registration.


Rigid Registration Axis-based Registration Registration Accuracy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cripton, P. A., Sati, M., Orr, T. E., Bourquin, Y., Dumas, G. A., Nolte, L. P.: Animation of in vitro biomechanical tests. J Biomech. 34(8), 1091-1096 (2001).CrossRefGoogle Scholar
  2. 2.
    Alam, F., Rahman, S. U., Ullah, S., Gulati, K.: Medical image registration in image guided surgery: Issues, challenges and research opportunities. Biocybernetics and Biomedical Engineering. 38(1), 71 – 89 (2018).CrossRefGoogle Scholar
  3. 3.
    Grunert, P., Darabi, K., Espinosa, J.; Filippi, R.: Computer-aided navigation in neurosurgery. Neurosurg Rev. 26(2), 73-99 (2003).CrossRefGoogle Scholar
  4. 4.
    Cleary, K., Peters, T.: Image-guided interventions: Technology review and clinical applications. Annual Review of Biomedical Engineering. 12, pp.119-142 (2010).CrossRefGoogle Scholar
  5. 5.
    Conconi, M., Sancisi. N., Parenti-Castelli, V.: Reconstruction of Knee Cartilage Distribution from Joint Motion, Proceedings of AIMETA, 602-610, Salerno, Italy (2017).Google Scholar
  6. 6.
    Forlani, M., Sancisi, N., Conconi, M., Parenti-Castelli, V.: A new test rig for static and dynamic evaluation of knee motion based on a cable-driven parallel manipulator loading system. Meccanica. 51(7), 1571-1581 (2016).CrossRefGoogle Scholar
  7. 7.
    Martelli, S., Sancisi, N., Conconi, M., Parenti-Castelli, V., Reynolds, K.: Sensitivity of musculoskeletal models to planar simplification of tibiofemoral motion. Proceedings of 8th World Congress of Biomechanics - WCB, Dublin; Irland (2018).Google Scholar
  8. 8.
    Smale, K. B., Conconi, M., Sancisi, N., Krogsgaard, M., Alkjaer, T., Parenti-Castelli, V., Benoit, D. L.: Effect of implementing magnetic resonance imaging for patient-specific OpenSim models on lower-body kinematics and knee ligament lengths. Journal of Biomechanics, in Press (2018).Google Scholar
  9. 9.
    Merriaux, P., Dupuis, Y., Boutteau, R., Vasseur, P., Savatier, X.: A study of Vicon system positioning performance. Sensors, 17, 1591 (2017).CrossRefGoogle Scholar
  10. 10.
    Morozov, M., Riise, J., Summan, R., Pierce, S. G., Mineo, C., MacLeod C. N., et al.: Assessing the accuracy of industrial robots through metrology for the enhancement of automated non-destructive testing. Proceedings of 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI) (2016).Google Scholar
  11. 11.
    Oliveira, F. P., Tavares, J. M.: Medical image registration: a review. Comput Methods Biomech Biomed Engin. 17(2), 73-93, (2014).CrossRefGoogle Scholar
  12. 12.
    Livyatan, H., Yaniv, Z., Joskowicz, L.: Gradient-based 2-D/3-D rigid registration of fluoroscopic X-ray to CT. IEEE Transactions on Medical Imaging. 22(11), 1395-1406 (2003).CrossRefGoogle Scholar
  13. 13.
    Hill, D. L., Batchelor, P. G., Holden, M., Hawkes, D. J.: Medical image registration. Phys Med Biol. 46(3), 1-45 (2001).CrossRefGoogle Scholar
  14. 14.
    Peters, T. M.: Image-guidance for surgical procedures. Phys Med Biol. 51(14), R505-540 (2006).CrossRefGoogle Scholar
  15. 15.
    Schonemann, P. H.: A generalized solution of the orthogonal procrustes problem. Psychometrika. 31(1), 1-10 (1966).MathSciNetCrossRefGoogle Scholar
  16. 16.
    Clarke, J., Deakin, A., Picard, F., Nicol, A.: Technical evaluation of the positional accuracy of computer assisted surgical systems. Journal of Bone and Joint Surgery, British Volume. 91-B(SUPP I), 398 (2009).Google Scholar
  17. 17.
    Kronreif, G., Ptacek, W., Kornfeld, M., Furst, M.: Evaluation of robotic assistance in neurosurgical applications. J Robot Surg. 6(1), 33-39 (2012).CrossRefGoogle Scholar
  18. 18.
    Fitzpatrick, J. M., West, J. B., Maurer, C. R.: Predicting error in rigid-body point-based regis-tration. IEEE Trans Med Imaging. 17(5), 694-702 (1998).CrossRefGoogle Scholar
  19. 19.
    Danilchenko, A., Fitzpatrick, J. M.: General approach to first-order error prediction in rigid point registration. IEEE Trans Med Imaging. 30(3), 679-693 (2011).Google Scholar
  20. 20.
    West, J. B., Fitzpatrick, J. M., Toms, S. A., Maurer, C. R., Maciunas, R. J.: Fiducial point placement and the accuracy of point-based, rigid body registration. Neurosurgery. 48(4), 810-816 (2001).Google Scholar
  21. 21.
    Wang, M., Song, Z.: Improving target registration accuracy in image-guided neurosurgery by optimizing the distribution of fiducial points. Int J Med Robot. 5(1), 26-31 (2009).CrossRefGoogle Scholar
  22. 22.
    Shamir, R. R., Joskowicz, L., Shoshan, Y.: Fiducial optimization for minimal target registration error in image-guided neurosurgery. IEEE Trans Med Imaging. 31(3), 725-737 (2012).CrossRefGoogle Scholar
  23. 23.
    Franaszek, M., Cheok, G. S.: Selection of Fiducial Locations and Performance Metrics for Point-Based Rigid-Body Registration. Precis Eng. 47, 362-374 (2017).CrossRefGoogle Scholar
  24. 24.
    Carlson, C.: How I Made Wine Glasses from Sunflowers url:, last ac-cessed 2018/12/12.
  25. 25.
    Balachandran, R., Welch, E. B., Dawant, B. M., Fitzpatrick, J. M.: Effect of MR distortion on targeting for deep-brain stimulation. IEEE Trans Biomed Eng. 57(7), 1729-1735 (2010).CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michele Conconi
    • 1
    Email author
  • Nicola Sancisi
    • 1
  • Vincenzo Parenti-Castelli
    • 1
  1. 1.Department of Industrial EngineeringUniversity of BolognaBolognaItaly

Personalised recommendations