Fast and robust localization of surgical array using Kalman filter

Abstract

Problem

Intraoperative tracking of surgical instruments is an inevitable task of computer-assisted surgery. An optical tracking system often fails to precisely reconstruct the dynamic location and pose of a surgical tool due to the acquisition noise and measurement variance. Embedding a Kalman filter (KF) or any of its extensions such as extended and unscented Kalman filters (EKF and UKF) with the optical tracker resolves this issue by reducing the estimation variance and regularizing the temporal behavior. However, the current KF implementations are computationally burdensome and hence takes long execution time which hinders real-time surgical tracking.

Aim

This paper introduces a fast and computationally efficient implementation of linear KF to improve the measurement accuracy of an optical tracking system with high temporal resolution.

Methods

Instead of the surgical tool as a whole, our KF framework tracks each individual fiducial mounted on it using a Newtonian model. In addition to simulated dataset, we validate our technique against real data obtained from a high frame-rate commercial optical tracking system. We also perform experiments wherein a diffusive material (such as a drop of blood) blocks one of the fiducials and show that KF can substantially reduce the tracking error.

Results

The proposed KF framework substantially stabilizes the tracking behavior in all of our experiments and reduces the mean-squared error (MSE) by a factor of 26.84, from the order of \(10^{-1}\) to \(10^{-2}\) mm\(^{2}\). In addition, it exhibits a similar performance to UKF, but with a much smaller computational complexity.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    Aissa BC, Fatima C (2017) Neural networks trained with Levenberg-Marquardt-iterated extended Kalman filter for mobile robot trajectory tracking. J Eng Sci Technol Rev 10(4):191–198

    Article  Google Scholar 

  2. 2.

    Arun KS, Huang TS, Blostein SD (1987) Least-squares fitting of two 3-d point sets. IEEE Trans Pattern Anal Mach Intell 5:698–700

    Article  Google Scholar 

  3. 3.

    Chowdhary G, Jategaonkar R (2010) Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter. Aerosp Sci Technol 14(2):106–117

    Article  Google Scholar 

  4. 4.

    Dai JS (2015) Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections. Mech Mach Theory 92:144–152

    Article  Google Scholar 

  5. 5.

    Dorfmüller-Ulhaas, K (2007) Robust optical user motion tracking using a kalman filter

  6. 6.

    Elfring R, de la Fuente M, Radermacher K (2010) Assessment of optical localizer accuracy for computer aided surgery systems. Comput Aided Surg 15(1–3):1–12

    Article  Google Scholar 

  7. 7.

    Enayati N, De Momi E, Ferrigno G (2015) A quaternion-based unscented Kalman filter for robust optical/inertial motion tracking in computer-assisted surgery. IEEE Trans Instrum Meas 64(8):2291–2301

    Article  Google Scholar 

  8. 8.

    Hartmann, G., Huang, F., Klette, R (2013) Landmark initialization for unscented kalman filter sensor fusion for mo-nocular camera localization

  9. 9.

    Jazwinski AH (1970) Stochastic process and filtering theory. Academic Press, A subsidiary of Harcourt Brace Jovanovich Publishers, San Diego

    Google Scholar 

  10. 10.

    Joukhadar A, Hanna DK, Al-Izam EA (2020) Ukf-based image filtering and 3d reconstruction. In: Machine vision and navigation, pp. 267–289. Springer

  11. 11.

    Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. In: Signal processing, sensor fusion, and target recognition VI, vol 3068, pp 182–193. International Society for Optics and Photonics

  12. 12.

    Kraft E (2003) A quaternion-based unscented Kalman filter for orientation tracking. In: Proceedings of the sixth international conference of information fusion, vol 1, pp 47–54. IEEE Cairns, Queensland, Australia

  13. 13.

    Li L, Wang T, Xia Y, Zhou N (2020) Trajectory tracking control for wheeled mobile robots based on nonlinear disturbance observer with extended Kalman filter. J Franklin Inst 357(13):8491–8507

  14. 14.

    Ma T, Song Z, Xiang Z, Dai JS (2019) Trajectory tracking control for flexible-joint robot based on extended Kalman filter and PD control. Front Neurorobot 13:25

    Article  Google Scholar 

  15. 15.

    Mkhoyan T, de Visser CC, De Breuker R (2021) Adaptive state estimation and real-time tracking of aeroelastic wings with augmented kalman filter and kernelized correlation filter. In: AIAA Scitech 2021 Forum

  16. 16.

    Moore T, Stouch D (2016) A generalized extended kalman filter implementation for the robot operating system. In: Intelligent autonomous systems vol 13, pp 335–348. Springer

  17. 17.

    Pham DT, Verron J, Roubaud MC (1998) A singular evolutive extended kalman filter for data assimilation in oceanography. J Mar Syst 16(3–4):323–340

    Article  Google Scholar 

  18. 18.

    Prevost CG, Desbiens A, Gagnon E (2007) Extended Kalman filter for state estimation and trajectory prediction of a moving object detected by an unmanned aerial vehicle. In: 2007 American control conference, pp 1805–1810. IEEE

  19. 19.

    Singh RR, Godse MJ, Biradar TD (2013) Video object tracking using particle filtering. Int J Eng Res Technol 2(9):2987–2993

    Google Scholar 

  20. 20.

    Vaccarella A, De Momi E, Enquobahrie A, Ferrigno G (2013) Unscented Kalman filter based sensor fusion for robust optical and electromagnetic tracking in surgical navigation. IEEE Trans Instrum Meas 62(7):2067–2081

    Article  Google Scholar 

  21. 21.

    VanDyke MC, Schwartz JL, Hall CD (2004) Unscented Kalman filtering for spacecraft attitude state and parameter estimation. Adv Astronaut Sci 118(1):217–228

    Google Scholar 

  22. 22.

    Welch G, Bishop G (1995) An introduction to the Kalman filter

  23. 23.

    Xu Z, Yang SX, Gadsden SA (2020) Enhanced bioinspired backstepping control for a mobile robot with unscented Kalman filter. IEEE Access 8:125899–125908

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge funding from Natural Science and Engineering Research Council of Canada (NSERC).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Md Ashikuzzaman.

Ethics declarations

Conflict of interest

Md Ashikuzzaman, Noushin Jafarpisheh, Sunil Rottoo, Pierre Brisson and Hassan Rivaz declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ashikuzzaman, M., Jafarpisheh, N., Rottoo, S. et al. Fast and robust localization of surgical array using Kalman filter. Int J CARS 16, 829–837 (2021). https://doi.org/10.1007/s11548-021-02378-1

Download citation

Keywords

  • Optical tracking
  • Computer-assisted surgery
  • Kalman filter
  • Robust localization