Advertisement

Simultaneous intrinsic and extrinsic calibration of a laser deflecting tilting mirror in the projective voltage space

  • 143 Accesses

Abstract

Purpose 

During the past five decades, laser technology emerged and is nowadays part of a great number of scientific and industrial applications. In the medical field, the integration of laser technology is on the rise and has already been widely adopted in contemporary medical applications. However, it is new to use a laser to cut bone and perform general osteotomy surgical tasks with it. In this paper, we describe a method to calibrate a laser deflecting tilting mirror and integrate it into a sophisticated laser osteotome, involving next generation robots and optical tracking.

Methods 

A mathematical model was derived, which describes a controllable deflection mirror by the general projective transformation. This makes the application of well-known camera calibration methods possible. In particular, the direct linear transformation algorithm is applied to calibrate and integrate a laser deflecting tilting mirror into the affine transformation chain of a surgical system.

Results 

Experiments were performed on synthetic generated calibration input, and the calibration was tested with real data. The determined target registration errors in a working distance of 150 mm for both simulated input and real data agree at the declared noise level of the applied optical 3D tracking system: The evaluation of the synthetic input showed an error of 0.4 mm, and the error with the real data was 0.3 mm.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Notes

  1. 1.

    Due to scaling in P, there are actually only 11 unknowns. Thus, \(5\frac{1}{2}\) correspondences are required from a mathematical point of view.

  2. 2.

    The attentive reader might be suspicious why the CIR bound of \(\varphi \) here is equal to \(\varphi \) in Fig. 7. This is a coincidence.

References

  1. 1.

    Abdel-Aaziz YI, Karara HM (1971) Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry. In: Proceedings of the Symposium on Close-Range Photogrammetry. American Society of Photogrammetry, Falls Church, VA, pp 1–18

  2. 2.

    Arun KS, Huang TS, Blostein SD (1987) Least-squares fitting of two 3-d point sets. Pattern Anal Mach Intell IEEE Trans 9(5):698–700

  3. 3.

    Baek KW, Deibel W, Marinov D, Griessen M, Dard M, Bruno A, Zeilhofer HF, Cattin P, Juergens P (2015) A comparative investigation of bone surface after cutting with mechanical tools and Er: Yag laser. Lasers Surg Med 47:426–432

  4. 4.

    Deibel W, Schneider A, Augello M, Bruno AE, Juergens P, Cattin P (2015) A compact, efficient, and lightweight laser head for \({\rm carlo}^{\textregistered }\): integration, performance, and benefits. In: SPIE optical engineering+ applications. International society for optics and photonics, pp 957905

  5. 5.

    Hartley R, Zisserman A (2010) Multiple view geometry in computer vision. Cambridge Univ Press, Cambridge

  6. 6.

    Luhmann T (2009) Precision potential of photogrammetric 6DOF pose estimation with a single camera. ISPRS J Photogramm Remote Sens 64(3):275–284

  7. 7.

    Mönnich H, Stein D, Raczkowsky J, Wörn H (2010) An automatic and complete self-calibration method for robotic guided laser ablation. In: Robotics and automation (ICRA), 2010 IEEE international conference on, pp 1086–1087

  8. 8.

    Schneider A, Pezold S, Baek KW, Marinov D, Cattin PC (2015) Direct calibration of a laser ablation system in the projective voltage space. In: Medical image computing and computer-assisted intervention—MICCAI 2015. Springer, pp 274–281

  9. 9.

    Simek K (2012) Dissecting the camera matrix (2012). http://ksimek.github.io/2012/08/14/decompose/

  10. 10.

    Zhang Q, Pless R (2004) Extrinsic calibration of a camera and laser range finder. In: Intelligent robots and systems, 2004 (IROS 2004). Proceedings of the 2004 IEEE/RSJ international conference on, vol 3, pp 2301–2306

  11. 11.

    Zhang Y, Pfeiffer T, Ding J, Wieser W, Weller M, Huber R, Raczkowsky J, Wörn H, Klenzner T (2012) Optical coherence tomography as a tracking device for oct guided laser cochleostomy: algorithm and first results. In: CURAC, pp 39–43

Download references

Funding

This study was funded by the University of Basel and by the company Advanced Osteotomy Tools AG.

Author information

Correspondence to Adrian Schneider.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All applicable international, national, and/or institutional guidelines for the care and use of animals were followed.

Informed consent

This articles does not contain patient data.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 6247 KB)

Supplementary material 2 (mp4 9304 KB)

Supplementary material 1 (mp4 6247 KB)

Supplementary material 2 (mp4 9304 KB)

Supplementary material 3 (txt 0 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Schneider, A., Pezold, S., Baek, K. et al. Simultaneous intrinsic and extrinsic calibration of a laser deflecting tilting mirror in the projective voltage space. Int J CARS 11, 1611–1621 (2016). https://doi.org/10.1007/s11548-016-1435-y

Download citation

Keywords

  • Robotics
  • Navigation
  • Laser ablation
  • Mirror
  • DLT
  • Osteotomy