Abstract

Optical surgical navigation system has been a hot research topic because of its high accuracy. This paper focuses on identifying and tracking multiple surgical instruments to meet the requirements of applying multiple surgical instruments in clinical medicine. The methods of instrument identification based on the marker's geometrical arrangement and instrument tracking based on markers’ motion vector were applied in the proposed algorithm. The experiments of multiple instruments’ identification and tracking, the instruments’ stability, the space distance and rotation of a pair of instruments at the same tracking time were performed to verify the proposed algorithm. The stereoscopic camera is applied to capture images, and two 850 nm filters are added in front of the binocular camera. The tracking experiment shows that ten instruments can be fully and accurately identified, and then all of them can be quickly and accurately tracked at the same time. A pair of instruments is simultaneously measured in the stability test, such as the typical surgical instrument (TSI) and the miniature surgical instrument (MSI). The ranges of standard deviations (SD) of the stability test for the TSI in the X-, Y-, and Z- axes are from 0.016 mm to 0.127 mm, from 0.011 mm to 0.090 mm, and from 0.124 mm to 0.901 mm, respectively. And the ranges of SDs for the MSI’s stability test are from 0.011 mm to 0.133 mm in the X-axis, from 0.010 mm to 0.106 mm in the Y-axis, and from 0.093 mm to 0.932 mm in the Z-axis. The sub-millimeter SDs show that the proposed algorithm has a high stability. Moreover, the space distance test and the rotation test were performed for simultaneously tracking TSI and MSI. All experimental results indicate the proposed algorithm is able to meet the clinical accuracy requirements.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

2017 (3)

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

2016 (4)

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

2014 (3)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

2013 (2)

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

T. C. Clark and F. H. Schmidt, “Robot-Assisted navigation versus computer-assisted navigation in primary total knee arthroplasty: Efficiency and Accuracy,” ISRN Orthop. 2013, 794827 (2013).
[Crossref] [PubMed]

2007 (1)

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

2005 (1)

M. Bolognesi and A. Hofmann, “Computer navigation versus standard instrumentation for TKA: a single-surgeon experience,” Clin. Orthop. Relat. Res. 440(440), 162–169 (2005).
[Crossref] [PubMed]

2004 (1)

A. D. Wiles, D. G. Thompson, and D. D. Frantz, “Accuracy assessment and interpretation for optical tracking systems,” Proc. SPIE 5367, 421 (2004).
[Crossref]

2000 (2)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Allen, M. J.

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Al-Maisary, S.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Alotaibi, N. M.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Atkins, R.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Aubin, C. E.

H. Jobidon-Lavergne, S. Kadoury, D. Knez, and C. E. Aubin, “Biomechanically driven intraoperative spine registration during navigated anterior vertebral body tethering,” Phys. Med. Biol. (to be published).

Bale, R.

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

Bax, M. R.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Bertran, J.

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Bolognesi, M.

M. Bolognesi and A. Hofmann, “Computer navigation versus standard instrumentation for TKA: a single-surgeon experience,” Clin. Orthop. Relat. Res. 440(440), 162–169 (2005).
[Crossref] [PubMed]

Boyd, M.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Cai, K.

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

Chen, W.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Chen, X.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Chien, H. F.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Cho, H. M.

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

Clark, T. C.

T. C. Clark and F. H. Schmidt, “Robot-Assisted navigation versus computer-assisted navigation in primary total knee arthroplasty: Efficiency and Accuracy,” ISRN Orthop. 2013, 794827 (2013).
[Crossref] [PubMed]

Dagnino, G.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

De Simone, R.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Demertzis, N.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Deorajh, R.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Dogramadzi, S.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Duan, J.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Ehrendorfer, S.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Engelhardt, S.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Fehlings, M. G.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Fornaciari, P.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Frantz, D. D.

A. D. Wiles, D. G. Thompson, and D. D. Frantz, “Accuracy assessment and interpretation for optical tracking systems,” Proc. SPIE 5367, 421 (2004).
[Crossref]

Gan, M.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Georgilas, I.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Gibbons, P.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Guha, D.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Guo, N.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Gupta, S.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Han, Z.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Hofmann, A.

M. Bolognesi and A. Hofmann, “Computer navigation versus standard instrumentation for TKA: a single-surgeon experience,” Clin. Orthop. Relat. Res. 440(440), 162–169 (2005).
[Crossref] [PubMed]

Hsieh, T. M. H.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Hu, L.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Huang, L.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Hutter, E.

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Jakubovic, R.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Jaschke, W.

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

Javidi, B.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Jobidon-Lavergne, H.

H. Jobidon-Lavergne, S. Kadoury, D. Knez, and C. E. Aubin, “Biomechanically driven intraoperative spine registration during navigated anterior vertebral body tethering,” Phys. Med. Biol. (to be published).

Johnson, J. A.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Kadoury, S.

H. Jobidon-Lavergne, S. Kadoury, D. Knez, and C. E. Aubin, “Biomechanically driven intraoperative spine registration during navigated anterior vertebral body tethering,” Phys. Med. Biol. (to be published).

Karck, M.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Khadem, R.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Knez, D.

H. Jobidon-Lavergne, S. Kadoury, D. Knez, and C. E. Aubin, “Biomechanically driven intraoperative spine registration during navigated anterior vertebral body tethering,” Phys. Med. Biol. (to be published).

Ko, A. T.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Kolb, S.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Koulalis, D.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Lai, H. S.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Li, B.

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Li, W.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Liang, Z.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Lin, Q.

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

Liu, H.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Liu, T. J.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Mainprize, T. G.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Mavrogenis, A. F.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Meinzer, H. P.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Mimidis, G.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Morad, S.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Niehaus, R.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Papagelopoulos, P. J.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Papanastasiou, J.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Park, S. H.

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

Peters, K. M.

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Rhee, S. J.

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

Sadeghi-Tehrani, M.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Savvidou, O. D.

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Schilter, D.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Schmidt, F. H.

T. C. Clark and F. H. Schmidt, “Robot-Assisted navigation versus computer-assisted navigation in primary total knee arthroplasty: Efficiency and Accuracy,” ISRN Orthop. 2013, 794827 (2013).
[Crossref] [PubMed]

Shahidi, R.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Shen, S. G. F.

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Siston, R. A.

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Snyman, L. W.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Suh, J. T.

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

Sun, H.

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Swart, J. W.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Tang, Y. B.

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Tarassoli, P.

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Thompson, D. G.

A. D. Wiles, D. G. Thompson, and D. D. Frantz, “Accuracy assessment and interpretation for optical tracking systems,” Proc. SPIE 5367, 421 (2004).
[Crossref]

Wang, X.

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Wang, Y.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Wang, Z.

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

Weinand, C.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Welch, J. N.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Widmann, E.

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

Widmann, G.

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

Widmann, R.

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

Wiles, A. D.

A. D. Wiles, D. G. Thompson, and D. D. Frantz, “Accuracy assessment and interpretation for optical tracking systems,” Proc. SPIE 5367, 421 (2004).
[Crossref]

Wilkinson, E. P.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Wolf, I.

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Wu, B.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Xu, K.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Yang, B.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Yang, H.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Yang, R.

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

Yang, V. X. D.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Yee, A.

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

Yeh, C. C.

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Yu, K.

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Zhang, L.

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Zhang, N.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Zhang, X.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Zhang, Z.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhao, J.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Zhao, Z.

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Zhou, Z.

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

Ziswiler, M.

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Ann. Biomed. Eng. (1)

G. Dagnino, I. Georgilas, S. Morad, P. Gibbons, P. Tarassoli, R. Atkins, and S. Dogramadzi, “Image-Guided surgical robotic system for percutaneous reduction of joint fractures,” Ann. Biomed. Eng. 45(11), 2648–2662 (2017).
[Crossref] [PubMed]

Ann. Plast. Surg. (1)

T. J. Liu, A. T. Ko, Y. B. Tang, H. S. Lai, H. F. Chien, and T. M. H. Hsieh, “Clinical application of different surgical navigation systems in complex craniomaxillofacial surgery: The use of multisurface 3-Dimensional images and a 2-Plane reference system,” Ann. Plast. Surg. 76(4), 411–419 (2016).
[Crossref] [PubMed]

Clin. Orthop. Relat. Res. (1)

M. Bolognesi and A. Hofmann, “Computer navigation versus standard instrumentation for TKA: a single-surgeon experience,” Clin. Orthop. Relat. Res. 440(440), 162–169 (2005).
[Crossref] [PubMed]

Comput. Aided Surg. (1)

R. Khadem, C. C. Yeh, M. Sadeghi-Tehrani, M. R. Bax, J. A. Johnson, J. N. Welch, E. P. Wilkinson, and R. Shahidi, “Comparative tracking error analysis of five different optical tracking systems,” Comput. Aided Surg. 5(2), 98–107 (2000).
[Crossref] [PubMed]

Comput. Assist. Surg. (Abingdon) (1)

K. Cai, R. Yang, Q. Lin, and Z. Wang, “Tracking multiple surgical instruments in a near-infrared optical system,” Comput. Assist. Surg. (Abingdon) 21(1), 46–55 (2016).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Int. J. CARS (1)

S. Engelhardt, R. De Simone, S. Al-Maisary, S. Kolb, M. Karck, H. P. Meinzer, and I. Wolf, “Accuracy evaluation of a mitral valve surgery assistance system based on optical tracking,” Int. J. CARS 11(10), 1891–1904 (2016).
[Crossref] [PubMed]

Int. J. Oral Maxillofac. Implants (1)

G. Widmann, R. Widmann, E. Widmann, W. Jaschke, and R. Bale, “Use of a surgical navigation system for CT-guided template production,” Int. J. Oral Maxillofac. Implants 22(1), 72–78 (2007).
[PubMed]

ISRN Orthop. (1)

T. C. Clark and F. H. Schmidt, “Robot-Assisted navigation versus computer-assisted navigation in primary total knee arthroplasty: Efficiency and Accuracy,” ISRN Orthop. 2013, 794827 (2013).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

Z. Zhou, B. Wu, J. Duan, X. Zhang, N. Zhang, and Z. Liang, “Optical surgical instrument tracking system based on the principle of stereo vision,” J. Biomed. Opt. 22(6), 65005 (2017).
[Crossref] [PubMed]

J. Craniofac. Surg. (1)

B. Li, L. Zhang, H. Sun, S. G. F. Shen, and X. Wang, “A new method of surgical navigation for orthognathic surgery: optical tracking guided free-hand repositioning of the maxillomandibular complex,” J. Craniofac. Surg. 25(2), 406–411 (2014).
[Crossref] [PubMed]

Knee (1)

R. Niehaus, D. Schilter, P. Fornaciari, C. Weinand, M. Boyd, M. Ziswiler, and S. Ehrendorfer, “Experience of total knee arthroplasty using a novel navigation system within the surgical field,” Knee 24(3), 518–524 (2017).
[Crossref] [PubMed]

Knee Surg. Relat. Res. (1)

S. J. Rhee, S. H. Park, H. M. Cho, and J. T. Suh, “Comparison of precision between optical and electromagnetic navigation systems in total knee arthroplasty,” Knee Surg. Relat. Res. 26(4), 214–221 (2014).
[Crossref] [PubMed]

Materials science and engineering b-advanced functional solid-state materials (1)

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Materials science and engineering b-advanced functional solid-state materials 231, 28–31 (2018).

Orthopedics (1)

A. F. Mavrogenis, O. D. Savvidou, G. Mimidis, J. Papanastasiou, D. Koulalis, N. Demertzis, and P. J. Papagelopoulos, “Computer-assisted navigation in orthopedic surgery,” Orthopedics 36(8), 631–642 (2013).
[Crossref] [PubMed]

Proc. SPIE (1)

A. D. Wiles, D. G. Thompson, and D. D. Frantz, “Accuracy assessment and interpretation for optical tracking systems,” Proc. SPIE 5367, 421 (2004).
[Crossref]

Vet. Surg. (1)

K. M. Peters, E. Hutter, R. A. Siston, J. Bertran, and M. J. Allen, “Surgical navigation improves the precision and accuracy of tibial component alignment in canine total knee replacement,” Vet. Surg. 45(1), 52–59 (2016).
[Crossref] [PubMed]

Other (12)

D. Guha, R. Jakubovic, N. M. Alotaibi, R. Deorajh, S. Gupta, M. G. Fehlings, T. G. Mainprize, A. Yee, and V. X. D. Yang, “Optical topographic imaging for spinal intraoperative 3-dimensional navigation in the cervical spine: initial preclinical and clinical feasibility,” Clin. Spine Surg.1 (2019).

H. Jobidon-Lavergne, S. Kadoury, D. Knez, and C. E. Aubin, “Biomechanically driven intraoperative spine registration during navigated anterior vertebral body tethering,” Phys. Med. Biol. (to be published).

Z. Han, K. Yu, L. Hu, W. Li, H. Yang, M. Gan, N. Guo, B. Yang, H. Liu, and Y. Wang, “A targeting method for robot-assisted percutaneous needle placement under fluoroscopy guidance,” Comput. Assist. Surg. (AbfFingdon)1–9 (2019).

Northern Digital Inc, “NDI Products: Polaris Spectra and Vicra,” https://www.ndigital.com .

Medtronic, “Products: Surgical Navigation Systems,” http://www.medtronic.com/us-en/healthcare-professionals/products.html .

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Supplementary Material (2)

NameDescription
» Visualization 1       Ten simulated surgical instruments are accurately tracked when they are moved in groups.
» Visualization 2       Ten simulated surgical instruments are accurately tracked when they are moved individually.

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Figures (9)

Fig. 1
Fig. 1 Framework of the proposed optical tracking system.
Fig. 2
Fig. 2 The transformation between the camera coordinate system and the image coordinate system
Fig. 3
Fig. 3 The schematic view of the experimental setup.
Fig. 4
Fig. 4 Surgical instruments designed by authors with different markers’ geometrical arrangements.
Fig. 5
Fig. 5 Diagram of experimental measurements at different viewpoints. (a) Diagram of the Cameras, and the Grating Ruler; (b) Diagram of the Hori-camera, the Vert-camera and the Precision Optical Table, and (c) Diagram of the filters, the TSI and the MSI attached to the Total Station.
Fig. 6
Fig. 6 Calibration results demonstrating two cameras’ alignment. (a) The Hori-camera’s calibration result; (b) The Vert-camera’s calibration result.
Fig. 7
Fig. 7 Tracked trajectories of the ten instruments using the proposed algorithm under different conditions. (a) The trajectories of the ten instruments moving within groups (see Visualization 1); (b) The trajectories of the ten instruments moving independently (see Visualization 2).
Fig. 8
Fig. 8 Diagram of the TSI and MSI. (a) Markers’ geometrical arrangements for the TSI and MSI; (b) The TSI and MSI attach to the Total Station, and (c) The TSI and MSI attach to the Grating Ruler.
Fig. 9
Fig. 9 The SDs’ results for the TSI and MSI. (a) is the SDs for the TSI’s X-, Y-, and Z- axes, and (b) is the SDs for the MSI’s X-, Y-, and Z- axes.

Tables (3)

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Table 1 Horizontal distance results for the TSI and MSI

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Table 2 Vertical distance results of TSI and MSI

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Table 3 Rotation angle comparison for the TSI and MSI

Equations (17)

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{ u= i=1 n u i f( u i , v i ) i=1 n f( u i , v i ) v= i=1 n v i f( u i , v i ) i=1 n f( u i , v i )
η= D A l B l / D A l C l
{ D A l B l = [ ( u A l u B l ) 2 + ( v A l v B l ) 2 ] 1 2 D A l C l = [ ( u A l u C l ) 2 + ( v A l v C l ) 2 ] 1 2
| η δ l |< ε 1
{ x a = f Z A X A y a = f Z A Y A
E= [ ( X A X B ) 2 + ( Y A Y B ) 2 + ( Z A Z B ) 2 ] 1 2
E= [ ( x a Z A f x b Z B f ) 2 + ( y a Z A f y b Z B f ) 2 + ( Z A Z B ) 2 ] 1 2
E= Z f [ ( x a x b ) 2 + ( y a y b ) 2 ] 1 2
{ u= x dx + u 0 v= y dy + v 0
E= Z f [ ( u a u b ) 2 d x 2 + ( v a v b ) 2 d y 2 ] 1 2
E=dx Z f d
P=dx Z w f p
| P P l |< ε 2
I V,W (t)=| MV V,W |=| P W (t) P V (t1) |
{ M A l (t)=min{ I A l A 1 (t), I A l B 1 (t), I A l C 1 (t),..., I A l A L (t), I A l B L (t), I A l C L (t) } M B l (t)=min{ I B l A 1 (t), I B l B 1 (t), I B l C 1 (t),..., I B l A L (t), I B l B L (t), I B l C L (t) } M C l (t)=min{ I C l A 1 (t), I C l B 1 (t), I C l C 1 (t),..., I C l A L (t), I C l B L (t), I C l C L (t) }
SD= [ 1 N i=1 N ( s i s ¯ ) 2 ] 1 2
RMSE= [ 1 N i=1 N ( x obs,i x model,i ) 2 ] 1 2

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