Fast calibration of electromagnetically tracked oblique-viewing rigid endoscopes

  • Xinyang Liu
  • Christina E. Rice
  • Raj ShekharEmail author
Original Article



The oblique-viewing (i.e., angled) rigid endoscope is a commonly used tool in conventional endoscopic surgeries. The relative rotation between its two moveable parts, the telescope and the camera head, creates a rotation offset between the actual and the projection of an object in the camera image. A calibration method tailored to compensate such offset is needed.


We developed a fast calibration method for oblique-viewing rigid endoscopes suitable for clinical use. In contrast to prior approaches based on optical tracking, we used electromagnetic (EM) tracking as the external tracking hardware to improve compactness and practicality. Two EM sensors were mounted on the telescope and the camera head, respectively, with considerations to minimize EM tracking errors. Single-image calibration was incorporated into the method, and a sterilizable plate, laser-marked with the calibration pattern, was also developed. Furthermore, we proposed a general algorithm to estimate the rotation center in the camera image. Formulas for updating the camera matrix in terms of clockwise and counterclockwise rotations were also developed.


The proposed calibration method was validated using a conventional \(30{^{\circ }}\), 5-mm laparoscope. Freehand calibrations were performed using the proposed method, and the calibration time averaged 2 min and 8 s. The calibration accuracy was evaluated in a simulated clinical setting with several surgical tools present in the magnetic field of EM tracking. The root-mean-square re-projection error averaged 4.9 pixel (range 2.4–8.5 pixel, with image resolution of \(1280 \times 720)\) for rotation angles ranged from \(-40.3{^{\circ }}\) to \(174.7{^{\circ }}\).


We developed a method for fast and accurate calibration of oblique-viewing rigid endoscopes. The method was also designed to be performed in the operating room and will therefore support clinical translation of many emerging endoscopic computer-assisted surgical systems.


Camera calibration Single-image calibration Oblique-viewing endoscope Electromagnetic tracking Augmented reality Computer-assisted surgery 



This work was supported partially by the National Institutes of Health Grant 1R41CA192504. The authors would like to thank Joao P. Barreto a, Ph.D. and Rui Melo of Perceive3D, SA for providing the single-image calibration API. The authors would also like to thank Emmanuel Wilson for his assistance in building the clinical fCalib plate.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Human participants

This article does not contain any studies with human participants or animals performed by any of the authors.

Supplementary material

Supplementary material 1 (mp4 63134 KB)


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Copyright information

© CARS 2017

Authors and Affiliations

  1. 1.Sheikh Zayed Institute for Pediatric Surgical InnovationChildren’s National Health SystemWashingtonUSA
  2. 2.Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA

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