title: Hand-eye calibration for rigid laparoscopes using an invariant point.
abstract: OBJECTIVE
  Laparoscopic liver resection has significant advantages over open surgery due to less patient trauma and faster recovery times, yet it can be difficult due to the restricted field of view and lack of haptic feedback. Image guidance provides a potential solution but one current challenge is in accurate "hand-eye" calibration, which determines the position and orientation of the laparoscope camera relative to the tracking markers.
  
  
  METHODS
  In this paper, we propose a simple and clinically feasible calibration method based on a single invariant point. The method requires no additional hardware, can be constructed by theatre staff during surgical setup, requires minimal image processing and can be visualised in real time. Real-time visualisation allows the surgical team to assess the calibration accuracy before use in surgery. In addition, in the laboratory, we have developed a laparoscope with an electromagnetic tracking sensor attached to the camera end and an optical tracking marker attached to the distal end. This enables a comparison of tracking performance.
  
  
  RESULTS
  We have evaluated our method in the laboratory and compared it to two widely used methods, "Tsai's method" and "direct" calibration. The new method is of comparable accuracy to existing methods, and we show RMS projected error due to calibration of 1.95 mm for optical tracking and 0.85 mm for EM tracking, versus 4.13 and 1.00 mm respectively, using existing methods. The new method has also been shown to be workable under sterile conditions in the operating room.
  
  
  CONCLUSIONS
  We have proposed a new method of hand-eye calibration, based on a single invariant point. Initial experience has shown that the method provides visual feedback, satisfactory accuracy and can be performed during surgery. We also show that an EM sensor placed near the camera would provide significantly improved image overlay accuracy.
authors.affiliation: Centre for Medical Image Computing, Front Engineering Building, University College London, Malet Place, London, UK. s.thompson@ucl.ac.uk.
authors.forename: Stephen
authors.initials: S
authors.lastname: Thompson
authors.affiliation: Centre for Medical Image Computing, Front Engineering Building, University College London, Malet Place, London, UK.
authors.forename: Danail
authors.initials: D
authors.lastname: Stoyanov
authors.affiliation: Division of Surgery, Hampstead Campus, UCL Medical School, Royal Free Hospital, 9th Floor, Rowland Hill Street, London, UK.
authors.forename: Crispin
authors.initials: C
authors.lastname: Schneider
authors.affiliation: Division of Surgery, Hampstead Campus, UCL Medical School, Royal Free Hospital, 9th Floor, Rowland Hill Street, London, UK.
authors.forename: Kurinchi
authors.initials: K
authors.lastname: Gurusamy
authors.affiliation: Centre for Medical Image Computing, Front Engineering Building, University College London, Malet Place, London, UK.
authors.forename: Sébastien
authors.initials: S
authors.lastname: Ourselin
authors.affiliation: Division of Surgery, Hampstead Campus, UCL Medical School, Royal Free Hospital, 9th Floor, Rowland Hill Street, London, UK.
authors.forename: Brian
authors.initials: B
authors.lastname: Davidson
authors.affiliation: Centre for Medical Image Computing, Front Engineering Building, University College London, Malet Place, London, UK.
authors.forename: David
authors.initials: D
authors.lastname: Hawkes
authors.affiliation: Centre for Medical Image Computing, Front Engineering Building, University College London, Malet Place, London, UK.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Clarkson
mesh_terms: D002138:Calibration; D055590:Electromagnetic Phenomena; D006498:Hepatectomy; D006801:Humans; D007091:Image Processing, Computer-Assisted; D020706:Laparoscopes; D010535:Laparoscopy; D025321:Surgery, Computer-Assisted; D014584:User-Computer Interface
keywords: Augmented reality; Hand–eye calibration; Laparoscope; Tracking