title: Hand-eye and radial distortion calibration for rigid endoscopes.
abstract: BACKGROUND
  In this paper, we propose a non-linear calibration method for hand-eye system equipped with a camera undergoing radial distortion as the rigid endoscope. Whereas classic methods propose either a separated estimation of the camera intrinsics and the hand-eye transform or a mixed non-linear estimation of both hand-eye and camera intrinsics assuming a pin-hole model, the proposed approach enables a simultaneous refinement of the hand-eye and the camera parameters including the distortion factor with only three frames of the calibrated pattern.
  
  
  METHODS
  Our approach relies on three steps: (i) linear initial estimates of hand-eye and radial distortion with minimum number of frames: one single image to estimate the radial distortion and three frames to estimate the initial hand-eye transform, (ii) we propose to express the camera extrinsic with respect to hand-eye and world-grid transforms and (iii) we run bundle adjustment on the reprojection error with respect to the distortion parameters, the camera intrinsics and the hand-eye transform.
  
  
  RESULTS
  Our method is quantitatively compared with state-of-the-art linear and non-linear methods. We show that our method provides a 3D reconstruction error of approximately 5% of the size of the 3D shape.
  
  
  CONCLUSIONS
  Our experimental results show the effectiveness of simultaneously estimating hand-eye and distortion parameters for 3D reconstruction.
authors.affiliation: ALCoV-ISIT, UMR 6284 CNRS/Université d'Auvergne, Clermont-Ferrand, France.
authors.forename: Abed
authors.initials: A
authors.lastname: Malti
authors.forename: Joao Pedro
authors.initials: JP
authors.lastname: Barreto
mesh_terms: D000465:Algorithms; D016477:Artifacts; D002138:Calibration; D019723:Endoscopes / Q000592:standards*; D005123:Eye; D005602:France; D006225:Hand; D006801:Humans; D007089:Image Enhancement / Q000295:instrumentation* / Q000592:standards*; D015203:Reproducibility of Results; D012371:Robotics / Q000295:instrumentation* / Q000592:standards*; D012680:Sensitivity and Specificity
keywords: 3D reconstruction; endoscopy; hand-eye calibration; radial distortion