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Updated: May 15, 2026
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Published on: February 23, 2017
Hand-eye and radial distortion calibration for rigid endoscopes
Abed Malti1, Joao Pedro Barreto
1ALCoV-ISIT, UMR 6284 CNRS/Université d'Auvergne, Clermont-Ferrand, France.
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.
