Hand–eye and radial distortion calibration for rigid endoscopes

Authors


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. Copyright © 2013 John Wiley & Sons, Ltd.

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