ALCoV-ISIT, UMR 6284 CNRS/Université d'Auvergne, Clermont-Ferrand, France.
Int J Med Robot. 2013 Dec;9(4):441-54. doi: 10.1002/rcs.1478. Epub 2013 Jan 10.
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.
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.
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.
Our experimental results show the effectiveness of simultaneously estimating hand-eye and distortion parameters for 3D reconstruction.
在本文中，我们提出了一种用于配备相机的手眼系统的非线性校准方法，该相机作为刚性内窥镜存在径向失真。经典方法要么分别估计相机内参数和手眼变换，要么假设针孔模型混合非线性估计手眼和相机内参数，而所提出的方法仅使用三个校准图案的帧即可同时细化手眼和相机参数，包括失真因子。
我们的方法依赖于三个步骤：（i）使用最少帧数的线性初始手眼和径向失真估计：仅使用一张图像来估计径向失真，使用三张图像来估计初始手眼变换，（ii）我们建议将相机外参表示为手眼和世界网格变换，（iii）我们在手眼变换、相机内参数和失真参数的重投影误差上运行捆绑调整。
我们的方法与最先进的线性和非线性方法进行了定量比较。我们表明，我们的方法提供了大约 5%的 3D 形状大小的 3D 重建误差。
我们的实验结果表明，同时估计手眼和失真参数进行 3D 重建是有效的。
