引用本文: 李兴东, 郭伟, 李满天, 陈超, 孙立宁. 一种估计深度相机位姿精度的闭式算法[J]. 机器人, 2014, 36(2): 194-202,209.
LI Xingdong, GUO Wei, LI Mantian, CHEN Chao, SUN Lining. A Closed-form Solution for Estimating the Accuracy of Depth Camera’s Relative Pose[J]. ROBOT, 2014, 36(2): 194-202,209.
 Citation: LI Xingdong, GUO Wei, LI Mantian, CHEN Chao, SUN Lining. A Closed-form Solution for Estimating the Accuracy of Depth Camera’s Relative Pose[J]. ROBOT, 2014, 36(2): 194-202,209.

## A Closed-form Solution for Estimating the Accuracy of Depth Camera’s Relative Pose

• 摘要: 针对深度相机，提出了估计位姿变换精度的闭式解算法．相对位姿由6自由度向量 T=xyzα,β,γ表示，计算该向量的协方差矩阵来表征相对位姿精度．定义3维点对到相对位姿的隐式函数，利用隐式定理计算该隐式函数相对于点对集合的偏导数，从而根据隐式函数变化趋势和深度相机测量误差来计算协方差矩阵．该方法要求3维点对匹配准确无误，所以本文同时提出在给定相对位姿情况下匹配3维点对算法，该算法充分利用深度相机可以同时返回深度信息和灰度信息的特点．最后在随机生成数据和真实数据上验证了相对位姿精度估计算法的有效性．

Abstract: A closed form solution for estimating the accuracy of pose transformation of depth camera is proposed. In general, relative pose is represented by 6 DoF (degree of freedom) vector T=x, y, z, α, β, γ. The covariance matrix of T is used to measure the accuracy of the relative pose. An implicit function from the three dimensional point pairs to the relative pose is defined, and then implicit theorem is employed to compute the partial derivatives of the function with respect to such point pairs, after that the covariance matrix is computed from both the changing trend of the implicit function and the measuring error of depth camera. In order to compute covariance matrix accurately, 3D point pairs must be correctly matched, so an effective algorithm is also proposed to match 3D point pairs given the relative pose. This algorithm makes full use of the advantageous property of depth camera that both depth information and intensity information are returned after one exposure. At last, the effectiveness of the method for estimating the accuracy is validated based on both random synthetic and real data sets.

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