A closed-form solution for estimating the accuracy of depth camera's relative pose

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.