Uncertainty and sensitivity analysis for camera calibration

The purpose of this paper is to present a unified approach to uncertainty and sensitivity analysis for camera calibration.

The approach is based on the fact that camera calibration is a problem of parameter estimation and the parameters of interest are given by the optimal solution of a least‐squares problem.

A system of linear equations relating the errors of the extracted feature points to the errors of the estimated parameters is derived, and the expression of the covariance matrix of the estimated parameters is given. Also, a system of linear equations characterizing the influence of the uncalibrated parameters on the calibrated ones is presented. Simulation results show that the camera's position and orientation are less sensitive to the lens distortion than the offset of the image center.

The models developed can be applied to optimize the layout of the calibration marks and design multiple‐stage calibration algorithm. The rationale can also find applications in image registration and robot calibration.

A generic approach is proposed to perform uncertainty and sensitivity analysis for camera calibration. By using the optimality condition for an unconstrained optimization problem, two mathematical models are developed in a unified framework.