Uncertainty Analysis of Camera Parameters Computed with a 3D Pattern

Camera calibration is a necessary step in 3D modeling in order to extract metric information from images. Computed camera parameters are used in a lot of computer vision applications which involves geometric computation. These applications use camera parameters to estimate the 3D position of a feature in the image. Depending on the accuracy of the computed camera parameter, the precision of the position of the image feature in the 3D scene vary. Moreover if previously the accuracy of camera parameters is known, one technique or another can be choose in order to improve the position of the feature in the 3D scene.

Calibration process consists of a closed form solution followed by a non linear refinement. This non linear refinement gives always the best solution for a given data. For sure this solution is false since input data is corrupted with noise. Then it is more interesting to obtain an interval in which camera parameters are contained more than an accurate solution which is always false.

The aim of this paper is to present a method to compute the interval in which the camera parameter is included. Computation of this interval is based on the residual error of the optimization technique. It is know that calibration process consists of minimize an index. With the residual error of the index minimization an interval can be computed in which camera parameter is. This interval can be used as a measurement of accuracy of the calibration process.