Calibration of Digital Amateur Cameras for Optical 3D Measurements With Element-Wise Weighted Total Least Squares (EW-WTLS) and Classical Least Squares: A Comparison

Abstract

In order to improve the precision and accuracy of the calibration results, there are two general effects should be considered. One of them is the definition of the mathematical model of the calibration problem with respect to the physical nature of the problem, and the other one is the statistical model of the estimation of the calibration parameters. The estimation procedure is important for both dealing with the uncertainties of the observed measurements for computing the parameters and the numerical solution of the model. The classical least squares (LS) estimation model assumes that only the observation vector is erroneous while the data matrix is error free even its elements are the functions of the erroneous observations. These propagated errors in the data matrix elements stay as uncertainties in the classical LS model. The main purpose of this paper is to deal with those uncertainties in the camera calibration problem, by using the EW-WTLS estimation method and compare the results with the classical LS method. Both methods give almost the similar results. But at least in theory, the EW-WTLS estimation technique may be said to be more realistic than LS, by the means of its statistically more much realistic model.