A robust positioning algorithm of crosshair center based on grayscale weighting

In this study, the authors propose a robust one-step algorithm to position the center of the crosshair for image measurement based on gray weighting (or gray-squared weighting) (GWRCP, GSWRCP) and axisymmetric straight-line fitting, which is a crucial part of the positioning algorithm. The proposed algorithm is also capable of making robust estimations. The results of simulations to test it showed that error in the GWRCP and GSWRCP was below 0.01 pixels following the addition of different levels of Gaussian noise, and was below 0.05 pixels following the addition of the gross error. The outcomes of examples of its application showed that the GWRCP/GSWRCP with an error smaller than 0.01 pixels exhibited superior resistance to noise and the gross error than the method that involves artificially removing the latter.