Polarization Orientation Determination Algorithm Based on the Extremum of Moment of Inertia

A robust positioning algorithm of crosshair center based on grayscale weighting

“…Under these circumstances, the method to iteratively selected weights is used for robust estimation. The IGG method is used to construct the weight factor [13]:…”

“…, and 1 m m   to calculate ˆm k and ˆm b according to Formula (11), and to calculate m V , m  , and m P according to Formulae (4), (13), and ( 14).…”

“…For example, the horizontal axis of the crosshair is not parallel to that of the image in some methods, such as in case of the rotation of the crosshair with that of the illuminated section during the digital metrology of laser plummets [4]. If the horizontal axis of the crosshair is not parallel to that of the image, the results of fitting the lines of the cross-section and the vertical section are inconsistent [13]because the traditional least-squares line fitting is not invariant to the rotation of the coordinates. Some researchers have used axisymmetric line fitting instead of least-squares line fitting to address the above issue.…”

“…The criterion of fitting in this case is the smallest sum of the squares of distances from the point to the line. This method can obtain stable results in case of the rotation and translation of the image as well as changes in its scale, but it does not use grayscale information for weighted fitting [13,14].…”