Subpixel precision of straight-edged shapes for registration and measurement

The precision by which a region is located or measured on the image plane is limited by the sampling density. In this paper, the worst-case precision errors are determined for calculating the average image location of an edge, line, and straight-edged region. For each case, it is shown how the worst-case error can be minimized as a function of the geometric parameters. These results can be used to determine the worst case error by which the location of a known shape is measured. Another application is to design shapes for use in registration, such as fiducial marks used in electronic assembly. The main conclusion of this paper is that, to achieve better precision, measurement of a straight-edged region should be made at an angle askew to the sampling axis (not 0, 45, or 90 degrees) and this should be at a certain length that is a function of this skew angle.