Graylevel alignment between two images using linear programming

A critical step in defect detection for semiconductor process is to align a test image against a reference. This includes both spatial alignment and grayscale alignment. For the latter, a direct least square approach is not very applicable because the presence of defects would skew the parameters. Instead, we use a linear programming formulation which has the advantage of having a fast algorithm, while at the same time can produce better alignment of the test image to the reference. Furthermore, this is a flexible algorithm capable of incorporating additional constraints, such as ensuring that the aligned pixel values are within the allowable intensity range.