The first step above is for the case where the array positions of the coordinate points differ from those that would result from the projection from the sky. Examples are distortions of astrometric plates caused by imperfect optics or emulsion shrinkage and the effects of ionospheric refractions on radio maps. GC describe how to carry out this process through the use of a Pixel Regularization Image. This step involves only the correction for small distortions; all aspects of the coordinate transformation between the rectangular grid and physical space should be incorporated into the subsequent steps.