Image registration covers the set of techniques used in matching images of the same scene. A subset of the image registration problem, identifying the parameters in a similarity transformation, has emerged as useful in a recently defined area of machine design: designing mechanisms for rigidbody shape-change. First, this brief paper shows a potential use for image registration techniques outside the field of machine vision. Second, it presents a closed-form solution for the similarity transformation parameters when the point sets to be matched are restricted to two-dimensional space as is needed in the aforementioned design problem.