On many computer vision applications, it is often necessary to match a given image to one in an indexed set. One way this may done is by the identification and comparison of landmarks on the image. We call this discrete set of points in R^d a point configuration. We analyze different algorithms to decide whether or not two point configurations are identical up to a rigid motion. We call this identification, a match. We will also compare and analyze the possibility of using these algorithms for the problem of fingerprint identification.