SIMILARITY AND AFFINE INVARIANT DISTANCES BETWEEN 2D POINT SETS

We develop expressions for measuring the distance between 2D point set s, which are invariant to either 2D affine transformations or 2D simil arity transformations of the sets, and assuming a known correspondence between the point sets. We discuss the image normalization to be appl ied to the images before their comparison so that the computed distanc e is symmetric with respect to the two images. We then give a general (metric) definition of the distance between images, which leads to the same expressions for the similarity and affine cases. This definition avoids ad hoc decisions about normalization. Moreover, it makes it po ssible to compute the distance between images under different conditio ns, including cases where the images are treated asymmetrically, We de monstrate these results with real and simulated images.