Image invariance, scaling features and image similarity

Under image scaling transformation, the energy of a set of simple filtering templates display interesting scaling laws. These scalings are very universal in various kinds of images, robust against noise and local deformation and thus manifest themselves as the most salient property of images. The scaling exponents change from image to image and characterize image texture, edge and surface properties. An image similarity measure is built only in terms of these scaling laws. This similarity has many graceful properties such as invariance under rotation, scaling and translation transformation, and robustness against noise and image local deformation. The performance of this similarity is very promising, achieving very high average recognition rate. Thus scaling properties of images have great weight in perceptual evaluation of image similarity.