Set mapping induced image perceptual similarity distance

Perceptual similarity between any two independent images is addressed with a set mapping perspective by first expanding each image A into a set φ(A) of images, and then defining the similarity between any two images A and B as the smallest average distortion d per pixel between any pair of images, one from φ(A) and the other from φ(B). The resulting similarity metric is dubbed the set mapping induced similarity distance (SMID) between A and B and denoted by d_φ(A,B). Several examples of the set mapping φ are illustrated; each of them gives a set φ(A) of images, which may contain images perceptually similar to A to certain degree. It is shown that under some mild conditions, d_φ(A,B) is indeed a pseudo distance over the set of all images. Analytic formulas for and lower bounds to d_φ(A,B) are also developed for some set mappings φ. When compared with other similarity metrics such as those based on histogram-based methods, SIFT, autocorrelogram, etc., the SMID shows better discriminating power on image similarity. Experimental results also show that the SMID is well aligned with human perception for image similarity.