Images Identification Based on Equivalence Classes

The image identification problem consists in identifying all the equivalent forms of a given reference image. An image is equivalent to the reference image, if the former results from the application of an image operator (or a composition of image operators) to the latter. Depending on the application, different sets of image operators are considered. The equivalence quantification is done in three levels. In the first level, we construct the set of equivalent images which is composed of the reference and its modified versions obtained through the application of image operators. In the second level, visual features are extracted from images in the equivalence set and their distances to the reference image are computed. In the third level, an orthotope (generalized rectangle) is fit to the set of distance vectors corresponding to the equivalent images. The equivalence of an unknown image with respect to a given reference is defined according to whether the corresponding distance vector is inside, or outside, the orthotope. The results of our algorithm are assessed in terms of the false positive and false negative errors (computed over different choices of reference images and operators).