Different classes of image-distance functions are often used in computer vision. Robust pictorial indexes can be also constructed based on distance criteria for image retrieval purposes. This paper introduces two new classes of entropic distances that are based on the concept of convex transformations. Their formal properties are studied and tested on real images. Experiments on the comparison of images and the matching of objects are presented. A comparison of image distances, here, is proposed and carried out with measures of closeness.