Smoothlets — Multiscale Functions for Adaptive Representation of Images

In this paper a special class of functions, called smoothlets, is presented. They are defined as a generalization of wedgelets and second order wedgelets. Unlike all known geometrical methods used in adaptive image approximation, smoothlets are continuous functions. They can adapt to location, size, rotation, curvature and smoothness of edges. The M-term approximation of smoothlets is O(M −3). In this paper also an image compression scheme based on the smoothlet transform is presented. From the theoretical considerations and experiments, both described in the paper, it follows that smoothlets can assure better image compression than the other known adaptive geometrical methods, namely wedgelets and second order wedgelets