Signal characterization from multiscale edges

An algorithm that reconstructs one-dimensional signals and images from their sharper variation points at dyadic scales is described. This algorithm exactly reconstructs images from their multiscale edges. It is proved that the evolution across scales of the wavelet maxima characterizes the local shape of the sharp variations of the signal. One can thus not only detect edges but also classify them. The wavelet maxima representation is a new reorganization of the image information that makes it possible to develop algorithms uniquely based on edges for solving image processing problems