Characterization of Signals from Multiscale Edges

A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. We study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. We show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. We describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below our visual sensitivity. As an application, we implement a compact image coding algorithm that selects important edges and compresses the image data by factors over 30.