Multiscale Edge Grammars for Complex Wavelet Transforms
Baraniuk, Richard G.
complex wavelets; phase structure; edge detection
Wavelet domain algorithms have risen to the forefront of image processing. The power of these algorithms is derived from the fact that the wavelet transform restructures the image in a way that makes statistical modeling easier. Since the edge singularities in an image account for the most important information, understanding how edges behave in the wavelet domain is the key to modeling. In the past, wavelet-domain statistical models have codified the tendency for wavelet coefficients representing and edge to be large across scale. In this paper, we use the complex wavelet transform to uncover the phase behavior of wavelet coefficients representing an edge. This allows us to design a hidden Markov tree model that can discriminate between large magnitude wavelet coefficients caused by texture regions in the signal, and ones caused by edges.