Multiscale edge grammars for complex wavelet transforms

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 images in a way that makes statistical modeling simpler. Since edge singularities account for the most important information in images, 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 an edge to be large across scale. 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 and ones caused by edges.