A Geometric Hidden Markov Tree Wavelet Model Justin Romberg, Michael Wakin, Hyeokho Choi, Richard Baraniuk Dept. of Electrical puter Engineering, Rice University 6100 Main St., Houston, TX 77005 ABSTRACT In the last few years, it has e apparent that traditional wavelet-based image processing algorithms and models have significant ings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of the wavelet transform implies that these small coefficients will persist across scale (the canonical example is the venerable zero-tree coder). The edge contours in the image, however, cause more and more large magnitude wavelet coefficients as we move down through scale to finer resolutions. But if the contours are smooth, they e simple as we zoom in on them, and are well approximated by straight lines at fine scales. Standard wavelet models exploit the grayscale regularity of the smooth regions of the image, but not the geometric regularity of the contours. In this paper, we build a model that accounts for this geometric regularity by capturing the dependencies plex wavelet coefficients along a contour. The Geometric Hidden Markov Tree (GHMT) assigns each wavelet coefficient (or spatial cluster of wavelet coefficients) a hidden s
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