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Proceedings Paper

Directional multiscale statistical modeling of images
Author(s): Duncan D.-Y. Po; Minh N. Do
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Paper Abstract

The contourlet transform is a new extension to the wavelet transform in two dimensions using non-separable and directional filter banks. The contourlet expansion is composed of basis images oriented at varying directions in multiple scales, with flexible aspect ratios. With this rich set of basis images, the contourlet transform can effectively capture the smooth contours that are the dominant features in natural images with only a small number of coefficients. We begin with a detail study of the statistics of the contourlet coefficients of natural images, using histogram estimates of the marginal and joint distributions, and mutual information measurements to characterize the dependencies between coefficients. The study reveals the non-Gaussian marginal statistics and strong intra-subband, cross-scale, and cross-orientation dependencies of contourlet coefficients. It is also found that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can approximately be modeled as Gaussian variables with variances directly related to the generalized neighborhood magnitudes. Based on these statistics, we model contourlet coefficients using a hidden Markov tree (HMT) model that can capture all of their inter-scale, inter-orientation, and intra-subband dependencies. We experiment this model in the image denoising and texture retrieval applications where the results are very promising. In denoising, contourlet HMT outperforms wavelet HMT and other classical methods in terms of both peak signal-to-noise ratio (PSNR) and visual quality. In particular, it preserves edges and oriented features better than other existing methods. In texture retrieval, it shows improvements in performance over wavelet methods for various oriented textures.

Paper Details

Date Published: 13 November 2003
PDF: 11 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.506412
Show Author Affiliations
Duncan D.-Y. Po, Univ. of Illinois/Urbana-Champaign (United States)
Minh N. Do, Univ. of Illinois/Urbana-Champaign (United States)

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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