Directional multiscale modeling of images using the contourlet transform.

Area of Science:

• Image Processing
• Computer Vision
• Signal Analysis

Background:

• The contourlet transform is a novel 2D extension of the wavelet transform, utilizing multiscale and directional filter banks.
• It offers a rich set of basis images with flexible aspect ratios, enabling effective capture of smooth contours in natural images.

Purpose of the Study:

• To investigate the statistical properties of contourlet coefficients in natural images.
• To develop a statistical model for contourlet coefficients to enhance image processing applications.
• To evaluate the performance of the proposed model in image denoising and texture retrieval.

Main Methods:

• Statistical analysis of contourlet coefficients using histograms for marginal and joint distributions and mutual information for dependencies.
• Development of a hidden Markov tree (HMT) model with Gaussian mixtures to capture coefficient dependencies.
• Experimental evaluation of the HMT model in image denoising and texture retrieval tasks.

Main Results:

• Contourlet coefficients exhibit highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies.
• Coefficients can be approximated as Gaussian when conditioned on their generalized neighborhood magnitudes.
• The contourlet HMT model effectively captures these dependencies, outperforming wavelet methods in denoising and improving texture retrieval.

Conclusions:

• The statistical properties of contourlet coefficients are well-modeled by a hidden Markov tree with Gaussian mixtures.
• This model significantly enhances performance in image denoising, particularly around edges, and in texture retrieval for oriented textures.
• The contourlet transform, coupled with advanced statistical modeling, offers superior capabilities for analyzing and processing natural images.