Directional multiscale modeling of images using the contourlet transform

The contourlet transform is a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks. Because of its multiscale and directional properties, it can effectively capture the image edges along one-dimensional contours with few coefficients. This paper investigates image modeling in the contourlet transform domain and its applications. We begin with a detail study of the statistics of the contourlet coefficients, which reveals their non-Gaussian marginal statistics and strong dependencies. Conditioned on neighboring coefficient magnitudes, contourlet coefficients are found to be approximately Gaussian. Based on these statistics, we constructed a contourlet hidden Markov tree (HMT) model that can capture all of contourlets' inter-scale, inter-orientation, and intra-subband dependencies. We experiment using this model in image denoising and texture retrieval. In denoising, contourlet HMT outperforms wavelet HMT and other classical methods in terms of both visual quality and peak signal-to-noise ratio (PSNR). In texture retrieval, it shows improvements in performance over wavelet methods for various oriented textures.