A Complex Contourlet Transform and its HMT model for denoising and texture retrieval

This paper proposes a Complex Contourlet Transform (CCT) and develops the hidden Markov tree (HMT) model for it. Contourlet Transform (CT) has obvious advantages which are multiresolution, locality and multi-directional compared with traditional wavelet and can be considered as an effective tool in capturing geometric structure of natural images. Unfortunately, CT lacks of shift-invariance. The CCT keeps multi-directional of Contourlet and obtains higher shift-invariance by a structure of dual tree Laplacian pyramid (LP). The HMT model for CCT is developed to reveal the statistical dependence and the highly non-Gaussian distribution of the coefficients in subbands among inter- and intra-scales. To test the CCT-HMT model, we apply it on image denoising and texture retrieval. Experiments show that the HMT mode base on CCT achieves better performance compared with the HMT model based on Contourlet, either in denoising or in texture retrieval.