Study Of Multi-Directional Wavelet Construction Based On Human Visual System And Its Application

Image representation is the basic problem in image processing. Wavelet is the best base of functions, with point singularity, and it has wide application in image processing because of its time-frequency localization and multiscale features. On the other hand, since the separable wavelet is isotropic and has poor directional selectivety, it can only characterize the location and trait of point singularity, and can hardly characterize the high-dimensional geometrical structures such as edges and textures in images, so wavelet isn't the best base for images.To overcome the challenging problem, we make deeply study for the methods of mutilscal geometry analysis, and propose a novel directional wavelet transform based on trait of human visual system. This transform is named fanlet transform since the frequency spectrum support of directional subbands is fan-shaped. The bases of the fanlet transform overcome the poor directional selectivety limitation of the 2D separable wavelet, and it possess the characteristics of the simple cell receptive field in visual cortex V1 area, such as multi-resolution, localization, anisotropy and multi-directional selectivity etc. The fanlet transform is implemented by the circular symmetric multiresolution decomposition and directional filter banks, the circular symmetric filter bank decomposes image into multi-resolution detail subbands and one low-frequency subband, and the detail subbands are further decomposed into directional subbands by directional filter banks. The circular symmetric filter bank satisfying reconstruction conditions is designed by genetic algorithm. The 9/7 biorthogonal filter bank is mapped to fan filter bank by the mapping function which derived from the Bernstein polynomial.Translation invariant lies at the heart of many image processing and pattern recognition. Although the pyramidal decomposition in the fanlet transform is translation invariant, since the sub-sampling structures in directional filter bank, the fanlet transform isn't translation invatiant. To overcome the problem, four translation invariant fanlet transforms(TIFanlet) which combine translation invariant pyramidal decomposition and undecimated directional filter bank(UDFB) are proposed, and the implementation methods of the TIFanlet are given detailly. We have proven that the TIFanlet transformsatisfies the tight frame condition. The undecimated fan filter banks in UDFB are designed by mapping method using one-dimensional fractional splines orthogonal filter bank as prototype filter, and the magnitude frequency responses of the filter banks can be adjusted flexibly by adjusting the order of the prototype filter.The non-Gaussian and non-independence characteristics of the Fanlet and TIFanlet coefficients are studied by qualitative and quantitative measures. We have verified that the marginal distribution of the Fanlet and TIFanlet coefficients satisfy generalized Gaussian distribution by x2 hypothesis. The generalized bivariate model is proposed to characterthe joint-distribution of the Fanlet and TIFanlet coefficients. The statistical model parameters are estimated by moment method and maximum likelihood estimator.The image denosing algorithm which combines the statistical model of the Fanlet and TIFanlet coefficients with MAP estimator is proposed. The image which is denoised by using the proposed algorithm has high PSNR value while preserving the edges and textures of the images effectively. The effective image restoration algorithm is implementd by combining the proposed denoising algorithm with the Wiener filter, and the SNR and ISNR values of the restored image outperform the ForWaRD algorithm significantly.The texture image retrieval algorithm which fuses the local binary patterns and the subbands statistical model is proposed. Since visually distinct patterns may have matching subband statistics, and the subbands statistical features and the local binary patterns are complementary features in a certain sense, the combined features can character the intrinsic trait of the texture image. The experiments show that retrieval ratio obtained from combined features is higher than single features.