Research Of Texture Feature Extraction On Copula Driven Wavelet Domain

Texture extraction methods in the wavelet domain can be mainly divided into two categories:one is wavelet signature method, which calculates the energy features from each wavelet subband; the other one is the complex statistical model which uses statistical models such as the generalized Gaussian model, Gaussian mixture model or hidden Markov tree to capture the distribution of wavelet coefficients. It has been shown that the texture feature extraction method based on statistical analysis of the wavelet domain is one of the most useful texture feature extraction method, and has a wide range of applications in the domains of image analysis and pattern recognition. The research on statistical model in wavelet domain has a long history. Early methods mainly focus on establishing a statistical model for each wavelet subband independently. The mass literature indicates that dependencies in the domain of wavelet are widely existed; however it is very difficult to design an effective multidimensional joint distribution model in wavelet domain due to the complexity of these dependencies. Recent researches have demonstrated the method by using multidimensional joint distribution of wavelet domain can effectively improve the performance of wavelet for texture analysis.Copula is an excellent tool to characterize the dependence structure of variables, and it has been successfully applied in the field of finance. Introducing copula into wavelet domain is an effective and important measure. Using copula function enables the task of specifying the marginal distributions to be decoupled from the dependence structure of variables. This allows us to exploit univariate models in wavelet subband at the first step, and is directly linked to multivariate probability distributions at second step. However, how to design a suitable multivariate probability distribution by using copula on the domain of wavelet is still a difficult task because of the complex dependencies in the wavelet domain and the limitations of copula function.This dissertation focuses on researching the dependencies of wavelet domain, and building copula driven multivariate probability distribution on the wavelet domain. The main work and contributions are as follows: 1. Copula multivariate probability distributions were implemented on the real wavelet domain and complex wavelet domain. Regarding real wavelet, the multivariate probability distributions on the domains of traditional wavelet, contourlet and stationary wavelet are developed by using copula. Regarding complex wavelet, the magnitude coefficients of Gabor wavelet and dual-tree complex wavelet, and the phase coeffients of quaternion wavelets with copula multivariate probability distribution are explored.These selected wavelets are widely used, so it is very valuable to establish multivariate probability distribution on the domain of these wavelets. Detailed analysis and comparison for the performance of the Multivariate copula models among these wavelet domains are made through texture retrieval experiments.2. Due to the complexity of the dependencies on wavelet domain, in this work, scatter plots, mutual information, and chi-plot diagram are employed to analyze the dependence on the wavelet domains. The dependencies of the wavelet domain are categorized into four categories:intra-subband dependence, intra-scale dependence (inter-direction dependence), and color feature dependence in same subband. In order to effectively improve the representation ability of wavelet for texture features, we designed different dependent model for the different wavelets, and implemented multivariate probability distribution with copulas.3. Two-layer of inter-scale dependence model on the wavelet domain was proposed. The proposed model builds a5-dimensional vector on quad-tree structure between two adjacent wavelet decomposition layers. After establishing the marginal distributions, the copula is used to join these marginal distributions into a multivariate probability distribution. Two-layer dependences will be obtained from three wavelet level decompositions. Two-layer dependence model has two advantages:first, it can capture the intra-subband and inter-scale dependence; second, it has lower computational complexity than the intra-subband dependence model.4. A rotational invariant approach was developed based on Gabor wavelet and copula. The rotational invariant approach, which utilizes both the characteristic of Gabor and copula, can significantly improve the texture retrieval performance under rotational condition. By means of Kullback-Leibler distance of Gaussian copula the low computational complexity was also obtained. Experiments show that the method is remarkably insensitive to the change of rotation. 5. Multivariate copula models based on the phase coefficients of complex wavelet was proposed. The dependences of intra-subband, intra-scale and inter-scale on the phase coefficients of the complex wavelet phase were explored. In these copula models. Gaussian mixture model was used to fit phase coefficients, and Bayesian-ML was employed as the texture retrieval processing. Experiment results show that copula multivariate distribution has better retrieval performance than univariate distribution on the phase of the complex wavelet.