Image Modeling Based on Complex Wavelet Decomposition: Application to Image Compression and Texture Analysis

Natural image is defined in big dimensional space and it is not often easy to manipulate. It is necessary to use the projection of the image on the reduced space dimensions. Image modeling consists to find the best projection of the image allowing the good comprehension of the observed phenomenon and the good representation. Independently of the application, the modeling must give an efficient and an almost complete description of the image. The wavelet based image modeling is widely treated in the literature and in general the real wavelet decomposition is used. However, the real wavelet decomposition is not enough directional. Only three directions are considered in real wavelet decomposition: horizontal, vertical and diagonal directions. Complex wavelet decomposition allows these three directions and all other directions depending of the phase . This paper presents our contribution to the modeling of natural images using complex wavelet decomposition and its application to image compression and texture analysis. In this contribution, algorithms are developed, taking in account the wavelet coefficients and their arguments defining the phase information. In particular, an algorithm for magnitude modeling and an algorithm for phase modeling are implemented. Furthermore, a function is implemented which allows to determinate the model parameters as well for wavelet coefficients modeling as for phase modeling in the context of generalized Gaussian model. The simulations are done on some standard test images and the results are presented in terms of modeling curves and numerical parameters of the model. The modeling curves are obtained as well for coefficient magnitude as for phase information. The obtained results are applied to image compression and texture analysis. For image compression, one of the determined modeling parameters which is the standard deviation σ is used. The simulations are done on some standard test images and the results show that best image quality is possible, depending of the application, by the adjustment of the value of σ. For texture analysis, the phase information is used as a window to observe the texture; depending on the length of the angular interval, the texture may be observed or not in this window. The main contribution of this work is the modeling of the phase information and its application on the texture observation in one hand and the other hand the application of the magnitude coefficient modeling to image compression.