Optimal Design of Orthogonal Wavelet Bases for Texture Discrimination Based Upon Fisher Criterion

Several methods have been developed in past for texture analysis and discrimination, but none of them converged to single solution due to different underlying properties of texture images. In case of wavelet transform, choice of suitable wavelet bases for texture discrimination is a critical issue. There are several factors involved in wavelet design which can greatly affect the results such as regularity, length of wavelet, orthogonal or bi-orthogonal etc. In this research work, we propose a methodology for the optimal design of orthogonal wavelet bases for maximum possible texture discrimination. Our objective function is based on maximization of distinguishibility measure involving the computation of finer details subject to some wavelet constraints. In contrast to well known orthogonal wavelet families, we kept necessary number of zeros at ω=π for the convergence of scaling function. Furthermore, length of wavelet is also a critical issue which has also been addressed. Classification results of optimized wavelet were compared with the existing wavelet families which show that the results obtained are superior in terms of texture discrimination and class separability.