Wavelet packets are well-known for their ability to compactly represent textures consiting of oscillatory patterns such as fingerprints or striped cloth. In this paper, we report recent work on representing both periodic and granular types of texture using adaptive wavelet basis functions. The discrimination power of a wavelet packet subband can be defined as its ability to differentiate between any two texture classes in the transform domain, consequently leading to better classification results. The problem of adaptive wavelet basis selection for texture analysis can, therefore, be solved by using a dynamic programming approach to find the best basis from a library of orthonormal basis functions with respect to a discriminant measure. We present a basis selection algorithm which extends the concept of 'Local Discrminant Basis' (Saito and Coifman, 1994) to two dimensions. The problem of feature selection is addressed by sorting the features according to their relevance as described by the discriminant measure, which has a significant advantage over other feature selection methods that both basis selection and reduction of dimensionality of the feature space can be done simultaneously. We show that wavelet packets are good at representing not only oscillatory patterns but also granular textures. Comparative results are presented for four different distance metrics: Kullback-Leibler (KL) divergence, Jensen-Shannon (JS) divergence, Euclidean distance, and Hellinger distance. Initial experimental results show that Hellinger and Euclidean distance metrics may perform better as compared to other cost functions.