Texture are one of the basic features in visual searching and computational vision. In the literature most of the attention has been focussed on the texture features with minimal consideration of the noise models. In this paper, we investigate the problem of texture classification from a maximum likelihood perspective. We take into account the texture model, the noise distribution, and the inter-dependence of the texture features. Our investigation shows that the real noise distribution is closer to an exponential than a Gaussian distribution, and that the L/sub 1/ metric has a better retrieval rate than L/sub 2/. We also propose the Cauchy metric as an alternative for both the L/sub 1/ and L/sub 2/ metrics. Furthermore, we provide a direct method for deriving an optimal distortion measure from the real noise distribution, which experimentally provides consistently improved results over the other metrics. We conclude with results and discussions on an international texture database.