A maximum-likelihood solution to the joint parameter estimation problem of: a purely indeterministic component, a harmonic component, and a countable number of evanescent fields, from a single observed realization of the texture field is presented on the basis of a 2-D World-like decomposition model. The proposed solution is a two-stage algorithm. In the first stage, an estimate is obtained for the number of harmonic and evanescent components in the field, and a suboptimal initial estimate for the parameters of the spectral supports. In the second stage, the initial estimates is refined by iterative maximization of the likelihood function of the observed data. The World-based model and the resulting analysis and synthesis algorithms are seen applicable to a wide variety of texture types found in natural images. The model is very efficient in terms of the number of parameters required to represent and faithfully reconstruct the original texture.