Cumulants are employed for classification and synthesis of textured images because they suppress additive Gaussian noise of unknown covariance and are capable of resolving phase and causality issues in stationary non-Gaussian random fields. Their performance is compared with existing autocorrelation based approaches which offer sample estimates of smaller variance and lower computational complexity. Nonlinear matching techniques improve over linear equation methods in estimating parameters of non-Gaussian random fields especially under model mismatch. Seasonal 1-D sequences allow for semi-stationary 2-D models and their performance is illustrated on synthetic space variant textures. The potential of prolate spheroidal basis expansion is also described for parsimonious nonstationary modeling of space variant textured images.