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 that offer sample estimates of smaller variance and lower computational complexity. Nonlinear matching techniques are better than linear equation methods in estimating parameters of non-Gaussian random fields especially under model mismatch. Seasonal 1-D sequences allow for semistationary 2-D models, and their performance is illustrated on synthetic spacevariant textures. The potential of prolate spheroidal basis expansion is also described briefly for parsimonious nonstationary modeling of spacevariant textured images.