Texture is a phenomenon in image data that continues to receive wide-spread interest due to its broad range of applications. The paper focuses on but one of several ways to model textures, namely, the class of stochastic texture models. the authors introduce a new spatial stochastic model called partially ordered Markov models, or POMMs. They show how POMMs are a generalization of a class of models called Markov mesh models, or MMMs, that allow an explicit closed form of the joint probability, just as do MMMs. While POMMs are a type of Markov random field model (MRF), the general MRFs do not have such an explicit closed form of the joint probability. The authors present results on texture synthesis and texture classification, introducing a very fast one-pass texture synthesis algorithm, and show that parameter estimation of natural textures can give quite satisfactory results. They remark that, while the theory underlying POMMs has been applied only to texture analysis, in their most general form, POMMs have the potential to be applied to such diverse areas outside of imaging as probabilistic expert systems, Bayesian hierarchical modeling, influence diagrams, and random graphs and networks.