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A class of robust two-dimensional (2-D) tree coding procedures are described for efficient encoding of monochrome images. The encoding filter is designed on the basis of ensemble properties of a particular class of stochastic random fields which have been shown to provide a useful model for typical imagery data. We make use of the ( ) algorithm in instrumenting the 2-D tree search. Results are demonstrated for both synthetic images and a number of head-and-shoulders images. These results demonstrate the effectiveness of 2-D tree encoding using fairly moderate search intensities and the inherent robustness of 2-D tree encoding more generally. In particular, it is demonstrated that, by logical design of the encoding filter under an appropriate stochastic modeling assumption, the 2-D tree encoder provides relatively efficient performance for a rather wide range of real-world imagery.