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The purpose of this paper it to explore the relationship between the rate-distortion characteristics of multiscale binary shape and Markov random field (MRF) parameters. For coding, it is important that the input parameters that will be used to define this relationship be able to distinguish between the same shape at different scales, as well as different shapes at the same scale. We consider an MRF model, referred to as the Chien model, which accounts for high-order spatial interactions among pixels. We propose to use the statistical moments of the Chien model as input to a neural network to accurately predict the rate and distortion of the binary shape when coded at various scales.