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Two-dimensional (2D) autoregressive moving average (ARMA) random fields have been proven to be accurate models of ultrasound breast images. However, the stability properties of these models have not been examined. In this paper, we investigate the stability of 2D ARMA models in ultrasound breast images, and use the estimated 2D ARMA coefficients as a basis for statistical inference using artificial neural networks. Specifically, we use the estimated 2D ARMA coefficients as inputs to a multi layer perceptron (MLP) neural network to classify the ultrasound breast image into three regions: healthy tissue, benign tumor, and cancerous tumor. Our simulation results on various cancerous and benign ultrasound breast images illustrate the power of the proposed algorithm as attested by different learning algorithms and classification accuracy measures.