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A quantitative model is developed to predict the perceived direction of moving two-dimensional patterns. The model incorporates both a simple motion energy pathway and a “texture boundary motion” pathway that incorporates response squaring before the extraction of motion energy. These pathways correspond to Fourier and non-Fourier motion pathways and are hypothesized to reflect processing in the VI-MT and V1-V2-MT pathway, respectively. A cosine-weighted sum of these pathways followed by competitive feedback inhibition accurately predicts the perceived direction for patterns composed of two cosine gratings at different orientations (“plaids”). The model also predicts direction discrimination, differences between foveal and peripheral viewing, changes in perceived direction with exposure duration, motion masking, and motion transparency.