Perceptual dissociation of moving plaid patterns into independently moving bar gratings occurs most readily when the grating signals are combined as if the bars were semi-transparent objects (Ramachandran, V. S. (1990) in: AI and the Eye. Wiley, Chichester, pp. 21-77. Stoner, G. R., Albright, T. D. and Ramachandran, V. S. (1990) Nature 344, 153-155). These and other examples of motion transparency are exploited to constrain the set of viable models for human motion processing. For example, one may exclude any fixed recombination of local motion signals into a plaid motion signal. Broad classes of linear and non-linear mechanisms for tracking blobs, corners, and other unambiguous plaid motion cues can also be ruled out because they fail to reproduce the experimental results even qualitatively. The shifting balance between the 'coherent plaid' and 'sliding gratings' percepts are attributed to processing stages before any integration or combination of local motion signals. The first essential stage is a roughly logarithmic nonlinearity before orientation filtering. In general, the resulting cross-products (at the intersections) code unambiguously for the true plaid motion vector, but these signals will be nulled for multiplicatively combined plaid components. Supporting evidence for this idea is obtained in our measurements of detection thresholds for the 'plaid' and 'sliding' percepts. The essential element of the second stage consists of 'end-stop' cells which detect the nullable intersection signal, and so produce a plaid-motion signal with the required characteristics. Finally, it is argued that the ecological role of the proposed mechanism lies in the ability to handle movement of patterned objects in lighting conditions dominated by complicated cast shadows.