Precision in the perception of direction of a moving pattern

The precision of the model of pattern motion analysis put forth by Adelson and Movshon (1982) who proposed that humans determine the direction of a moving plaid (the sum of two sinusoidal gratings of different orientations) in two steps is qualitatively examined. The volocities of the grating components are first estimated, then combined using the intersection of constraints to determine the velocity of the plaid as a whole. Under the additional assumption that the noise sources for the component velocities are independent, an approximate expression can be derived for the precision in plaid direction as a function of the precision in the speed and direction of the components. Monte Carlo simulations verify that the expression is valid to within 5 percent over the natural range of the parameters. The expression is then used to predict human performance based on available estimates of human precision in the judgment of single component speed. Human performance is predicted to deteriorate by a factor of 3 as half the angle between the wavefronts (theta) decreases from 60 to 30 deg, but actual performance does not. The mean direction discrimination for three human observers was 4.3 plus or minus 0.9 deg (SD) for theta = 60 deg and 5.9 plus or minus 1.2 for theta = 30 deg. This discrepancy can be resolved in two ways. If the noises in the internal representations of the component speeds are smaller than the available estimates or if these noises are not independent, then the psychophysical results are consistent with the Adelson-Movshon hypothesis.