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Figures The aperture problem (A) Three instances of a vertical bar (thick black bar) translating in different directions, which all give rise to the same component of horizontal motion. The black arrows depict the true motion of the bar, whereas the gray arrows depict the horizontal component of the motion. The circles represent the spatial extent of a neuron's receptive field. The motion of the bar within this receptive field is identical for all three directions of bar motion. In the leftmost panel the true motion and the motion detector output are identical because the motion direction is orthogonal to the bar orientation. In the second panel the true motion is up and to the right and has a higher speed than in the first case, such that the horizontal component of motion in these two cases is the same. In the third panel, the bar is moving down and to the right but again has a horizontal component of motion equal to that of the first case. In general, an extended moving bar viewed through a small aperture provides only the component of motion perpendicular to the bar orientation. This is the aperture problem. Local measurements of motion within a restricted receptive field are thus consistent with many possible motion directions. As shown in the rightmost panel, all physical velocities with the same horizontal component lie along a constraint line that is parallel to the orientation of the bar. A motion detector tuned to rightward motion cannot distinguish between these three velocities or in fact any velocity that has an equivalent horizontal component. (B) Solving the aperture problem. The figure on the left shows a square translating diagonally upwards. As discussed for A, a detector responding to a single edge of the square can only code the component of motion perpendicular to the orientation of the edge. None of these individual detectors can signal the square's true motion, but its motion can be recovered by combining the constraints defined by the motion of at least two edges. The middle of the figure shows the constraint lines corresponding to the top and right edges of the square. The figure on the right shows that the square's true motion is determined by the intersection of these two constraint lines.

shown in Fig. 5. Figure 5A shows a moving vertical Since the preferred motion direction is perpendicular bar. The circle represents the receptive field of a motion to the preferred orientation, a unit that is selective for unit that is selective for the motion of vertical stimuli. vertical bars responds best to horizontal motion.

Figure 5A shows that this unit responds similarly to a small rightward motion as it does to a much larger diagonal (and rightward) motion. The true direction of object motion can lie anywhere along a constraint line parallel to the moving edge.

The directional ambiguity associated with local motion measurements can be resolved by combining motion estimates from more than one moving edge (Fig. 5B). Consider the case of a square that is moving diagonally upward. It has four edges at two different orientations. Local motion units that are selective for these orientations can only code the direction of motion orthogonal to these edges. Each of these measurements defines a constraint line. The intersection of these constraint lines gives the true direction of motion. The primate visual system also seems to implement such a solution. Units in V1 might detect motion of the top and bottom edges as upward and the motion of the left and right edges as rightward.

There is evidence that a proportion of units in the MT area of the brain, an area specialized for motion processing, combine these two component motions to give the true motion of the object. This corresponds to the direction specified by the intersection of constraint lines. Thus, these neurons are sensitive to the motion of 2D patterns. These pattern units respond best when the true direction of stimulus motion is in their preferred direction. Thus, they respond well to a single bar moving in their preferred direction and to a combination of bars whose intersection-of-constraints direction is their preferred direction. Furthermore, the receptive fields of cells in area MT are on average three times larger than those in corresponding retinal locations in V1, allowing them to integrate motion over a larger area. Their sensitivity to multiple directions of motion and their larger receptive fields make MT neurons well suited to solving the aperture problem. That humans are not normally subject to the aperture problem is proof that the primate visual system has implemented a solution.

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