Notes

The "Aperture Problem"

This is a fundamental issue in the perception of motion that arises due to the limited spatial extent of the receptive fields of visual neurons, such as those in the primary visual cortex (V1). When a neuron's receptive field is limited or "apertured", it can only "see" a small portion of the visual scene, making it challenging to accurately determine the true motion direction of an object or pattern. For example, in the barber pole illusion we have diagonal stripes on a vertically rotating cylinder that appear to move vertically rather than diagonally, which is their true motion direction. The illusion occurs due to the limited spatial extent of V1 neurons' receptive fields and their sensitivity to specific orientations. When observing the barber pole, V1 neurons with receptive fields that match the orientation of the diagonal stripes are activated. However, because of their small receptive fields, they only "see" a small portion of the stripes and cannot determine the true motion direction. Instead, they detect motion along the stripes' orientation, which is perpendicular to the stripes. At the same time, the edges of the cylinder constrain the visible motion of the stripes to the vertical direction. This vertical motion is consistent with the motion detected by V1 neurons along the stripes' orientation, and it becomes the dominance percept.

The "Aperture Problem" in the Visual System

This is problem is relevant because our visual system is "seeing" the world through a bunch of small apertures. In the experiment above, it was investigated how the visual system resolves the aperture problem by studying the responses of direction-selective MT neurons in the macaque monkey. Their findings demonstrated that MT neurons can integrate local motion signals from V1 neurons to determine the true global motion direction and that they are highly sensitive to coherent motion, even in noisy visual stimuli. Referring to the picture, we can notice that by using only the receptive field of a single V1 cell we are not sure regarding the velocity of movement of the object and multiple velocities are possible, however integrating over two V1 receptive fields allows us to disambiguate and identify the single velocity vector representing the global motion. Referring to the picture on the right: the left-hand diamond moves to the right; the right-hand diamond moves down. Note that in both cases, in the local region indicated on each diamond by the small circle, the border moves downward and to the right. The moving edge (under the "diamonds") which could represent a magnified view of the circled regions of the diamonds' borders can be generated by any of the motions shown by the arrows. Motion parallel to the edge is not visible, so all motions that have the same component of motion normal to the edge are possible candidates for the "true" motion giving rise to the observed motion of the edge. We may map this set of possible motions as a locus in "velocity space".

Intersection of Constraints: This concept summarizes what we have been discussing: each neuron sensitive to motion provides a constraint on the possible motion direction of an object or pattern in the visual scene, based on the neuron's preferred orientation. However, due to the aperture problem, the motion information provided by a single neuron is ambiguous. By combining the constraints from multiple neurons with different preferred orientations, the visual system can determine the true motion direction where the constraints intersect.