Figure 8.

Computing the D-AF. A, B, Change of reference coordinates, from a cellulocentric (A) to a motion-axis aligned (B) framework. Each of the three (among six) maps illustrated in A can be combined by realigning them (by rotation, θ) such as to share a common motion axis (0°, horizontal arrow) as shown in B (left). B, Horizontal axis indicates the motion axis, and not the cell's preferred orientation. Thus, the new framework combines responses from different parts of the visual field but corresponding to similar trajectories (B, right), defined by rotation invariance around the RF center (C, black arrows). In other words, once in the motion reference frame, the term “trajectory” designates a particular set of coordinates in this new reference frame, which in turn corresponds to the set of trajectories invariant by rotation around the RF center in the cellulocentric reference frame. C, D, Schematic explanation of the D-AF computation. The strength of the responses to a set of six trajectories invariant by rotation around the cell RF (black arrows) is schematically illustrated by the size of the colored arrows (C). The circular average of those responses is then computed in the motion reference frame (D). It consists of the vectorial average (over [−π,π]) of the colored arrows in C given the angle 2 × θ (with θ being the angle depicted in A), and results in the white arrow. The modulus of this sum vector (i.e., |R|) gives the selectivity index of the directional response for this trajectory (illustrated by the size of the gray bar). The angle with the motion flow axis of this sum vector, once divided by 2, gives the preferred RF orientation for the trajectory (orientation of the gray bar, within [−π/2, π/2]): that is, the RF orientation for which the response to the trajectory (in the motion-reference-frame's generic sense) would be maximal. The gray level intensity of the bar denotes the strength of the mean response for the trajectory (normalized to the maximum across trajectories).