The visual system can detect coherent motion in the midst of motion noise. This is accomplished with motion-sensitive channels, each of which is tuned to a limited range of motion directions. Our aim was to show how a single channel is affected by motions both within and outside its tuning range. We used a psychophysical reverse-correlation procedure. An array of dots moved coherently with a new, randomly chosen, direction every 14 or 28 ms. Human subjects pressed a key whenever they saw upwards movement. The results were analyzed by finding two motion directions before each key-press: the first preceded the key-press by the reaction time, and the second preceded the first by a variable interval. There were two main findings. First, the subject was significantly more likely to press the key when the vector average of the two motions was in the target direction. This effect was short-lived: it was only seen for inter-stimulus intervals of several tens of milliseconds. Second, motion detection was reduced when the target direction was preceded by a motion of similar direction 100–200 ms earlier. The results support the idea that a motion-sensitive channel sums sub-optimal inputs, and is suppressed by similar motion in the long term.

*x*= 0.288,

*y*= 0.308) with a luminance of 64 cd/m

^{2}, and the room lights were off. Subjects used a chin- and forehead-rest to reduce head movements. The stimulus was enclosed within a black border, as shown in Figure 1. The inner dimensions of the border were 2.5° × 2.5° and border width was 0.25°. A white dot 0.1° in diameter was placed at the center of the bordered area; both border and dot helped to stabilize fixation. The stimulus comprised 30 black dots, each dot being 0.1° in diameter. The luminance of the border and black dots was 0.9 cd/m

^{2}and that of the fixation dot was 115 cd/m

^{2}.

*n*

_{ i }is the number of key-presses preceded by motion direction

*i,*and

*m*is the mean number of key-presses (∑

*n*

_{ i }/20). Figure 2C plots chi-square as a function of time prior to a key-press for all five subjects. Four subjects have a reaction time of around 400 ms and one subject about 550 ms. Although this subject's reaction time was unusual, her results from the remaining analyses were consistent with those of the other subjects.

*d*

_{1}precedes the key-press by the reaction time, and the direction

*d*

_{2}immediately precedes

*d*

_{1}. Figure 4A shows the probability

*p*

_{obs}(

*d*

_{1},

*d*

_{2}) of observing this combination of stimuli before a key-press. There is a bright area at the center of this plot indicating that the most likely stimuli leading to a key-press are two targets. This is not surprising as each target could contribute to a key-press independently of the other. To see whether there was any interaction between the two stimuli in producing a key-press we performed two further analyses. First, the probability density in part A of the figure was recalculated under the assumption that the two stimuli act independently:

*p*

_{1}(

*d*

_{1}) in this equation was obtained by summing the observed probabilities across values of

*d*

_{2}and, similarly,

*p*

_{2}(

*d*

_{2}) was obtained by summing probabilities across

*d*

_{1}. (Examples of

*p*

_{1}(

*d*

_{1}) and

*p*

_{2}(

*d*

_{2}), obtained more directly, are shown in Figure 3.) The result of applying Equation 2 is shown in Figure 4B. If

*d*

_{1}and

*d*

_{2}interact in producing a key-press, the independence model

*p*

_{ind}will differ from the observations

*p*

_{obs}. The last step in the analysis therefore subtracted one from the other:

*d*

_{1}, as described in the Methods) and averaged. The plots in Figure 4 and in the following figures were all calculated with this weighted averaging procedure.

*Facilitation*. Similarly, dark areas are labeled

*Suppression*. To test for statistical significance, the interaction plot was tested with a two-way analysis of variance. The two factors were

*d*

_{1}and

*d*

_{2}, each with 20 levels, and subjects provided the five replicates. The interaction term in this test,

*d*

_{1}×

*d*

_{2}, was highly significant (

*F*(361, 1200) = 3.54,

*p*< 0.001). The most interesting feature of the interaction plot is that the area of facilitation lies on the negative diagonal. This means that, for example, a motion 36° anticlockwise from the target combines with a following motion 36° clockwise from the target to make a key-press more likely. Put otherwise, a target motion is more likely to be seen when the vector sum of consecutive motions is in the target direction.

*d*

_{1}immediately followed

*d*

_{2}. The result can therefore be compared with the upper right plot in Figure 5. Facilitatory areas for the model lie on the negative diagonal, lending support to the idea that they are due to summation in a broadly tuned detector. The Discussion expands on these ideas. The model's interaction plot contains areas of suppression as well as of facilitation. These do not arise from inhibition, as the model contains no inhibitory mechanisms. Rather, they result from the analysis method. The probabilities in each of the observations (Figure 4A) and independence model (Figure 4B) plots sum to unity (the certain event). The values in the interaction plot (Figure 4C) therefore sum to zero, and the presence of facilitation in one part of the plot leads to suppression elsewhere. The most useful aspect of an interaction plot, therefore, is not so much the existence of facilitatory and suppressive areas, but their relative locations within the plot.

*p*= 0.047). This indicates that preceding a target motion with a motion in the opposite direction makes a key-press less likely. This finding fits well with previous observations that motion is less visible when presented along with another motion in the opposite direction (Iyer & Freeman, 2009; Lindsey & Todd, 1998; Mather & Moulden, 1983).

*b,*observed at the briefest inter-stimulus intervals (28 ms for the 36 Hz movie, and 14 ms for the 72 Hz movie). This pattern is a function of motion directions

*d*

_{1}and

*d*

_{2}and is therefore denoted

*b*(

*d*

_{1},

*d*

_{2}). The second pattern,

*l*(

*d*

_{1},

*d*

_{2}), is seen in the long-term and can be characterized by the mean plots shown at the bottom of the figure. This second pattern can be calculated by noting that it is symmetric about the horizontal midline (the line for which

*d*

_{2}is equal to the target direction). Accordingly, the long-term pattern was set equal to the mean over all inter-stimulus intervals,

*t,*of the symmetric component of the interaction plot,

*i*(

*t, d*

_{1},

*d*

_{2}):

*f*(

*t*) and

*s*(

*t*) are the time courses of the two patterns, and

*ɛ*is error not accounted for by the model. This model was fitted to the empirical interaction plots by least-squares regression, and the resulting time courses are shown in Figure 9 with

*f*(

*t*) and

*s*(

*t*) labeled

*Facilitation*and

*Suppression,*respectively. Data for the 36 and 72 Hz movies are shown on the left and right, respectively, time courses for individual subjects are shown in the upper row, and the decompositions of the mean across subjects in the lower row. F-testing showed that all regressions were significant at the 5% level; 95% confidence intervals are provided. The results show that the facilitatory pattern is limited to inter-stimulus intervals of less than about 100 ms, whereas the suppression between similar motions peaks between 100 and 200 ms, and lasts for at least 500 ms.

*i*= 1, 2, …,

*m,*tuned to motion directions,

*c*

_{ i }, that are evenly distributed across the full 360° of motion directions (see Figure 6A for an illustration). The sensitivity of channel

*i*to motion direction

*d*has amplitude

*σ*

_{ d }is the standard deviation of its tuning curve. In keeping with previous work (Fredericksen et al., 1994; Simpson & Newman, 1998), each channel is assumed to be a low-pass temporal filter

*r*

_{ i }(

*t*) is the channel's response as a function of time

*t, τ*is its time constant, and

*s*(

*t*) is the motion stimulus. The stimulus to channel

*i*is a sequence of motion impulses with direction

*d*

_{ j },

*j*= 1, 2, …,

*n,*at times

*t*

_{ j }:

*δ*(

*t*) is a (Dirac) delta function at time

*t*. The time course therefore consists of a step increase at each stimulus, followed by an exponential decay. The size of the step declines as the stimulus direction shifts from the direction to which the channel is tuned.

*ode45*). Simulation time was 200 minutes. The response in the channel tuned to the target direction was monitored, and a key-press was triggered each time this response exceeded that of all other channels. A variable delay was added to the time of the key-press to simulate the variability of reaction times shown in Figure 2. This delay was a random sample from a Gaussian probability density with standard deviation

*σ*

_{ t }. The analysis of key-press times was the same as that used for the empirical data.

*m,*is not critical provided it is no less than the number of motion directions, 20. The tuning curve bandwidth,

*σ*

_{ d }, was taken from Britten and Newsome (1998) who measured the bandwidth in a population of MT cells (their Figure 3, stimulus coherence of 100%, bandwidth divided by √2 to convert it to a standard deviation). The time constant,

*τ,*was set so that the facilitation was relatively small at an inter-stimulus interval of 28 ms, consistent with the data in Figure 5. The standard deviation,

*σ*

_{ t }, was set equal to that found empirically in Figure 2.