The perceived direction of motion of a brief visual stimulus that contains fine features reverses if static coarser features are added to it. Here we show that the reversal in perceived direction disappears if the stimulus is reduced in size from 2.8 deg to 0.35 deg radius. We show that for a stimulus with 1.4 deg radius, the reversals occur when the ratio between the contrast of the fine features and of the coarser features is higher than 0.8 and lower than 4. For stimulus with 0.35 deg radius, the reversals never appear for any contrast ratio. We also show that if the stimulus is presented within an annular window with small radius, errors disappear but they return if the radius is increased to 2 deg. The errors in motion discrimination described here can be explained by a model of motion sensing in which the signals from fine-scale and coarse-scale sensors are subtracted from one another (I. Serrano-Pedraza, P. Goddard, & A. M. Derrington, 2007). The model produces errors in direction when the signals in the fine and coarse sensors are approximately balanced. The errors disappear when stimulus size is reduced because the reduction in size differentially reduces the response of the low spatial frequency motion sensors.

*σ*

_{ xy }= 0.35 deg) and other large (

*σ*

_{ xy }= 1.4 deg). For very small stimuli, the reversals did not appear for any contrast ratio.

^{2}.

*n*

_{1}and

*n*

_{2}are anisotropic filtered white Gaussian noises with peak spatial frequencies of 1 and 3 cycles/deg, respectively (see the filter used in Equation 3);

*L*

_{0}is the mean luminance, in cd/m

^{2};

*σ*

_{ xy }is the spatial standard deviation, in degrees of visual angle (deg);

*m*is the Michelson contrast as a function of time given by the next Gaussian function:

*m*(

*t*) = exp{−

*t*

^{2}/(2

*σ*

_{ t }

^{2})}, where

*σ*

_{ t }is the temporal standard deviation, in milliseconds (ms);

*υ*

_{1}and

*υ*

_{2}are the velocities of each noise, in deg/s;

*m*

_{1}and

*m*

_{2}are the contrasts that were calculated to ensure that the two filtered noise samples have equal contrast energy.

*r*

_{ i }is the radius of the annulus, in degrees; the remaining symbols have the same meaning as in Equation 1.

*σ*

_{ u }(parameter that determines the bandwidth in frequency) and

*σ*

_{ v }(parameter that determines the bandwidth in orientation) were obtained by the following equations:

*B*= 1 octave (bandwidth in frequency, full width at half-height);

*α*= 30 deg (bandwidth in orientation, full width at half-height); and the center frequency

*ρ*

_{0}of the filter was 1 cycle/deg for the low spatial frequency noise (coarse scale) and 3 cycles/deg for the high spatial frequency noise (fine scale; see an example of the spectrum in Figures 1b, 1c, 1e, and 1f).

*m*

_{1}and

*m*

_{2}. To obtain the values

*m*

_{1}and

*m*

_{2}, we need to know the Root Mean Square contrast (

*c*

_{RMS}). For Experiments 1 and 2, it was 0.0748 for each filtered noise (see procedure to obtain the

*m*value for a specific

*c*

_{RMS}in Serrano-Pedraza et al., 2007, their Equations 5, 6, and 7).

*σ*

_{ t }∈ {12.5, 25, 50} ms (durations of 2

*σ*

_{ t }∈ {25, 50, 100} ms). The temporal Gaussian window was truncated to obtain the overall duration of 500 ms. Each experiment was carried out in different sessions. Once the fixation cross had disappeared the subjects saw one random presentation of the five possible configurations described above.

*σ*

_{ xy }∈ {0.35, 0.7, 1.4, 2.8} deg; and in Experiment 2 (annular window) , we used three radii

*r*

_{ i }∈ {1, 2, 3} deg with a fixed size of the annulus of

*σ*

_{ xy }= 0.35 deg.

*σ*

_{ xy }∈ {0.35, 1.4} deg; three contrast for the static low frequency component

*m*

_{1}∈ {0.06, 0.12, 0.24}; and six contrast ratios between the contrast of the high frequency component (

*m*

_{3}) and the contrast of the low frequency component (

*m*

_{1}),

*m*

_{3}/

*m*

_{1}∈ {0.1, 0.2, 0.4, 0.8, 1, 1.6, 3.2, 6.4}. The stimuli were displayed using a temporal Gaussian function with a temporal standard deviation of

*σ*

_{ t }= 12.5 ms (duration of 2

*σ*

_{ t }= 25 ms).

*σ*

_{ xy }∈ {0.35, 0.7, 1.4, 2.8} deg). For every stimulus, and for every size, performance is effectively perfect at the longest durations: plots converge in the upper right-hand corner of each panel.

*σ*

_{ xy }= 0.35 deg) and is close to chance for bigger Gaussian windows.

*r*

_{ i }∈ {1, 2, 3} deg). The leftmost panel shows the same results as in the leftmost panel of Figure 2b (

*σ*

_{ xy }= 0.35 deg) just for comparison.

*σ*

_{ xy }= 0.35 deg) and one bigger (

*σ*

_{ xy }= 1.4 deg), and changed the absolute and the relative contrast of the components of the complex stimulus in order to affect the balance between the mechanisms. We expect that for both windows, the reversals will appear for a limited range of contrasts as previously shown for big windows by Derrington and Henning (1987).

*σ*

_{ xy }= 1.4 deg, white symbols). When the contrast of the low frequency component is high, there is a slight tendency for reversals, indicated by performance below 0.5, to occur for a wider range of relative contrasts. However, in all cases, at the highest contrast ratios, performance rises above 0.5, indicating that motion is seen in the correct direction. This pattern of performance presumably reflects the fact that the high-contrast, brief, low spatial-frequency component of the stimulus activates motion sensors tuned to opposite directions of motion. It activates both directions equally because it is static. When the moving high spatial frequency component is introduced, its motion is not as salient as the reversed motion percept caused by the fact that it disturbs the balance between the low spatial frequency motion sensors. Consequently, the dominant sensation is one of reversed motion. When its contrast is high, the high spatial frequency stimulus gives rise to a more salient sense of motion in the correct direction.

*σ*

_{ xy }= 0.35 deg, dark symbols), no reversals were found and the proportion of correct responses increases with the contrast ratio from chance to perfect performance. The lack of reversals when the window size is small could be caused by the fact that low spatial frequency motion sensors are not strongly activated by a small stimulus.

*x*′ ∈ {−3, −2, −1, 0, 1, 2, 3} deg and

*y*′ ∈ {−3, −2, −1, 0, 1, 2, 3} deg. The equations and parameters of the spatial weighting functions of the sensors and the temporal impulse response functions are the same as described in Serrano-Pedraza et al. (2007); their Appendix, Equations A1 and A6). Sensor responses to movies used in experiments are calculated (by the inner product of the stimulus with the spatial weighting function of the sensor and convolving the output with the temporal impulse response) within each orientation band and summed across locations. The high frequency response is subtracted from the low frequency response (and vice versa) for the same direction of motion (right or left) and orientation. Responses are half-wave rectified and pooled across different orientations using cosine weighting and the final response is taken from the spatial frequency channel that has the highest difference between right and left. The highest difference is converted to a direction index and then converted into a performance score using a sigmoidal response function in order to obtain the probability of correct response. It is important to notice that the model is not fitted to the psychophysical data; the parameters of the model were fixed a priori and were always the same for all simulations.

*σ*

_{ xy }= 0.35 degrees, then the probability of correct response was 0.5. This threshold only makes a difference to the response of the model when the window is small and the contrast ratio is low. It is probable that the addition of noise either to the stimulus or to the responses of the motion sensors would remove the need for a threshold but that is beyond the scope of this paper.

*σ*

_{ xy }= 1.4 degrees, white symbols), independently of the contrast of the low frequency component, the proportion of correct responses is at chance for contrast ratios from 0.1 to 0.4, then reversals in direction discrimination appear for ratios from 0.8 to 1, and finally the proportion of correct responses goes to perfect performance for higher contrast ratios. However, the results show that for the smallest size tested (

*σ*

_{ xy }= 0.35 degrees, dark symbols), independently of the contrast of the low frequency component, no reversals were found and the proportion of correct responses increased with the contrast ratio from chance to perfect performance.

- First, the coarse sensors for opposite directions of motion must
*both*have a strong signal. This will occur when the stimulus is a briefly presented static (or slowly moving) low spatial frequency pattern, which is sufficiently large in size and high in contrast. - Second, there must be a moderately strong signal for one direction only in the high spatial frequency sensors.

*σ*

_{ x }) and 30 degrees in orientation (

*σ*

_{ y }). These values are relative to the spatial frequency of the sensor so for the low frequency sensors the dimensions of the spatial window are

*σ*

_{ x }= 0.5622 and

*σ*

_{ y }= 0.6994; and for the high frequency sensors, the dimensions are smaller:

*σ*

_{ x }= 0.1874 and

*σ*

_{ y }= 0.2331. Because the small stimulus (

*σ*

_{ xy }= 0.35) is smaller than the receptive field of the low frequency sensors, the response of those sensors is reduced considerably. However, even the small stimulus is larger than the receptive field dimensions of the high frequency sensors so there is no significant reduction in response. Consequently, when the stimulus size is reduced, condition 1 above fails to apply. The response of the high frequency sensors dominates perception because the response of the low frequency sensors is too small for any imbalance to give rise to a motion percept and therefore motion will be seen in the correct direction.