In the optic flow illusion, the focus of an expanding optic flow field appears shifted when uniform flow is transparently superimposed. The shift is in the direction of the uniform flow, or “inducer.” Current explanations relate the transformation of the expanding optic flow field to perceptual subtraction of the inducer signal. Alternatively, the shift might result from motion capture acting on the perceived focus position. To test this alternative, we replaced expanding target flow with contracting or rotating flow. Current explanations predict focus shifts in expanding and contracting flows that are opposite but of equal magnitude and parallel to the inducer. In rotary flow, the current explanations predict shifts that are perpendicular to the inducer. In contrast, we report larger shift for expansion than for contraction and a component of shift parallel to the inducer for rotary flow. The magnitude of this novel component of shift depended on the target flow speed, the inducer flow speed, and the presentation duration. These results support the idea that motion capture contributes substantially to the optic flow illusion.

^{−2}on a 0.08 cd m

^{−2}background). Viewing was binocular.

*L*

_{ i}is the location that the observer indicated,

*L*

_{ r}is the real focus location, and

*V*is the speed of the inducer. This plane was fit separately to the subsets of (unaveraged) data corresponding to each panel in Figure 3. The fit lines in each panel in Figure 3 correspond to cross sections of this plane at 5, 0, and −5°/s inducer speeds

*V*used in this experiment.

*γ,*obtained by fitting Equation 1, multiplied with the magnitude of the inducer speed

*V*used in the experiment in question. The direction of the shift is indicated by the sign. In the horizontal direction, a positive value signifies that the shift was in the direction of the inducer, and a negative value signifies that the shift was opposite to the inducer direction. In the vertical direction, positive values signify shifts in a direction 90° away from the inducer direction in the counterclockwise direction. Negative vertical shifts are directed 90° away from the inducer direction in the clockwise direction.

*p*= 1,

*n*= 6; vertical

*p*= .39,

*n*= 6). Mean per subject ratio between horizontal and vertical shifts in this experiment was 42% ± 8% standard deviation.

*p*< 0.001,

*n*= 11). The mean FOE shift was 3.67°; the mean FOC shift was −1.37°. Vertical focus shifts were negligible in the radial OFI ( Figure 4d). Note that in this radial OFI experiment, more data are available on the horizontal than on the vertical shifts. Seven subjects took part in an experiment that only required horizontal localization of the FOCs and FOEs (by means of a mouse pointer that was a vertical line spanning the height of the screen) instead of the two-dimensional localization employed in the rest of this study.

*γ*and absolute

*V*) varied with the speed of the target flow.

*Y*is the vertical shift and

*R*is the spin rate. This function reflects the idea of vector subtraction of the uniform flow from the rotary flow because at increasing

*R,*the rotary flow vectors are decreasingly influenced by the relatively small uniform flow field vectors, resulting in small vertical shifts

*Y*. At near zero spin rates

*R,*

*Y*goes asymptotically to plus and minus infinity. This is no problem because the flow field has no focus when the spin rate is zero.

*R*reflects the horizontal shift's independence of the direction of rotation. This function also captures the observed diminishing of the horizontal shifts at high spin rates and the increase at lower rates.

*a*

_{ y}was negligible in all observers. And although the horizontal offset

*a*

_{ x}ranged from about one half to one degree, it was significant in one subject (JD) only. On the other hand, the spin rate term parameters

*b*

_{ y}and

*b*

_{ x}were significantly non-zero in all observers, emphasizing the influence of target flow speed on both the vertical and the horizontal illusory focus shifts in the rotary OFI.

*T*denotes translation speed in m/s. The values obtained for

*c*

_{ y}and

*d*

_{ y}are negligibly small in all three subjects ( Figure 5d), which indicates that no mislocalization occurred in the vertical direction.

*d*

_{ x}indicate that observers experienced large illusory shifts, especially in slowly contracting and expanding flow fields. (Note that the magnitudes of the gain parameters

*d*and

*b*cannot be directly compared, see 1.) Interestingly, the values of

*c*

_{ x}are significantly greater than zero in all three observers (mean 1.06° ± 0.12°

*SEM*). This shows that the illusory FOE shifts were, on average, 1.06° larger than the illusory FOC shifts over the range of speeds used in our experiment.

*σ*of the residuals of a linear fit to the real and indicated position data obtained in the trials in which the inducer was static. Large

*σ*means imprecise localization of the focus of flow: fuzzy targets. The results are shown in Figure 6.

*σ*. Linear regression showed that per degree fuzziness, the captured shift was about two-thirds of a degree in the rotary OFI, and about one-third of a degree in the radial OFI.

*σ*) suggests that the focus of optic flow is represented at a coarser scale as

*σ*increases (cf. the relation between diffusion and spatial scale in Koenderink, 1988). When the scale of a model gain-field increases, its limit for dynamic shifting also increases (Beintema & van den Berg, 1998). Thus, a captured shift caused by dynamic tuning may increase as

*σ*increases until it is limited at the largest receptive field scale.

*R*by the translation speed

*T*multiplied by a scaling factor

*k*(in m

^{−1}) resulting in

*a*

_{ y},

*b*

_{ y},

*a*

_{ x}, and

*b*

_{ x}fixed at the values obtained in fitting the focus shift data with Equations 2 and 3, and

*k*as the only free parameter. These fits are shown in Figure 5b as dashed lines. The model fits the observed horizontal shifts well (mean r

^{2}for all subjects is 0.97). The fitted values of

*k*were 0.030, 0.034, and 0.025 for subjects AH, JD, and JF (mean 0.029). This means that the horizontal shifts in a radial OFI at, for example, 1.9 m/s ego-translation were equal to the sum of the horizontal and vertical shifts in the rotary OFI when the spin rate was 1.9 m/s × 0.029 m

^{−1}= 0.056 Hz. The spin rate and the translation speed of this example were used in making the flow fields pictograms in Figures 2b and 2c. As shown in the corresponding speed profile plot in Figure 2d, the retinal dot speeds in the 0.056-Hz rotation stimulus are equal to the retinal dot speeds in the 1.9-m/s translation condition of dots at an intermediate distance of about 5 meters from the observer. Note that the mean distance of the visible subset of dots in the volume of dots was about 7.5 meters. That our subjects appear to have judged the focus position on these nearer than average dots seems plausible: these dots moved faster and thus conveyed clearer information on the location of the focus. We think this comparison suggests that the observed difference between FOC and FOE shifts likely result from the same effect that caused the horizontal shifts in the rotary OFI.

*X*) and vertical shift (

*Y*) values thus obtained are shown in Figure 8a. Significant horizontal (captured) and vertical (induced) shifts could be observed in all three observers and are comparable to the shifts presented in Figures 3 and 4a, c.

*p*-values). However, the absolute differences between mean gaze traces (indicated with thick lines in Figure 8b) are of a much smaller magnitude than the captured shifts observed ( Figure 8a). Moreover, as is shown in Figure 8c, correlating the per trial trace means with the per trial mislocalization of the focus revealed no significant correlation between the horizontal eye position and the horizontal focus shifts in any of our subjects. For this correlation, only the trials with a moving inducer were used (hence the lower

*n*-values in Figure 8c compared to Figures 8a and 8b), and clockwise and counterclockwise flow trial data were made congruent (as described in the previous paragraph). For completeness, the correlations between the vertical eye positions and the vertical focus shifts are shown in Figure 8c, right column. We conclude from this control experiment that the horizontal captured shifts reported in this study were not related to eye movements.