The perceived orientation and position of Gabor elements can be influenced in a number of ways. For example, the perceived orientations of a Gabor's carrier and its envelope are dependent upon each other (Dakin, Williams, & Hess,
1999; Morgan, Mason, & Baldassi,
2000; Skillen, Whitaker, Popple, & McGraw,
2002): the orientation of the envelope attracts the perceived orientation of the carrier, while the orientation of the carrier can either attract or repulse the perceived orientation of the envelope depending on their relative orientations. These interactions between first-order (Gabor carrier) and second-order (envelope) orientation information have been linked to two well-known visual illusions, the Fraser and Zöllner illusions (Dakin et al.,
1999; Morgan & Moulden,
1986; Tyler & Nakayama,
1984). In the case of the Fraser (Münsterberg or twisted cord) illusion (Fraser,
1908; Münsterberg,
1897), when a line is made up of tilted elements, its orientation is perceptually biased
toward the orientation of the elements. In the case of the Zöllner illusion (Zöllner,
1862), when a line is intersected by oblique elements its orientation is biased
away from the orientation of the elements. The relationship between the orientations of the line and those of the elements can explain these opposite illusions (Dakin et al.,
1999; Morgan & Moulden,
1986; Tyler & Nakayama,
1984).
Skillen et al. (
2002) investigated the effect of spatial scale on the Fraser and Zöllner illusions. Their results indicate that the attraction (Fraser) and repulsion (Zöllner) effects between the orientation of the envelope and that of the carrier depend on the relationship between the spatial scales of the carrier and envelope. Largely independent of the orientation difference between the carrier and envelope, if the spatial scales of the carrier and envelope are similar, attraction is seen; if the spatial scales are very different, primarily repulsion results. There is no agreement about scale invariance of these effects. Skillen et al. (
2002) observed scale invariance while Dakin et al. (
1999) did not. We see scale invariance and a dependence on carrier wavelength, suggesting that our effect, like those reported by Skillen et al. (
2002), depend on relative rather than absolute spatial scale. However our experiments differ in a critical point from those above. Biases in the earlier studies depend on the interaction between two orientation signals, that of the carrier and that of the envelope. In our experiments, only the carrier had a dominant orientation since the Gabor envelope was circular. The perceived orientation of individual Gabors can therefore only be determined by the carrier orientation. As a result, we would not expect biases of carrier orientation on envelope orientation, or vice versa, to affect our results. Rather, we see a perceptual shift of the location of the second-order envelope by the carrier orientation of neighboring elements.
Cases where the presence of surrounding elements can shift the perceived position of a central Gabor have also been reported (Keeble & Hess,
1998; Popple & Sagi,
2000; Whitaker, McGraw, Keeble, & Skillen,
2004). These might be broadly divided into effects elicited by carrier phase or carrier orientation. As an example of the first class, observers perceive a string of vertically oriented Gabors placed directly above each other as if they were positioned on a tilted line if the carrier phases of successive Gabors are gradually shifted (Popple & Levi,
2000; Popple & Sagi,
2000). Phase has also an effect on positional judgments of Gabors. Whitaker et al. (
2004) showed that positional judgments of first- (carrier) and second-order (envelope position) information are dependent upon each other. Relative to surrounding elements, the envelope of a Gabor can bias the perceived phase of its carrier and the phase of the carrier can bias the perceived position of the envelope. This effect depends on the separation between elements and their phase relationship. While element separation is also relevant for the data presented here, phase shows little effect on our illusion.
Levi, Li, and Klein (
2003) also studied the effect of element phase on element position for a string of five Gabors arranged on a straight line or a curved arc. Their study is a conceptual analogue to ours, both investigating the interactions between carrier and envelope information in shape perception. While Levi et al. studied the effect of carrier phase on envelope position, we measured the effect of carrier orientation on envelope position. The phase of adjacent elements can capture perceived position of a central target with the strongest capturing effect at small inter-element separations (Levi et al.,
2003). Our results show that orientation too can capture position but we see the strongest effect of the carrier (in our case orientation) for intermediate separations and no effect for small separations (where position is dominant). Moreover, Levi et al. reported a linear, monotonic relationship between separation and perceived position rather than our non-monotonic dependence. In spite of these differences, it is clear that, in the process of shape computation, positional information can be subjected to adjustments by phase as well as orientation. It is clear from our study that the effect of orientation on position is independent of any effect that carrier phase might have since randomizing the phase of elements has no detrimental effect on our results. Hence, while there are interesting similarities between other studies concerned with phase versus position and ours on orientation versus position, they are independent.
Concerning the effect of orientation on position, Keeble and Hess (
1998) showed that the perceived position of a central element could be shifted by the carrier orientation of adjacent Gabors. When 3 Gabors are positioned vertically above one another, the position of a central element is biased toward the right if the orientation of the peripheral Gabors are consistent with a rightward curved contour (i.e., the orientation of the upper Gabor is “\” and that of the lower is “/”). Although this illusionary bias was not seen for each observer (one showed an opposite bias), the general trend is in the direction of the illusion reported here. However, the magnitude of the shift in the earlier study is considerably smaller than what we find. Keeble and Hess (
1998) report a shift that is “relatively small compared with the shift required to actually put the central Gabor on the contour.” The measured shift was only about 10% of the total shift needed if the element was actually on the contour. The differences in the magnitude of the effect between the earlier study and ours might be due to the different number of elements (Keeble and Hess used only 3 elements) or the comparatively larger difference between element orientations (orientations differed by 45° in the study of Keeble and Hess). The capturing effect of orientation on position in our study shows a clear dependence on relative orientation and essentially disappears if the orientation difference between adjacent elements exceeds a certain limit.
Prins, Kingdom, and Hayes (
2007) did use more elements with smaller orientation differences than Keeble and Hess. They sampled sinusoidal lines to determine which component, position, or orientation is critical when discriminating a straight contour from one that is sinusoidally modulated. In contrast to our results on “rectilinear” contours, they found element position to be dominant, at least for low sinusoidal frequencies. For high frequency sinusoids, both features contributed equally to discrimination. What makes a direct comparison between studies difficult is the fact that it is not clear that the computations involved in contour discrimination and those involved in contour appearance are the same. Connected to this, it is conceivable that different task requirements (detecting a deviation from a straight line versus discrimination between two closed contour shapes) may dictate which source of information is primarily utilized by the observer (position versus orientation). In addition, different mechanisms might process different curved contours. Prins et al. (
2007) tested curvature detection against a straight line. We concentrated on sinusoids with amplitudes considerably above threshold (by at least an order of magnitude). Evidence suggests that curvature discrimination is subserved by different mechanisms depending on the magnitude of curvature (Whitaker & McGraw,
1998; Wilson & Richards,
1989). In any case, the effect seen with rectilinear stimuli is significantly smaller (by 30%) than with the closed contours, which was the main focus of our study, and it is therefore not clear that the two are the consequence of the same mechanism.
The role of orientation versus position has also been studied for discrimination thresholds with circular and quasi-circular shapes. Levi and Klein (
2000) measured detection thresholds for perturbation of the positions of oriented Gabor elements placed on the circumference of a circle. When element orientations are tangential to the circle (collinear), performance is slightly better than when they are not. This modulating effect of orientation is, however, only evident when the inter-element separation is small (Keeble & Hess,
1999; Levi & Klein,
2000) contrary to our findings where orientation shows the strongest effect for intermediate rather than small separations. On the basis of the small effect of collinearity, Keeble and Hess (
1999) argue that when detecting small perturbations in the position of elements on a circle, the element location (Gabor envelope) is more important than their orientation (carrier). Note that, contrary to our results, Keeble and Hess found that randomizing dimensions such as patch size and wavelength degrades performance in their shape task.
The positional dominance over orientation seen by Keeble and Hess for circular contours has not been seen in other cases. Wang and Hess (
2005) tested observers' ability to discriminate between sampled RF shapes and circles. Depending on sampling location, the shapes to be discriminated differed either only by position (when sampling from the “corners” and ”sides” of RF patterns), only by orientation (when sampling from the ”zero-crossings” of RF patterns), or both. Shape discrimination is twice as good with orientation cues than with position cues but neither yields as good a performance as when they are combined. Apart from the fact that Wang and Hess (
2005) measured shape discrimination at threshold, there is another critical difference between their and our stimulus design: both element position
and orientation in their study were always consistent with a sampled RF pattern. In contrast, in our experiments, element orientation was always consistent with one shape, while element position was consistent with another.
In summary, evidence is mixed with respect to whether orientation or position information is more important for contour perception. It appears that many parameters, including element orientation, position as well as phase can be important and their relative weights depend on the task and stimulus details. Our study, where the two sources of information are in conflict, offers an example in which perception of contour shape shifts from being dominated by orientation to being dominated by position depending, presumably, on the weight of each or these two cues.