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Article  |   June 2012
The role of motion streaks in the perception of the kinetic Zollner illusion
Author Affiliations
  • Sieu K. Khuu
    The School of Optometry and Vision Science, The University of New South Wales, Sydney, New South Wales
    skhuu@unsw.edu.au
Journal of Vision June 2012, Vol.12, 19. doi:10.1167/12.6.19
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      Sieu K. Khuu; The role of motion streaks in the perception of the kinetic Zollner illusion. Journal of Vision 2012;12(6):19. doi: 10.1167/12.6.19.

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Abstract
Abstract
Abstract:

Abstract  In classic geometric illusions such as the Zollner illusion, vertical lines superimposed on oriented background lines appear tilted in the direction opposite to the background. In kinetic forms of this illusion, an object moving over oriented background lines appears to follow a titled path, again in the direction opposite to the background. Existing literature does not proffer a complete explanation of the effect. Here, it is suggested that motion streaks underpin the illusion; that the effect is a consequence of interactions between detectors tuned to the orientation of background lines and those sensing the motion streaks that arise from fast object motion. This account was examined in the present study by measuring motion-tilt induction under different conditions in which the strength or salience of motion streaks was attenuated: by varying object speed (Experiment 1), contrast (Experiment 2), and trajectory/length by changing the element life-time within the stimulus (Experiment 3). It was predicted that, as motion streaks become less available, background lines would less affect the perceived direction of motion. Consistent with this prediction, the results indicated that, with a reduction in object speed below that required to generate motion streaks (< 1.12°/s), Weber contrast (< 0.125) and motion streak length (two frames) reduced or extinguished the motion-tilt-induction effect. The findings of the present study are consistent with previous reports and computational models that directly combine form and motion information to provide an effective determinant of motion direction.

Introduction
In classic examples of optical geometric illusions such as the Zollner and Hering illusions (Burmester, 1896; Coren & Girgus, 1978; Hering, 1861; Orbison, 1939; Zollner, 1860), straight target lines appear tilted in the direction opposite to the oriented background lines upon which they are superimposed. Geometric distortions of space are not limited to static stimuli, also occurring when the path of a moving object traverses tilted background lines. This so-called “motion-tilt induction” effect has been reported for kinetic versions of both the Zollner and Hering illusions (Swanston, 1984); analogous to static forms of these illusions, tilted background lines deflect the path of motion in the opposite direction. A similar effect was reported by Cesaro and Agostini (1998): an object traversing a straight horizontal path across a background of lines that alternate in tilt direction appears to take on a sinusoidal “slalom” trajectory. Likewise, motion-tilt induction has been noted for a kinetic version of the Poggendorff illusion. In this case, the motion path of an obliquely translating element appears misaligned when passing behind a static occluder (Nihei, 1973, 1975; also see Fineman & Melingonis, 1977; Wenderoth & Johnson, 1983; c.f., Watamaniuk, 2005). 
Despite the fact that geometric illusions are simplistic in construction and form, their investigation provides valuable insight into the functional nature of mechanisms that code orientation and, more generally, the way in which the visual system represents space (see Gilliam, 1998; Westheimer, 2008). For example, it is the consensus view that tilt-induction effects observed in static geometric illusions reflect lateral/mutual inhibition between orientation-tuned detectors with overlapping orientation-tuning profiles (see Blakemore, Carpenter, & Georgeson, 1970; Carpenter & Blakemore, 1973; Day, 1973; Eagleman, 2001; Westheimer, 2008; Wallace, 1975; note that, though this explanation is by no means exhaustive, see Gilliam, 1998; Morgan & Casco, 1990; Tyler & Nakayama, 1984). Line-repulsion effects arise because orientation-tuned detectors coding both the target and background lines (that differ slightly in orientation) are mutually inhibiting, shifting the peak of their tuning profile in opposite directions. Indeed, previous studies have shown that lateral inhibition accurately predicts the degree and direction of tilt induction as the angular separation between target and background lines increases. However, while both physiological (Blakemore & Tobin, 1972) and computational models proposing lateral inhibition (e.g., Morikawa, 1987) are well developed to account for tilt induction in static geometric illusions, it remains unclear whether analogous operations apply to kinetic versions of these illusions. 
Swanston (1984) speculated that distortion to the motion path induced by oriented background lines in kinetic forms of the illusion reflects reciprocal interactions between separate mechanisms sensitive to spatial orientation and motion direction. It is indeed possible that mutual inhibition between the tuning profiles of orientation-tuned detectors coding the background lines and direction selective cells sensing the direction of object motion can account for the reported motion-tilt-induction effects. However, while it has been well demonstrated that inhibition occurs between detectors both selective for either orientation or motion (and accounting for repulsion effects in each stimulus domain), it is unclear whether such a process occurs between cells separately selective for orientation and motion. Importantly, previous studies have instead established that cells in the visual cortex are sensitive to both orientation and motion information (e.g., see Albright, 1984; Krekelberg, Dannenberg, Hoffmann, Bremmer, & Ross, 2003; Lennie, 1998), and the outputs of such cells are likely to represent a combination of orientation and motion information rather than mutual inhibition. Indeed, evidence that the visual system combines form and motion information is well supported by recent behavioral studies demonstrating that the perceived direction of moving oriented elements is influenced by its orientation (e.g., Krekelberg et al., 2003; Or, Khuu, & Hayes, 2010). These observations therefore cast doubt on existing assumptions about the mechanisms underpinning kinetic geometric illusions. The goal of the present study is to revisit geometric illusions, seeking a more inclusive and comprehensive explanation; one that, by necessity, considers the interaction between form and motion to account for the effect. 
Recently, Geisler (1999) proposed that the visual system directly considers the outputs of orientation-tuned neurons (e.g., simple cells) when determining direction of motion. Because such neurons integrate information over brief periods (50–100 ms; see Barlow, 1958; Burr, 1980; Peterson, Ohzawa, & Freeman, 2001; Snowden & Braddick, 1991), the image of a rapidly translating object will be smeared (along the cell's receptive field), producing a “motion streak” that extends away from the object (Badcock & Dickinson, 2009; Geisler, 1999; Or et al., 2007; Ross, 2004). According to Geisler, the visual system is sensitive to this orientation signal and computes direction of motion by combining the output of a motion-selective cell with that of an orientation-selective cell tuned for extracting the orientation of the motion streak. The advantage of this neural circuitry is that, because motion streaks have comparatively narrower bandwidths than motion-selective units, orientation-tuned mechanisms provide greater precision in signaling direction, aiding the computation of motion. Indeed, if motion streaks are effectively masked or degraded, it has been shown that luminance thresholds for detecting a moving dot (Geisler, 1999) and discriminating the direction of motion are comparatively elevated (Burr & Ross, 2002). 
The reliance of the visual system on the orientation of motion streaks in signaling direction of motion presents a new hypothesis for the mechanisms underpinning kinetic geometric illusions. In the present study, it is proposed that kinetic geometric illusions reflect a reciprocal interaction between orientation-tuned detectors sensing the motion streak produced by the movement of the object and the orientation of background lines. Background lines may distort the orientation of the motion streak, and when combined with the output of a motion detector (as proposed by Geisler, 1999, and confirmed by Or et al., 2007), the perceived direction of motion is distorted. The possibility that motion streaks are important to the explanation of kinetic geometric illusions is supported by a recent investigation by Apthorp and Alais (2009), who showed that motion streaks produced by a background of moving dots tilt the perceived orientation of a centrally presented grating. The effect is analogous to static forms of the tilt illusion. Tilt induction only arose when moving dots produced strong motion streaks at fast speeds or followed extended trajectories. While Apthorp and Alais showed that motion streaks affect the perceived orientation of static lines, it is still unclear whether the motion-tilt induction observed in kinetic geometric illusions arises because background lines affect orientation-tuned units extracting motion streaks. The present study investigates this possibility. 
If motion-tilt induction does indeed arise from lateral inhibition (or an analogous operation) between the background orientation and the motion streak produced by object motion, it would be predicted that reduction in the availability of motion streaks would result in a veridical percept of the object's trajectory. Previous studies have well established that reducing object speed, stimulus contrast, and motion length are effective means of attenuating the salience of motion streaks (see Edwards & Crane, 2007; Li et al., 2008). The present study adopted these stimulus manipulations and investigated whether attenuating the salience of motion streaks by reducing image speed (Experiment 1), object contrast (Experiment 2), and streak length (Experiment 3) impacts the perception of the kinetic Zollner illusion, which typifies motion-tilt-induction effects observed in kinetic geometric illusions. The present study reports that reducing dot speed, dot contrast, and streak length attenuated the perception of motion-tilt induction. These findings are discussed and compared against the expected outcomes of both a motion streaks and lateral inhibition hypothesis. 
Experiment 1: the effect of object speed on the perceived path of motion
According to Geisler (1999) motion streaks effectively cue direction of motion for object speeds greater than approximately 1-element width per 100 ms. However, integration times have been shown to be dependent on luminance contrast with shorter integration periods at higher contrasts (e.g., see Kelly, 1961). It follows that, if motion streaks do indeed account for induced motion tilt in kinetic geometric illusions, tilt will be most noticeable at comparatively fast object speeds at which streaks provide a reliable cue for perception. Conversely, object movement ought to be unaffected by the background at slower speeds for which the motion streak is absent. 
Studies relating object speed to perceived motion-path distortion in kinetic geometric illusions have produced unclear results. Both Nihei (1973) and Fineman and Melingonis (1977) reported a speed-dependent effect for the kinetic Poggendorff illusion over a very broad range of speeds of 2–43°/s. However, Swanston (1984) reported no dependence on object speed for the kinetic Zollner Illusion, and Cesaro and Agostini (1998) reported an inverse relationship between object speed and motion-tilt induction for their “slalom” illusion. These observations may be accounted for by the fact that only a few slow speeds were used in the studies by Swanston and Cesaro and Agostini, which might not be of sufficient magnitudes to produce streaks capable of reliably influencing perception. This finding contrasts with those used by Nihei and Fineman and Melingonis who employed comparatively faster speeds over a broader range capable of generating motion streaks. Indeed, Swanston measured the kinetic Zollner illusion with speeds of 2 and 4°/s that—given the stimulus size employed, which was 0.2° in visual angle—is near the critical value required for motion streaks to aid in the perception of motion. On the other hand, Cesaro and Agostini examined motion-path distortion for speeds of 0.78, 1.55, and 3°/s with a single dot of a diameter of 0.022°. While the speeds adopted by Cesaro and Agostini are sufficient to generate a motion streak, it can be questioned whether a motion streak is perceptible given the very small size of the stimulus, and the fact that motion streaks are likely to be low contrast given the fact that they arise from temporal integration (Alais, Apthorp, Karmann, & Cass, 2011; Apthorp, Cass, & Alais, 2010; Kelly, 1961). The fact that increasing speed produces a reduction in the “slalom” effect is consistent with a reduction in the visibility of the object at faster speeds. Given these inherent differences, it is highly likely that the “slalom illusion” might altogether reflect a different percept (given that there is no static equivalent), but one that is perceptually analogous to the kinetic Zollner illusion. 
The conflicting reports of Nihei (1973) and Swanston (1984) might be accounted for by the presence or absence of speed-related motion streaks. Experiment 1 sought to elucidate this issue by using a broader range of speeds. As mentioned, the present study employed a variant of the kinetic Zollner illusion. The extent of motion-tilt induction was measured as a function of object speed over a range of 0.56 to 18°/s in which motion streaks are not or are generated (see following). If motion streaks account for tilt induction in the kinetic Zollner illusion, it would be predicted that greater motion-path distortion would occur at fast object speeds for which a motion streak is generated and less at slower speeds for which motion streaks are absent. However, if motion streaks are not involved in the perception of kinetic geometrical illusions, the extent of tilt induction ought not to be speed dependent. 
Methods
Observers
Six experienced observers (aged 21–35 years) participated. One was the author while the others were naïve to the goals of the study. All had normal or corrected-to-normal visual acuity. 
Stimuli
The stimulus was a 40-frame movie sequence (each frame was shown for 25 ms in rapid succession; entire duration of the stimulus was 1 s) in which a circular cloud (radius: 0.750°) of 20 circular antialiased dots (radius: 0.042°, luminance: 80 cd/m2, dot density of the dot cluster: 11.318 dots/deg2) moved vertically from bottom to top, over light increment tilted lines (width 0.084°, luminance, 80 cd/m2). Both the dot cloud and lines were overlaid on a midgray background set to a luminance of 40 cd/m2, making the Weber contrast of the dots and lines 1. Tilted lines were separated by a distance of 0.336° (separation equal to the width of four dots) and windowed within a black circular aperture (luminance: 6 cd/m2, line width: 0.1°) with a radius of 10°. A circular aperture was used to prevent bias in motion-direction judgments by using the edge of the stimulus as a point of reference. At the beginning of a presentation, the cloud of dots was positioned at the “6 o'clock” position resting near the lower edge of the circular aperture. On each and subsequent frames of the movie sequence, the cloud of dots subsequently moved upward (at a fixed spatial step-size) and appeared throughout the presentation. All dots were generated asynchronously with a limited lifetime of 10 frames (250 ms), after which they disappeared and were replotted to a random position in the stimulus area. This procedure prevented the tracking of individual dots, requiring the visual system to rely on the global direction of dots (see Khuu & Badcock, 2002). Previous research has shown that the visual system is well able to discriminate the motion direction of this stimulus with discrimination thresholds of approximately 0.25° of visual angle over a broad range of speeds (Westheimer & Wehrhahn, 1994). Observers viewed this stimulus in a dark room at a viewing distance of 80 cm. Stimuli were generated using MATLAB version 7 and displayed on a linearized 24-inch Mitsubishi Diamond Pro monitor driven at a frame rate of 120 Hz. 
Procedures
A schematic of the testing procedure is shown in Figure 1. Observers were instructed to maintain central fixation, and the aforementioned stimulus was presented to a location so the dot cloud was 3° either to the right or to the left (randomly chosen from trial-to-trial) of central fixation for 1 s. After the stimulus presentation, the screen was blank (set to background luminance), and two vertical black lines (width: 0.25°, length: 2°, luminance: 4 cd/m2), which acted as reference lines, were displayed at the 6 and 12 o'clock positions on the circumference of the aperture. The task of the observer was to indicate whether the path of motion of the dot cloud was to the left or right of the reference lines by pressing left or right keys on the keyboard. This key press also initiated the next stimulus presentation, which began after a display of 1 second of 10 Hz dynamic pixilated noise was presented within the circular aperture to prevent any image aftereffects. 
Figure 1
 
Schematic representation of the stimulus presentation sequence employed in the present study. Initially, a cloud of moving dots is presented on a background consisting of tilted lines for 1 second. After vertical lines appear above and below the stimulus area, the task of the observer was to judge whether the dot cloud moved left or right from vertical. After judgment, 10 Hz dynamic white noise was shown for 1 second.
Figure 1
 
Schematic representation of the stimulus presentation sequence employed in the present study. Initially, a cloud of moving dots is presented on a background consisting of tilted lines for 1 second. After vertical lines appear above and below the stimulus area, the task of the observer was to judge whether the dot cloud moved left or right from vertical. After judgment, 10 Hz dynamic white noise was shown for 1 second.
Swanston (1984) quantified the extent of path displacement in the kinetic Zollner illusion by requiring observers to rate the extent of tilt with reference to the height of the moving object. The present study instead used a “nulling” procedure; illusory motion tilt was cancelled by physically changing the motion direction of the dot cloud (in the opposite direction to the perceived motion tilt) until it appeared to move vertically. This procedure is efficient because it simultaneously quantifies the extent and direction of motion-tilt induction (previously used by Prinzmetal & Beck, 2001, to quantify tilt in the static Zollner illusion). A staircase procedure (converging on the 79% performance level of the psychometric function) was used to modify the motion direction of the cloud of dots until it appeared vertical. The staircase began with a motion direction randomly chosen from a range of −10 to 10° (negative and positive values signify leftward and rightward movement respectively) of visual angle (from vertical). The initial absolute step-size was 0.5°. Subsequently, the step-size was halved. After the third reversal, the step-size was 0.125° and remained at this value until the end of the staircase run. The staircase lasted for eight reversals, and the average of the last four reversals was used as an estimate of the path of motion judged to be vertical. 
The staircase procedure was repeated for six different speed levels: 0.56, 1.12, 2.25, 4.5, 9, and 18°/s produced by displacing dots at the following step-sizes: 0.014, 0.028, 0.056, 0.113, 0.225, and 0.45°/frame. Note that, for the two slowest speeds of 0.56 and 1.12°/s, the stimulus was presented for longer at 3 s (by increasing the number of movie frames) rather than for 1 s for faster speeds. A longer stimulus presentation time for slower speed conditions was adopted to ensure that the stimulus traversed a sufficiently long distance for observers to reliably detect its motion direction. In addition to the speed condition, this study included a condition in which background lines were tilted 15° to the left and right from vertical. As Swanston (1984) noted (consistent with the line-repulsion effect observed by Carpenter & Blakemore, 1974), this orientation difference (relative to the trajectory of motion) produces maximum path displacement. Additionally, a control condition in which background lines were horizontal (i.e., 90°) was included. Previous studies (e.g., Swanston, 1984) have demonstrated that, when lines are physically horizontal, no motion-tilt induction is observed. Therefore, this condition provides a good baseline comparison for conditions in which lines are oriented obliquely. 
A block comprised 18 staircase runs: background lines orientated −15°, 15°, and 90° from vertical for six different speeds. Observers each completed five blocks, and results were averaged over the five thresholds for each condition. The order of stimulus presentation was randomized within and between blocks. No feedback was given to indicate the correctness of response. 
Results and discussion
The average results (error bars signify 95% confidence intervals) of Experiment 1 are given in Figure 2, which plots the physical angular path of motion required for observers to judge that the object is moving vertically (i.e., the angle required to nullify the motion-tilt illusion) against the dot speed on a log scale. The results for background lines tilted at 15° (black squares), −15° (light-gray diamonds), and 90° (gray circles) are plotted as different symbols. Positive values on the y-axis signify physical rightward movement, negative values physical leftward movement, and 0° indicates vertical movement. There were a number of noteworthy findings. 
Figure 2
 
The judged angle of motion (in°) required to perceive vertical motion plotted against the speed of dots (in log scale) for different background line orientations (90° gray circles, 15° black squares, −15° light-gray diamond). Error bars signify 95% confidence intervals.
Figure 2
 
The judged angle of motion (in°) required to perceive vertical motion plotted against the speed of dots (in log scale) for different background line orientations (90° gray circles, 15° black squares, −15° light-gray diamond). Error bars signify 95% confidence intervals.
First, for the baseline condition comprising a background of horizontal lines (gray circles), observers accurately judged the perceived direction of motion of the dot cloud regardless of dot speed. The adjusted angle of motion was approximately 0° across the speed range in this condition. Observers were therefore cognizant of the task and consistent in their performance regardless of speed. 
Second, where background lines were tilted, the perceived angle of motion required to nullify the illusory tilt deviated from 0°. For leftward-tilted background lines (gray diamonds), observers judged that the dot cloud needed to follow a path physically tilted to the left (negative numbers on the y-axis) to be perceived as travelling vertically. Conversely, for rightward-tilted background lines (black squares), observers judged that the dot cloud needed to follow a path physically tilted to the right (positive numbers on the y-axis) to be perceived as travelling vertically. 
To assess the absolute effect of dot speed and background lines on the judged direction of motion, results for the two oriented background conditions of 15 and −15° were combined as they are mirror opposites, produced similar absolute effects (see Figure 2), and compared to the baseline condition (90°) in a two-way ANOVA. This analysis revealed significant main effects for background orientation (F[1, 96] = 165.55, p < 0.0001) and dot speed (F[5, 96] = 15.95, p < 0.0001), indicating that both factors affected the perceived direction of motion (see following for discussion). Additionally, their interaction was significant (F[5, 96] = 15.67, p < 0.0001), indicating that the judged direction of motion of the stimulus was very much dependent on both the background orientation and the speed level. 
These findings are consistent with previous descriptions of both static and kinetic versions of the Zollner illusion in which the angular separation between straight lines/motion paths and background lines are exaggerated. Thus, in Experiment 1, to null the motion-tilt-induction effect and perceive vertical movement, the motion path of the dot cloud had to be physically displaced in the direction of the background lines. 
Third, the judged angle of motion tilt is dependent on object speed. For the slowest dot speed of 0.56°/s, there was no apparent tilt; the judged angle of motion was approximately 0° regardless of the background line orientation, indicating veridical vertical movement. Post-hoc Bonferoni multiple comparisons (see Neter, Wasserman, & Kutner, 1990) revealed no significant differences between the baseline condition (in which the line orientation was 90°) and when the background line was oriented (mean difference: 0.006, p = 0.87). Given that the radius of individual dots was 0.042°, according to Giesler (1999), the critical speed at which motion streaks should be produced and contribute to perception is approximately 0.84°/s. The lack of an effect observed at this slow speed is consistent with the view that it is not sufficiently fast to generate a motion streak, and thus, motion judgments are veridical. However, as dot speed is increased, the judged motion direction deviated from 0° and was significantly different (from the baseline condition) by a dot speed of 1.12°/s (mean difference: 0.94°, p < 0.05). Thus, the speed at which motion-tilt induction is observed in the present study is close to the critical speed value at which motion streaks are thought to contribute to perception. It was additionally observed that, for greater dot speeds (e.g., 9°/s and 18°/s), there is an increase in the extent of illusory tilt. This increase in illusory tilt suggests that motion streaks provide a more effective cue in signaling motion direction at fast speeds, perhaps because of a reduction in sensitivity to motion at fast speeds (e.g., de Bruyn & Orban, 1988). Alternatively, at faster speeds, the length of motion streaks would mean that they intersect with a number of background lines, producing a more compelling tilt effect. This is consistent with previous studies showing that, for static versions of the Zollner illusion, increasing line length (Wallace, 1969) and line density (e.g., Wallace & Crampin, 1969) increases the extent of illusory tilt. 
The speed-dependent effect with tilted background lines shown in Figure 2 is consistent with an explanation of the motion-tilt-induction effect in terms of motion streaks. At slow speeds, motion streaks are not generated, and observers are able to perceive the true direction of motion as given by the output of direction-selective cells. However, motion-tilt induction is strongest at the faster speeds that are sufficient to generate motion streaks. These results are consistent with the present hypothesis that the orientation of the motion streak generated by rapid motion is affected by background lines and creates illusory tilt in the perceived direction of motion (see General discussion). 
It could be argued that the results shown in Figure 2 are accounted for by lateral inhibition between an orientation-tuned and motion-selective cell, particularly if it is assumed that slower speeds result in reduced activation/response of motion-selective units. In this situation, the extent of lateral inhibition changes because the activation of direction-selective units is weaker. However, this account is improbable simply because the visual system does not code image speed in this way. Existing research strongly indicates that image speed is coded in a few speed-tuned channels (low and high) (see Edwards, Badcock, & Smith 1998; Khuu & Badcock, 2002) with each mechanism equally sensitive to speeds within a given range. The suggestion that weaker motion-tilt induction occurs at slower speeds because motion detectors are not effectively activated is therefore at odds with this evidence. Indeed, evidence exists showing that cells in cortical areas such as in V1 and MT are selective for different speeds (see Priebe, Cassnello, & Lisberger, 2003; Priebe, Lisberger, & Movshon, 2006). 
Experiment 2: the effect of stimulus contrast on the perceived path of motion
Experiment 1 indicated that motion-tilt induction is strongest at speeds sufficient to generate a strong motion streak. In Experiment 2, the possibility that motion streaks underpin this illusion is further investigated by varying stimulus contrast. Edwards and Crane (2007) showed that reducing the luminance contrast, and therefore eliminating the availability of motion streaks, reduced the detectability of global direction of motion at high speeds. The logic of Edwards and Crane can be applied to the kinetic Zollner illusion; if the availability of motion streaks is decreased or eliminated via a reduction in the luminance contrast of dots, a corresponding reduction in their contribution to determining motion direction should be expected. Accordingly, at low contrasts, the perceived direction of motion of a fast-moving object ought to be unaffected by background tilted lines. Both Wallace (1975) and Li and Guo (1995) reported that the static Zollner illusion is dependent on luminance contrast with the strength of the illusion much weaker at low contrasts. In further considering the role of motion streaks in the kinetic Zollner illusion, Experiment 2 examined the effect of contrast change on the extent of motion-tilt induction. 
Methods
Observers were the same as those in Experiment 1. The stimuli and procedures were similar to those used in Experiment 1, except only one dot speed of 18°/s was used, and the background lines were either 15° (rightward)-tilted lines or lines tilted at 90° (horizontal). As noted in Experiment 1, these background line orientations produced only either strong motion-tilt induction or none. In different conditions, the Weber contrast of the dots forming the cloud stimulus was changed to the following levels: 2, 1, 0.5, 0.25, 0.125, and 0.0625. The lines forming the background were fixed to a contrast of 1. 
Results and discussion
Data were similar across observers and were therefore averaged. The average results are shown in Figure 3 (error bars signify 95% confidence intervals). The judged angle of motion required to perceive the stimulus as moving vertically is plotted as a function of the Weber contrast of the dot cloud in log scale for backgrounds tilted at 15° and 90° (from vertical). A two-way repeated measures ANOVA performed on these data revealed that both the orientation of background lines (F[1, 60] = 237, p < 0.0001) and dot contrast (F[5, 60] = 16.45, p < 0.0001) significantly affected the illusory motion-tilt effect. Additionally, a significant interaction effect was found indicating that the effect of dot contrast at different levels is different for the two background line orientations (F[5, 60] = 15.63, p < 0.0001). Particularly, as shown in Figure 3, when background lines are oriented 90°, the perceived direction of the cloud stimulus was unaffected by background lines with the judged angle of motion 0° irrespective of contrast (gray squares). However, where background lines were tilted at 15°, the judged angle of motion (required to cancel the illusion) was dependent on stimulus contrast with the extent of tilt evident for high, but not at low contrasts. Post-hoc tests (Bonferroni multiple comparisons) between the two background orientations of 15° and 90° for each contrast level indicated that the judged angle of motion was not significantly different (p > 0.05) for the two low contrasts 0.0625 (mean difference: 0.76°, p = 0.42) and 0.125 (mean difference: 0.28°, p = 0.63), but were significantly different for higher contrasts of 0.25 (mean difference: 2.33°, p < 0.0001), 0.5 (mean difference: 2.88°, p < 0.0001), 1 (mean difference: −3.04°, p < 0.0001), and 2 (mean difference: 3.737°, p < 0.0001). 
Figure 3
 
The judged angle of motion of a cloud of dots moving over tilted lines is plotted as a function of the Weber contrast of dots (in log scale). Black circles indicate judgments with background lines tilted 15°, while gray squares depict the results for conditions in which background lines were tilted 90° from vertical.
Figure 3
 
The judged angle of motion of a cloud of dots moving over tilted lines is plotted as a function of the Weber contrast of dots (in log scale). Black circles indicate judgments with background lines tilted 15°, while gray squares depict the results for conditions in which background lines were tilted 90° from vertical.
The results of this experiment are consistent with those of Wallace (1975) who noted that the extent of illusory tilt in the static Zollner illusion is dependent on the contrast difference between background and target lines (also see Westheimer, Brincat, & Wehrhahn, 1999, for comparable effects with the static tilt illusion and Poggendorff illusions). Particularly, large contrast differences between the target and background produces a larger tilt effect. According to Wallace, this effect can be accounted for by the degree of inhibition between two orientation-tuned detectors responding differently to target and background lines of different contrasts. In Experiment 2, it is presumed that, at very low contrasts, motion streaks are not present, and motion direction is derived solely from the output of motion detectors unaffected by background lines. This observation with low-contrast stimuli is consistent with those of Edwards & Crane (2007). However, at higher contrasts, motion streaks present and are affected by background lines leading to an observable change in the perceived direction of motion. This effect with high-contrast stimuli is in agreement with the observations of Apthorp et al. (2010) who demonstrated that motion streaks produced by fast-moving elements can mask the detection of a static grating provided that moving elements are high contrast. 
An alternative account of the results of Experiment 2 might be that reducing the contrast of the object directly produces a change in lateral inhibition between a motion- and orientation-tuned cell because the activation of motion-direction-selective cells to a low-contrast moving object might be comparatively weaker. In this case, a reduction in contrast will decrease the neural response of direction-selective units leading to a change in the extent of motion-tilt induction. However, this account is improbable. A lateral inhibition mechanism would predict an enlargement of the tilt effect at low contrasts as higher-contrast background lines exert greater influence on the perceived motion direction. This is the opposite of the findings of the present study. Additionally, previous findings have shown that the response of direction-selective units is largely unaffected by changes in luminance contrast, suggesting that contrast gain control is implemented to attenuate neuronal response relative to the contrast level (see Albrecht & Geisler, 1991). This physiological evidence is well supported by behavioral data showing that motion detection is largely independent of contrast above a critical value estimated to be as low as 5% (e.g., McKee, Silverman, & Nakayama, 1986). The contrast range employed in the present study is above this level, making it unlikely that the reported reduction in the extent of motion tilt at very low contrasts is due to a reduction in activation of motion detectors leading to a change in lateral inhibition. 
It is important to note that reducing the contrast of a moving object also reduces its apparent speed (see Stone & Thompson, 1992), and therefore the noted reduction in motion path distortion reported in Figure 3 may reflect an elimination of motion streaks due to a reduction in speed and not apparent contrast. To ensure that this was not the case, a supplementary speed-matching experiment was performed using Method of Adjustment. The same observers (who participated in Experiment 2) had to match the speed of two dot clouds that differed in contrast. In this supplementary experiment, high- (Weber contrast: 1) and low- (Weber contrast: 0.0625, the lowest contrast value used in Experiment 2) contrast dot clouds were presented (for 1 s) in sequential order (separated by a blank interval of 0.5 s). After the presentation of both stimuli, observers were required to reduce the speed of the high-contrast stimulus at steps of 0.56°/s until it perceptually matched the speed of the lower-contrast cloud (which always moved at a speed of 18°/s). This procedure was repeated five times and the results averaged. Results indicated that observers perceived the low-contrast stimulus as moving much slower than the higher-contrast object. Observers on average had to reduce the speed of the high-contrast object by approximately 30% for it to appear to move at the same perceptual speed as the lower-contrast object. While speed reduction was observed, the perceived speed (approximately 12.6°/s) is still sufficiently fast to generate a motion streak. On the basis of this finding, it would appear that that a reduction in speed at low contrasts cannot account for the findings of Experiment 2
Experiment 3: the effect of streak length on the perceived path of motion
Previous research has shown that changing the spatial length/trajectory of motion modulates motion-streak perceptibility (Apthorp & Alais, 2009; Edwards & Crane, 2007). For the present stimulus, this can be achieved by changing the lifetime of dots within the cloud before they are replotted to a random location in the stimulus. Long streaks are produced by ensuring dots move along a fixed direction and extended duration (i.e., a long lifetime). By consequence, the arising motion streak extends over a large spatial distance. Conversely, short streaks are produced by assigning dots a short lifetime of one or two motion frames. Because such dots are present at a particular spatial location for only a brief period of time, the traversed spatial distance is small, likewise the motion streak. Consistent with Edwards and Crane, if motion streaks account for induced motion tilt, it would be expected that short streaks would produce less motion tilt compared with long streaks. Alternatively, if motion-tilt induction is due to inhibition between form- and motion-selective units, and not motion streaks, the extent of the distortion might be the same for both types of stimuli because motion produced with these spatial step-sizes will effectively drive local direction-selective cells (provided that they fall within a cell's receptive field; see Anderson & Burr, 1987; Morgan, 1992; Rudolph, Ferrera, & Pasternak, 1994). In Experiment 3, the impact of short motion streaks was examined by repeating the conditions of Experiment 1, but with a background line spacing of 0.672° (double that of Experiment 1) and with an object speed of 9°/s, which corresponds to a spatial step-size of 0.225°/frame. These conditions are sufficient to optimize any differences in motion-tilt induction elicited by long and short motion streaks should such a difference exist. 
Methods
The same observers who participated in the previous experiments were observers in Experiment 3. Stimuli and procedures were similar to Experiment 1 except the dot speed was 9°/s and the background lines were tilted 90° and 15° from vertical. As shown in the previous experiments, tilted background of 15° produced compelling distortion in the path of object motion, but not at 90°. In different conditions, dots moved along a fixed trajectory for six frames (as in Experiments 1 and 2) to generate long motion streaks or were randomly replotted after one frame-transition to generate short motion streaks. As in the previous experiments, observers were required to judge whether the cloud of dots was moving to the left or to the right of vertical, and the same staircase procedure was employed to null the motion-tilt-induction effect. 
Results and discussion
Figure 4 plots the averaged results of Experiment 3. The judged motion direction of the cloud stimulus is plotted for short (white bars) and long (gray bars) streak conditions for background orientations of 90° and 15°. Error bars signify 95% confidence intervals. A repeated measures two-way ANOVA confirmed that the judged motion direction were dependent on streak length (F[1, 16] = 5.50, p < 0.01) and background orientation (F[1, 16] = 116.62, p < 0.0001) as well their interaction (F[1, 16] = 11.64, p < 0.001) indicating that the effect of streak length was different for the two types of background-line orientations. Particularly as shown in Figure 4, where background lines were tilted 90° from vertical, observers were able to accurately detect the veridical motion of the stimulus with the judged angle of motion approximately 0°. Moreover, with background lines at 90°, there was no difference between short and long streak conditions. However, when background lines were tilted, the perceived direction of motion indicated an induced motion tilt. To nullify this illusory effect, the judged angle of motion was tilted in the direction of tilted lines. Importantly, for these background types, the extent of the distortion is dependent on streak length. Long streaks resulted in a larger motion displacement compared with short streaks (mean difference: 2.30°, which was significantly different, see following for details). 
Figure 4
 
The judged angle of motion is plotted for long (white bars) and short (gray bars) streaks conditions for background line orientations of 90° and 15° denoted along the x-axis. The black bar for background line orientation of 15° represents the judged angle of motion for short motion streaks in which the spatial step-size was much smaller at 0.056°/frame.
Figure 4
 
The judged angle of motion is plotted for long (white bars) and short (gray bars) streaks conditions for background line orientations of 90° and 15° denoted along the x-axis. The black bar for background line orientation of 15° represents the judged angle of motion for short motion streaks in which the spatial step-size was much smaller at 0.056°/frame.
While shortening the lifetime of dots resulted in a reduction in illusory motion tilt, it did not completely eliminate the effect. A likely explanation for this outcome is that, though streaks were made shorter, the spatial step-size (0.255°/frame) of the dots used in Experiment 3 might have been sufficiently large to generate motion streaks capable of affecting motion perception. Comparatively, shorter motion streaks can be generated by making dots jump over much smaller distances, but at much higher refresh rates. It would be expected that, if motion was generated in this manner, motion streaks will be considerably shorter, and under these stimulus conditions may not affect perception. To verify this possible outcome, a control experiment in which Experiment 3 was repeated (only for a background line orientation of 15° and with the same observers as in Experiment 3) with a higher refresh rate of 120 Hz (such that each frame presented for 8.33 msec) and the spatial step-size of each dot of 0.056°/frame to produce a speed of 9°/s. Thus, the spatial step-size used in the control experiment was four times smaller than that used in the main experiment (which was 0.225°/frame). 
The results of this control condition are shown in Figure 4 (black bar). A repeated measures ANOVA conducted on the results of Experiment 3 (for conditions in which background lines were 15°) including the control data revealed a significant effect of streak length (F[2, 4] = 30.65, p < 0.0001) on the judged motion direction. As evident in Figure 4, dot motion producing shorter motion streaks (gray and black bars) resulted in a comparatively smaller illusory motion-tilt effect than when motion streaks were long (white bar). Indeed, post-hoc mean comparisons (Tukey, Honestly Significant Difference test) between the long motion streaks condition and the two short motion streaks conditions indicated that were significantly different: long and shorter motion streaks in which the spatial step-size was 0.225°/frame (mean difference 2.297, p < 0.01); long and shortest motion streaks in which the spatial step-size was 0.056°/frame (mean difference 3.663, p < 0.001). Additionally, the two short motion streaks were also significantly different such that the illusory motion tilt observed with motion streaks generated with a spatial step-size of 0.225°/frame was higher than when the spatial step-size was 0.056°/frame (mean difference 1.365, p < 0.05). The results of this control experiment demonstrates that motion streaks underlie the perception of the kinetic Zollner illusion such that reducing the length of motion streaks, by shortening the lifetime of dots, decreases the extent of illusory motion-tilt induction. Particularly, for the shortest motion streaks condition (black bar), there appears to be little or no illusory effect (mean: 0.516°, 95% confidence limits: ± 0.866°) as the judged motion direction for this condition is close to zero indicating veridical motion perception. 
General discussion
The goal of this study was to determine whether the induced motion-tilt effect in the kinetic Zollner illusion could be understood in terms of motion streaks. It was reasoned that, if motion streaks were responsible for tilt induction, attenuating the availability or salience of streaks would reduce or eliminate the illusory effect. In three experiments, the relative contribution of motion streaks to the perception of motion was examined by changing dot speed, dot contrast, and dot lifetime to generate shortened streaks. Previous investigations have shown that such manipulations impact on the availability of motion streaks in the computation of motion direction (Apthorp & Alais, 2009, 2010; Edwards & Crane, 2007; Li et al., 2008). Experiment 1 examined the effect of dot speed on the extent of tilt induction. It was found that increasing dot speed resulted in a large motion-tilt effect, particularly at speeds sufficient to generate a motion streak. Experiment 2 examined the salience of motion streaks by altering the luminance contrast of dots. It was found that the motion-tilt-induction effect was significantly reduced at comparatively low dot contrasts. Finally, Experiment 3 varied motion-streak length by changing the lifetime of dots. It was found that short streaks produced a weaker tilt-induction effect than long streaks. Together, these findings demonstrate that, while motion streaks may not be perceptible (due to motion deblurring rendering clear vision: Burr, 1980; Burr & Morgan, 1977), the visual system is sensitive to this form cue and that they contribute directly to the perception of motion. 
The present findings add to a growing body of literature highlighting the importance of motion streaks to the perception of motion, and more specifically, add to the literature indicating that the processing of form and motion is interactive at early stages of processing. Kinetic illusions represent a situation in which background form information affects the perceived path of motion. Clearly then, the prevailing assumption of separate form and motion analysis in the early stages of visual processing (see De Yoe & Van Essen, 1988; Livingstone & Hubel, 1987) does not account well for these percepts. Separate early form and motion analysis would predict that the perception of motion is unaffected by spatial orientation. The influence of form information on direction of motion in these kinetic illusions would instead suggest interaction between form and motion processing in the visual system (see Lorenceau & Alais, 2001; Or et al., 2007; Ross, 2004; Ross et al., 2000). The cumulative evidence from the three experiments presented here suggests that this interaction is instead likely to arise from the influence of motion streaks on the perceived direction of motion. 
As previously mentioned, Geisler (1999) describes a computational model in which perceived direction of motion can be viewed as a product of the output of a motion-tuned cell and a line-sensitive cell tuned to the orthogonal orientation. The findings of the present study are best explained by Geisler's model. Under conditions in which strong motion streaks are produced (i.e., fast dot speeds, high contrast, and extended lifetimes), tilt induction is observed because background lines distort the streak (arising from lateral inhibition between cells coding orientation). When combined with the output of direction-selective cells, the perceived path of motion is itself distorted. However, when motion-streak information is reduced, this process does not occur. Under these circumstances, the visual system relies solely on the output of motion-selective cells to determine motion direction, which remains unbiased by background lines. This account of the kinetic Zollner illusion differs from that offered by Swanston (1984) who suggests that motion-tilt induction arises from lateral inhibition directly between motion-selective and orientation-tuned mechanisms. Importantly, as mentioned, this solution does not provide an adequate account of the changes in motion-tilt induction accompanying a reduction in object speed, contrast, and motion-streak length that are reported in the present study. 
The findings of the present study are consistent with the observations of Krekelberg et al. (2003), Ross (2004), and Or et al. (2007, 2010) who demonstrated that perceived direction of motion is a combination of the spatial orientation of an object and its motion direction. In those studies, Glass patterns were used to show that dipole orientation is treated as a motion streak that affects the perceived direction of motion. It is likely that an analogous operation occurs for motion-tilt induction; static background lines induce tilt in the orientation of motion streaks. 
The findings of the present study indicate that motion streaks can influence the direction of motion even though they are imperceptible. It is known from studies of visible persistence (e.g., Coltheart, 1980; Di Lollo & Hogben, 1985) that the percept of a briefly presented visual object persists for approximately 120 ms. One would predict, then, that the percept of a fast-moving object ought to be highly blurred. However, this does not occur. Moving objects are typically sharp in appearance, and their apparent position is clear (Ögmen, 2007). Previous studies have attributed clear perception of the form of a moving object to the active processes of motion “deblurring” (Burr, 1980, 1981). While the nature of the mechanisms underlying motion deblurring is still a matter of debate (see Morgan & Burr, 1997; Ögmen, 2007; Bex, Edgar, & Smith, 1995), the process obviously removes the presence of motion streaks from conscious perception (under normal viewing conditions), especially when the stimulus is high contrast and at fast speeds (see Bex et al., 1995). Despite this, motion streaks are unequivocally used by the visual system to compute direction of motion before motion deblurring occurs. As Geisler (1999) notes, this arrangement exists because form mechanisms offer greater precision to the computation of motion direction. However, as the present study suggests, the integration form and motion information does not always lead to accurate estimation of motion direction, but can cause measurable misperception in motion direction. 
Conclusion
In conclusion, the present study reports that the motion-tilt induction due to oriented background lines can be explained by interactions between orientation-tuned mechanisms processing the motion streak produced by object motion and background lines. Motion streaks are used by the visual system to signal the direction of motion, leading to tilt in the perceived path of object motion. This was confirmed in the present study by showing that attenuation of the availability of motion streaks through a reduction of speed, contrast, and streak length reduced the extent of motion-tilt induction. 
Acknowledgments
I thank the observers who participated in the study and Joanna Kidd for her helpful comments. I also thank the two anonymous reviewers for their helpful comments. This research was supported by an Australian Research Council (ARC) Discovery Project Grant (DP110104713) to S. Khuu. 
Commercial relationships: none. 
Corresponding author: Sieu K. Khuu. 
Email: s.khuu@unsw.edu.au. 
Address: The School of Optometry and Vision Science, The University of New South Wales, Sydney, New South Wales. 
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Figure 1
 
Schematic representation of the stimulus presentation sequence employed in the present study. Initially, a cloud of moving dots is presented on a background consisting of tilted lines for 1 second. After vertical lines appear above and below the stimulus area, the task of the observer was to judge whether the dot cloud moved left or right from vertical. After judgment, 10 Hz dynamic white noise was shown for 1 second.
Figure 1
 
Schematic representation of the stimulus presentation sequence employed in the present study. Initially, a cloud of moving dots is presented on a background consisting of tilted lines for 1 second. After vertical lines appear above and below the stimulus area, the task of the observer was to judge whether the dot cloud moved left or right from vertical. After judgment, 10 Hz dynamic white noise was shown for 1 second.
Figure 2
 
The judged angle of motion (in°) required to perceive vertical motion plotted against the speed of dots (in log scale) for different background line orientations (90° gray circles, 15° black squares, −15° light-gray diamond). Error bars signify 95% confidence intervals.
Figure 2
 
The judged angle of motion (in°) required to perceive vertical motion plotted against the speed of dots (in log scale) for different background line orientations (90° gray circles, 15° black squares, −15° light-gray diamond). Error bars signify 95% confidence intervals.
Figure 3
 
The judged angle of motion of a cloud of dots moving over tilted lines is plotted as a function of the Weber contrast of dots (in log scale). Black circles indicate judgments with background lines tilted 15°, while gray squares depict the results for conditions in which background lines were tilted 90° from vertical.
Figure 3
 
The judged angle of motion of a cloud of dots moving over tilted lines is plotted as a function of the Weber contrast of dots (in log scale). Black circles indicate judgments with background lines tilted 15°, while gray squares depict the results for conditions in which background lines were tilted 90° from vertical.
Figure 4
 
The judged angle of motion is plotted for long (white bars) and short (gray bars) streaks conditions for background line orientations of 90° and 15° denoted along the x-axis. The black bar for background line orientation of 15° represents the judged angle of motion for short motion streaks in which the spatial step-size was much smaller at 0.056°/frame.
Figure 4
 
The judged angle of motion is plotted for long (white bars) and short (gray bars) streaks conditions for background line orientations of 90° and 15° denoted along the x-axis. The black bar for background line orientation of 15° represents the judged angle of motion for short motion streaks in which the spatial step-size was much smaller at 0.056°/frame.
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