How fast is the barberpole? Interactions of motion and depth in the perception of velocity. Fauzia Mosca & Nicola Bruno

How fast is the barberpole? Interactions of motion and depth in the perception of velocity Fauzia Mosca & Nicola Bruno Università di Trieste, Trieste, Italy Submitted to: Perception & Psychophysics, August 2000 Revision: March 2001 Running Head: Barberpole Speed Correspondence: Nicola Bruno Dipartimento di Psicologia Università di Trieste via S. Anastasio, 12 34134 TRIESTE, Italy E-mail:Nicola.Bruno@univ.trieste.it

How fast is the barberpole? 2 Abstract We developed and tested a new method to study motion perception and integration as a function of binocular disparity. Observers viewed contours in one of two disparity conditions (in front of a rectangular frame, intrinsic contour terminators, or behind, extrinsic terminators) within a vertically or horizontally oriented rectangular aperture ("barberpole"). Before the onset of motion, observers adjusted the disparity of a small probe to a preset depth. Next, the first stimulus was moved for 204 ms. Finally, a second stimulus was presented for 204 ms. Observers had to decide which was faster. Discrimination data were used to compute matching speeds as a function of presentation conditions. Speed matches confirmed that motion integration is influenced by depth according to a simple coplanarity rule. However, integration was not influenced by aperture orientation as claimed in other studies. Differences with previous studies that used direction judgments are interpreted as due to our better control of fixation, convergence, and pursuit.

How fast is the barberpole? 3 Introduction When a stimulus varies along a single spatial dimension, its motion is inherently ambiguous. The component of motion parallel to stimulus orientation does not change the spatiotemporal structure of the generated optic array. Thus, only the component perpendicular to stimulus orientation (Vp) can be detected and a class of different motions cannot be distinguished (P. Stumpf, 1911/1996; Wallach, 1935/1996). Because local kinematic ambiguity is often demonstrated by looking at a contour through a circular aperture (see Figure 1a), this fundamental feature of 1D motion signals is often termed the «aperture» problem (Hildreth, 1984; 1987). There is substantial consensus that the aperture problem arises in human vision because of the existence of motion-sensitive cortical units that are selective for stimulus orientation (Movshon, Adelson, Gizzi & Newsome, 1985). To recover the true motion of objects in the environment, the human visual system must be able to integrate local signals in ways that effectively reduce local ambiguities. Several investigators have argued that solutions to the aperture problem may involve velocity computations, either by intersecting constraints in velocity space (Adelson & Movshon, 1982) or, more likely, by computing a spatially-weighted vector average of local signals (Castet, Lorenceau, Shiffrar & Bonnet, 1993; Ferrera & Wilson, 1990; Mingolla, Todd, & Norman, 1992; Rubin & Hochstein, 1993). --Figure 1--

How fast is the barberpole? 4 Critical to a spatially-weighted integrative mechanism is the idea that ambigous motion signals can be integrated («motion linking») with unambiguous signals from surface corners or edge terminators. For instance, when a grating or a contour is moved in a rectangular window, motion is perceived predominantly in the direction of the longer side of the window. This is generally referred to as the «barberpole» effect (Wallach, 1935/1996, see Figure 1b). Traditionally, the barberpole effect is explained by noting that the terminators of the moving line do move along the preferred perceived direction. A weighted-integration process that assigns greater weight to the unambiguous terminator component (Vt) would therefore predict motion along the longer side of the rectangular window. Consistent with the notion of long-range interactions between Vp and Vt signals, several studies have noted effects from remote motion signals on the motion of an edge seen through an aperture. For instance, Ben-Av & Shiffrar (1995) investigated the spatial integration of moving edges and corners seen through separate apertures. The study found that the unambiguous signal provided by the corners could propagate to the ambigous moving edges if the edges were properly aligned in space. In a related study, Mussap & Grotenhuis (1996) assessed the effect of external prolongations as a function of orientation and phase differences relative to an edge that moved within a rectangular aperture. In general, they found that the larger the difference (in phase or orientation) between the external prolongations and the inner edge, the smaller the capture effect of the external

How fast is the barberpole? 5 prolongations. Finally, Kim & Wilson (1997) investigated the direction of motion in a center circular aperture as a function of the properties of a surrounding annular aperture. They found directional shifts as a function of surround direction, size of the gap between disk and annulus, contrast, speed, and extent of the surround area. However, dependencies of disk motion on surround motion did not occur if the two moving sinewaves differed in spatial frequency. Taken in consort, these findings suggest that the processing of motion within one aperture can be influenced by more remote motions presented either in the surround of the test aperture or in other apertures. Although the factors governing motion linking in these complex conditions are still not clear, they may involve similarities in relatively low level stimulus properties, such as orientation, alignment, contrast, and spatial frequency. Besides contextual constraints on the cooperation/competion between local motion signals, other investigators have argued that the spatial integration of motion is also affected by higher-level constraints arising from surface occlusions and depth ordering. For instance, if the barberpole contour is placed at a farther depth plane than the rectangular window via binocular disparity, the barberpole effect is abolished and motion is again perceived in the direction of Vp (Shimojo, Silverman & Nakayama, 1989). In support of the importance of occlusion constraints, figural factors controlling depth ordering in occlusion configurations have also been shown to yield effects comparable to binocular disparity in causing partial abolition of the barberpole effect (Bressan, Ganis, &

How fast is the barberpole? 6 Vallortigara 1993; Gerbino & Bruno, 1997; Ramachandran, 1990; Tommasi & Vallortigara, 1999; Trueswell & Hayhoe, 1993; Vallortigara & Bressan, 1991). In the model of Shimojo, Silverman & Nakayama (1989), local disparity information acts as a sort of gate mechanism, allowing Vt signals to spread to the rest of the moving contour when disparity is consistent with an object (intrinsic) terminator, but not when Vt signals are classified as belonging to spurious terminators due to occlusion (extrinsic). Later on, we characterize this hypothetical mechanism in terms of a capture/suppression model: intrinsic terminators predominate over perpendicular signals, causing the barberpole effect, whereas extrinsic terminators are suppressed, abolishing the barberpole effect. However, it is presently not clear whether such mechanism is rigid, such that Vt signals are always fully suppressed with extrinsic terminators, or modulated by other factors. In fact, the data reported by Shimojo et al suggest that this modulation from additional factors is possible. In their paradigm, three expert observers performed a forcedchoice task between vertical and perpendicular directions with intrinsic or extrinsic terminators. Shimojo et al reported that the proportion of "vertical" choices was essentially 1 with intrinsic terminators, whereas it reduced to about 0.4 with extrinsic terminators. This seems to imply that extrinsic terminators were not always excluded from the integration process. However, other interpretations are possible. In their reanalysis of depth-motion interactions in the barberpole effect, Castet, Charton & Dufour (1999) examined näive observers but kept track of individual direction

How fast is the barberpole? 7 judgements. They found that the distributions of such judgments exhibited a marked tendency towards bimodality with extrinsic terminators, centering around Vt and Vp; whereas they exhibited a single central tendency at Vt with intrinsic terminators. On the basis of these findings, they argued that extrinsic terminators fail to completely suppress Vt components, essentially producing directional bistability in these conditions. On the basis of this finding, they argued that the reponses shift towards perpendicula directions with extrinsic terminators may be due to averaging two kinds of responses. In their proposed explanation, therefore, the terminator effect may be characterized in terms of a capture/bistability model. Intrinsic terminators predominate over perpendicular components, causing the barbepole effect; whereas extrinsic terminators actively compete with perpendicular components, causing bistability. Averaging over different trials then causes final estimates of directions to shift towards the perpendicular components. Although the finding of Castet et al is interesting, the question remains open as to what may cause the apparent bistability under extirnsic terminators. Given relatively long presentations, it is possible that directional judgements were contaminated by where observer fixated or by pursuit of certain features over time. For instance, intrinsic terminators may tend to attract an observer's foveation even if observers were required to fixate the center of the display. This in turn might enhance Vt signals relative to comparable extrinsic terminator conditions. In this paper, we sought to investigate the integration process while controlling for fixation and pursuit. To this aim, we did two things. First, we performed a preliminary experiment using a between-observer design to

How fast is the barberpole? 8 collect forced-choice directional judgments from naïve observers seeing extrinsic- or intrinsic-terminator barberpoles. Our own observations in this preliminary experiment readily demonstrated that the effect is not abolished by extrinsic terminators for all observers. To test the hypothesis that the effect of extrinsic terminators may have been contaminated by the lack of control of fixation and pursuit, we then performed three additional experiments. In these experiments, we developed and tested a different method for assessing motion integration in stereoscopic barberpoles. The core idea of the method lies in the use of a speed discrimination paradigm rather than collecting directional judgments. Use of this method allowed us to study motion integration with brief presentations (that effectively minimize pursuit). We also added an initial depth adjustment task to each trial in order to force observers to the appropriate convergence and to control fixation during the presentation. Our speed discrimination results, as well as their variability, provide support for suppression of extrinsic terminator component in these conditions and no evidence for bistability. In addition, they also suggest that intrinsic terminator components are averaged with perpendicular components to yield a final velocity in these conditions. Experiment 1 We showed a standard barberpole display having either intrinsic (rectangular frame behind the monitor plane) or extrinsic (frame in front of the monitor plane) bar terminators, and collected direction judgments from independent groups of naïve observers. The aim of

How fast is the barberpole? 9 this experiment was to evaluate the variability of such judgments under relatively unconstrained conditions of observation. Methods Equipment. The experiment was performed on a Silicon Graphics - Indigo workstation equipped with a stereo-ready SGI monitor (1280 x 1024 pixel resolution, 256 simultaneously displayable grey-levels, approximately 2 log units luminance range). Stereoscopic viewing was achieved by means of a Crystal Eyes field-sequential system. In this system, an emitter broadcasts an infrared signal to switch liquid crystal lenses on and off in exact synchronization with the monitor (60 Hz per eye rate). The lenses are mounted on glasses worn when observing the displays. The swap interval between screen buffers was set to two screen refreshes, allowing us to control stimulus speeds up to 0.5 pixels/60 Hz frame. Observers. Fifty members of the University of Trieste community participated. All observers were fully naïve to our purpose and had never served in a psychophysical experiment before. All were tested for normal stereoscopic vision by means of a randomdot stereogram before serving. Twenty-five were shown a stereoscopic barberpole with intrinsic terminators. The other twenty-five were shown the barberpole with extrinsic terminators.

How fast is the barberpole? 10 Displays. Displays consisted of a gray rectangular frame (6.5 cd m -2, 2.5 degs horizontally x 7.5 degs vertically) surrounded by a larger circular surround (diameter 20 degs). The inside part of the rectangle and the outer surround were white (20 cd m -2 ). Inside the rectangular frame, we presented a single line (2.5 cd m -2 ) oriented at 45 deg. Outside the larger circular surround, screen luminance was effectively zero yielding a deep black surround. The disparity of the rectangular frame relative to the line, either crossed or uncrossed, was always 10 min of visual angle. The line was translated vertically with a Vt speed equal to 4.5 pixels/frame (Vp component equal 3.18 pixels/frame). The starting and ending positions for the motion of the line were calculated so that the terminators always remained on the longer sides of the aperture. Line motion always begun from the top position and cycled up and down until the observer entered a response. Procedure. Observers sat at a 57 cm distance from the monitor. They viewed the displays while wearing stereo goggles (on top of prescriptions if needed) for as long as they wished and simply performed a forced choice between vertical and perpendicular motion directions. They were required to fixate the center of the display but no attempt was made to enforce this requirement or check that they complied with it. Results Proportions of "vertical" judgments in extrinsic and intrinsic conditions are presented in Figure 2. In the intrinsic terminator condition, observers unanimously reported

How fast is the barberpole? 11 vertical motion. In the extrinsic terminator condition, only 40% of the observers reported vertical motion (standard error 10%). -- figure 2-- Discussion Our preliminary result is basically consistent with that reported by Shimojo and collaborators using expert observers, and confirms that extrinsic terminators do not necessarily produce suppression of Vt signals in all trials. To test whether apparent failures to completely suppress extrinsic terminators can be ascribed to incomplete control over fixation and pursuit, we performed a series of additional experiments using a speed matching paradigm. Overview of Experiments 2-4 In an attempt to control for unwanted influences of fixation, eye movements, and spatial attention, we have developed a speed discrimination paradigm to study motion perception within stereoscopic apertures while carefully controlling for exposure time and fixation. The core idea lies in the joint use of two tasks. An initial task, performed on the stationary barperpole pattern, involves fixating a stereoscopically presented target square and adjusting its disparity to position it in depth at the same distance as the surrounding

How fast is the barberpole? 12 rectangular aperture. This task ensures that the observer is fixating the center of the display and that convergence is appropriate for the desired stereoscopic effect. Upon completion of the first task, observers performed a discrimination task on the same display. This second task required comparing the speed of the contour moving within the rectangular aperture with the speed of a second stimulus, presented immediately afterwards. The presentation of both stimuli is of the order of 200 ms, so as to effectively minimize the possibility of ocular pursuit (see Hallet, 1986) and the potential temporal integration of successive fixations. Using the above discrimination procedure, we obtained estimates of the matching speed of contours within rectangular apertures. This matching speed, in turn, provides indirect information about the relative importance of the Vt and Vp components in the integration process. The relationship between these two components is illustrated, for a contour oriented at 45 degrees (such as those investigated here), in Figure 3. Note that Vt = Vp 2 in these conditions. Hence, if Vt signals for extrinsic terminators are excluded from the integration, we expect speed matches to correspond to the law match = Vp standard speed (a line with slope = 1). If Vt signals for intrinsic terminators are instead included in the integration and fully capture the motion of the contour, we expect speed matches to correspond to the law match = Vp standard speed 2. This pattern of results would thus yield two diverging lines with an angular difference of about 10 degrees. --Figure 3--

How fast is the barberpole? 13 General Methods Equipment. The equipment was the same as in experiment 1. Procedure. The structure of the basic experimental trial is summarized in Figure 4. Before performing speed discriminations, observers were presented with a static barberpole display having the rectangular frame either in front of the line (intrinsic terminator condition) or behind the line (extrinsic terminator condition). In the center of the rectangle was a small green square which was stereoscopically placed at same disparity as the line. Before initiating each trial, observers were requested to adjust the disparity of this square probe until its position in depth was the same as that of the currently presented frame. As soon as they had done this, observers started the animation by pressing the space bar on the computer console. Speed matches were derived from comparative judgements of the standard and test stimuli, each standard - test pair being presented in succession with a blank interval equal to 1 screen refresh (approx. 17 ms ) in between. The standard stimulus always preceded the test stimulus and they both lasted 12 screen refreshes (about 204 ms). Observers were instructed to press one console button if they believed that the standard was faster, and another button if they believed that the test was. The standard displays were always the same throughout experiments 2-4, as detailed in the next subsection, except for their orientation which was vertical in experiments 2 and 3 and horizontal in experiment 4. The nature and number of test stimuli above and below the speed of the standard stimulus

How fast is the barberpole? 14 depended on the psychophysical procedure implemented in any given experiment, as reported in the relevant subsections. --Figure 4-- Standard Stimuli. In experiments 2-4, barberpole standard stimuli consisted of a gray rectangular frame identical to that used in experiment 1. This frame was oriented vertically in the second and third experiments, whereas it was horizontal in the fourth experiment. The inside part of the rectangle and the outer surround were white (20 cd m -2 ). Inside the rectangular frame, we presented a single line ( luminance approximately 2.5 cd m -2 and orientation 45 deg). Outside the larger circular surround, screen luminance was effectively zero yielding a deep black surround. The disparity of the rectangular frame relative to the line, either crossed or uncrossed, was always 10 min of visual angle. In all experiments, the Vp components of the speed of the standard line were 2.12, 3.18, and 4.24 pixels/frame, corresponding to Vt motion components equal to 3, 4.5, and 6 pixels/frame. The starting and ending positions for the motion of the standard line were calculated so that the terminators always remained on the longer sides of the aperture (in experiments 2-3, the vertical ones; in experiment 4, the horizontal ones). This also insured that the line did not change length during its motion. Test Stimuli. Test stimuli consisted of single lines 1 having the same length and orientation as the lines presented in the standards, and moving either in the Vp direction or in the Vt

How fast is the barberpole? 15 direction. This single line was presented within the larger circular surround. Given that the line was exactly the same length and orientation as the lines presented in the standards, it was much smaller than the circular surround and essentially appeared as a line moving over a homogeneous field. Data plotting. For each experiment, 95% confidence intervals around speed matches were plotted individually for each observer as a function of the Vp component of the speed of the standard. If perceived speeds are entirely determined by this component, they should lie on a line having slope equal to 1 and zero intercept. If instead they are entirely determined by the Vt motion component, they should lie on a line having slope equal to 2 or about 1.41. Because in many cases the plotted error bars were very small, companion graphs of standard deviations were also prepared for direct comparison of variability in the crossed and uncrossed disparity conditions. Analysis. The data from all the experiments were analyzed in three steps. As a first step, we examined speed matches by subjecting them to a series of 2 (disparity) x 3 (Vp component of the standard) repeated measures general linear model analyses. The effect of the binocular disparity on the speed of the standard line predicts that the data should lie on two lines having different slopes but both intersecting the axes at zero. The linear model that tests this pattern implies a significant effect of the covariate and a significant interaction between the standard Vp component and disparity, but no difference between the adjusted disparity means as the intercepts of the two lines are both at zero. Because matches in

How fast is the barberpole? 16 different experiments were collected using different types of test stimuli and with different psychophysical procedures, these analyses were performed separately for each experiment. As a second step, we estimated the variability of the matches in the different experiments. In experiments 2 (method of constant stimuli), the standard deviations of these matches were estimated by probit analysis. In experiments 3 and 4 (staircase method), standard deviations were estimated from the variability of reversals, by computing the SD of each set of reversals and by then averaging them across the five sessions. As a third step, finally, we computed the differences between slopes in the two experimental conditions in all experiments and evaluated the results against an expected difference of 10 degrees. Experiment 2 Participants to this experiment compared intrinsic or extrinsic standards with test stimuli that moved in the direction predicted by the hypothesized effect of terminator type. Thus, observers compared intrinsic standards with lines that moved in the Vt direction, but they compared extrinsic standards with line that moved in the Vp direction. To estimate matching speeds from discrimination performance, this experiment used the method of constant stimuli. Methods Observers. Three observers participated. One of them (F.M.) was the first author. The

How fast is the barberpole? 17 other two (I. C. and S. L.) were unpaid members of the University of Trieste community and were naïve to the purpose of the study. All observers had normal or corrected-tonormal acuity and normal stereoscopic vision. Test Stimuli and Procedure. Test stimuli moved either in the Vp direction (extrinsic condition) or in the Vt direction (intrinsic condition). Speed matches were collected using the method of constant stimuli. For each level of the standard speed, 13 test speeds were presented. For a Vp standard speed of 3 pixel/frame the range was between 0.5 and 6.5 pixel/frame. For a Vp standard speed of 4.5 pixel/frame the range was between 2 and 8 pixel/frame. Finally, for a Vp standard speed of 6 pixel/frame the range was between 3.5 and 9.5 pixel/frame. In each experimental block, each test stimulus was presented twice, yielding a total of (13 speed levels x two terminator types x two presentations) 52 trials per block. Each observers served in 25 blocks. Therefore, each psychometric function used to estimate a matching speed was based on 650 trials in this experiment. Analysis. Matching speeds (points of subjective equality) were computed for each level of the standard speed in intrisic and extrinsic standards by subjecting the proportion of «test faster» responses to probit analysis. The variability associated to the estimates of matching speeds was evaluated from the standard deviations of the distributions underlying the comparative responses. Results

How fast is the barberpole? 18 Figure 5 presents a typical pair of psychometric functions of discrimination judgements in the extrinsic and intrinsic terminator conditions. Note that the sigmoid from the intrinsic condition appears slightly displaced to right relative to the sigmoid for the extrinsic condition, as one would expect if discriminative judgments were affected by terminator type. Matching speeds (points of subjective equality) were estimated using probit analysis. Thus, standard Vp values corresponding to 50% "test faster" judgments were taken as estimates of matching speeds for each standard speeds. The inverses of the slope of the probit-transformed proportions were taken as estimates of standard deviation of the matching speeds. Matching speeds and associated standard deviations are presented individually in Figure 6. A clear difference is apparent as a function of terminator condition. Confidence intervals around individual regression fits of observers F. M. and I. C. demonstrated that their matches were consistent with the Vp- and the Vt-component expectations in the extrinsic and intrinsic conditions, respectively (see Table 2). Fits of the data from observer S. L. yielded higher slopes than the expectations. Even for this observer, however, the difference between the slopes was essentially the same as the expected one (11 deg difference in the arctangent of the observed slopes, against 10 deg expected). Statistical analysis of this pattern confirmed that the matches were linear functions of the standard speed with different slopes but equal intercepts. Matching speeds varied

How fast is the barberpole? 19 linearly with the Vp component speed of the standard, F (1, 2) = 24.7, p < 0.04, the interaction between Vp component and disparity was significant, F (1, 2) = 109.5, p < 0.009, whereas the main effect of disparity was not, F (1, 2) = 0.3, p > 0.66. Finally, matching speeds were different in different observers, F (2, 6) =11.1, p < 0.01, as was the interaction between Vp component and observer, F (2, 6) = 11.2, p < 0.01. These results suggest that a barberpole line having intrinsic terminators move at the same speed as a single line having equal length, orientation, and Vt and Vp components. Conversely, a barberpole line having extrinsic terminators moves at the same speed as a single line having equal length, orientation, and Vp component only. Thus, the present results may be taken as evidence for suppression of the terminator components under extrinsic conditions. In addition, we note that there was little difference in variability between conditions (lower part of the figure). We will comment on this latter result in the general discussion section. --Figure 5 e 6-- Experiment 3 The results of the previous experiment may be confounded by a test stimulus effect. In experiment 2, test stimulus directions were matched to the expected direction of the standard barberpole stimulus, assuming a suppression effect due to terminator

How fast is the barberpole? 20 classification. Thus, intrinsic terminator standards were matched with tests moving in the Vt direction, whereas extrinsic terminator standards were matched with tests moving in the Vp direction. Given this matching, we cannot rule out that the observed results were at least in part due to an unknown effect of test motion direction rather than terminator classification. To test this possibility, we performed a third experiment using both a "matched" and a "crossed" set of test motion directions. Thus, both intrinsic and extrinsic terminator standards were compared with tests moving in the Vp and Vt directions. To test all four discrimination conditions within observers without excessively long sessions, an interleaved staircase procedure was adopted instead of the method of constant stimuli. Methods Observers. Three observers participated. One of them (F.M.) was the first author. The other two (F.S. and R.D.) were unpaid members of the University of Trieste community and were naïve to the purpose of the study. All observers had normal or corrected-tonormal acuity and normal stereoscopic vision. Procedure and Design. Matches were estimated using an interleaved staircase procedure (Cornsweet, 1962). Because randomizing the ascending and descending staircases yielded markedly more variable responses in a pilot run of the experiment, strict alternation was implemented with a 1 up -1 down stepping rule to control the speed of the test stimulus. Step size was set at 1 pixel/frame. Initial values were always 3 steps above or below the

How fast is the barberpole? 21 Vp standard speed for the descending and ascending staircases, respectively. The experimental design consisted in 3 standard speeds x 2 test directions x 2 terminator conditions. Therefore, 12 pairs of interleaved staircases were presented to each observer in a randomized order. In each presentation, the procedure was halted after 7 reversals in each direction. Matching speeds were computed by averaging reversals in both directions. Matching variability was estimated by computing the standard deviations of the 14 reversals. Each observer contributed five experimental sessions, each yielding six matching speeds for the the same standard speeds used in experiment 2. Test Stimuli and Analysis. They were the same as those of experiment 2, except for the pairings of standard and test stimuli. In experiment 2, intrinsic standards were only paired with tests moving vertically whereas extrinsic standards were only paired with tests moving perpendicularly. In the present experiment, terminator conditions and test stimulus directions were manipulated factorially, yielding two types of speed discriminations: matched (intrinsic vertical vs. extrinsic-perpendicular) or crossed (intrinsic-perpendicular vs. extrinsic-vertical) with respect to the expected directions of the standard barberpole. This manipulation allowed us to measure the effects of terminator type and test type independently. Results Matching speeds are presented individually in figure 7 as a function of the Vp

How fast is the barberpole? 22 component speed of the standard, as well as terminator type (top) and test type (bottom). These plots confirm that matching speeds were influenced systematically by the classification of terminators into intrinsic or extrinsic, based on the provided disparity. However, they also confirm that matches varied in a systematic fashion according to the direction of the test stimulus. A general linear model analysis of these main effects demonstrated that both the effect of terminator type, F (1, 2) = 19.7, p < 0.0001, and the effect of test type F (1,2) = 43.3, p < 0.0001, were statistically reliable when controlling for standard speed, F (1, 2) = 104.3, p < 0.001. To better illustrate the nature of these two effects, we replotted the results after dividing the data into matched- or crossed-set discriminations. Matching speeds as well as match standard deviations in the intrinsic and extrinsic terminator conditions are presented in the two parts of Figure 8. Figure 8a presents matching speeds from the matched set. Thus, the data presented in Figure 8a are an exact replication of those presented in Experiment 2. Figure 8b presents matching speeds from the crossed set. As can be seen from comparing the graphs in Figure 8 with those in Figure 7, matching speeds tended to be systematically higher both in the intrinsic relative to the extrinsic condition and with vertical relative to perpendicular tests. In the matched set, these two tendencies combined, yielding results similar to those observed in experiment 2. In the crossed set, they worked against each other, essentially removing the difference due to terminator type. This interpretation was confirmed by subjecting the matching speeds to a 3 (Vp component standard speed) x 2 (2 terminator type) x 2 (set type, matched or crossed) general linear

How fast is the barberpole? 23 model analysis. This analysis yielded a significant three way interaction (standard speed x terminator x set), F(1, 14) = 12.3, p < 0.0035, and significant main effects of standard speed, F(1, 2) = 31,2, p < 0.03 as well as terminator type, F(1, 2) = 81.6, p < 0.012. The main effect of set type failed to reach significance, F(1, 2) < 1, as did all other interactions, all F's < 1.1. --Figures 7 and 8-- The nature of the observed three way interaction is further illustrated in table 3, which summarizes individual regression slopes as a function of terminator and set type. In the matched-set data, these slopes were similar to those of experiment 2 (see table 2), with marked differences in slope as a function of terminator type. In the crossed set data, the slopes were essentially indistinguishable. Finally, and again as in the previous experiment, we note that no obvious increase in the variability of matches could be observed as a function of terminator type in either matched or crossed conditions (bottom graphs of Figure 8). Discussion of experiments 2-3 The pattern of results observed in experiments 2 and 3 support the hypothesis that speed discrimination is affected by terminator type, as predicted from a model of motion

How fast is the barberpole? 24 integration that takes depth information into account. However, the results of experiment 3 also revealed an unexpected effect of the direction of the test stimulus. At first blush, this effect may seem evidence that the direction of the test stimulus can alter the perception of the standard speed. Although the results of our experiment 1, as well as previous similar findings, confirm that the effect of disparity on motion integration is not an all-or-none phenomenon and is probably influenced by additional factors such as fixation and eye movements, we doubt that an explanation of the present results in terms of a direct bias from the test direction would be convincing. Recall that our test stimuli were always presented after, not before or together with, the standard barberpoles. If test motion direction could bias the perception of a previously presented standard, this would entail a sort of backwards priming effect. To our knowledge, no such effect has ever been reported in the literature. As an alternative, we believe that a simple explanation for the observed difference between the matched- and the crossed-set data can be found in a simple modification of the motion integration model that motivated our experiments. Recall the motion integration model that was used to derive the predictions for the present experiments (Shimojo, Silverman & Nakayama, 1989; see also th overview of experiments 2-4). In this model, the speed of the standard stimulus is entirely determined by the Vt component when the terminators are classified as intrinsic, whereas it is entirely determined by the Vp component when the terminators are classified as extrinsic. We call this a capture/suppression model of motion integration. With intrinsic terminators, the Vt components from the line terminators are fully included in the integration, and therefore

How fast is the barberpole? 25 capture the motion of the line entirely. With extrinsic terminators, the Vt components are fully suppressed and therefore the line moves only in the Vp direction. Within the capture/suppression model, both the matched and the crossed-set matching speeds vary as a function of terminator type, according to the following laws: match = Vt (intrinsic terminators) or match = Vp (extrinsic terminators). In the matched set discriminations, this amounts to saying that the intrinsic barberpole appears to have the same speed as a test line moving vertically with speed equal to Vt, whereas the extrinsic barberpole appears to have the same speed as a test line moving perpendicularly with speed equal to Vp. In the crossed set discriminations, this amounts to saying that the intrinisic barberpole appears to have the same speed as a test line moving perpendicularly with speed equal to Vt, whereas the intrinsic barberpole appears to have the same speed as a test line moving vertically with speed equal to Vp. Clearly, the pattern of results observed in experiment 3 is not consistent with such a capture/suppression model. A simple modification of this model, however, can predict the observed pattern without invoking a backwards bias from the test motion direction. A number of studies have demonstrated that the local integration of motion signals resembles a form of vector averaging (Castet, Lorenceau, Shiffrar & Bonnet, 1993; Ferrera & Wilson, 1990; Mingolla, Todd & Norman, 1992; Rubin & Hochstein, 1993). It is therefore plausible to hypothesize that terminator components, when included in the integration process, do not fully capture the motion of the test line. Instead, they may compete with the perpendicular components, causing the line to move with speed and directions that compromise between the two

How fast is the barberpole? 26 components. We may call this an averaging/suppression model. In this model, when terminators are classified as extrinsic or when a test line moves in the Vp direction, the speed of the line corresponds to Vp. Conversely, when terminators are classified as intrinsic or when a test line moves in the Vt direction, the speed of the line corresponds to a weighted average of Vt and Vp. It is easy to see that such an averaging/suppression model makes the same predictions as the capture/suppression model for the matched-set discriminations, whereas it predicts essentially no effect of terminator type in the crossedset discriminations. Consider a simple numerical example. Suppose that Vp = 1 pixel/s and therefore Vt = 1.4 pixel/s with the present orientations. In the matched set, when observers compare an extrinsic standard with a perpendicular test, they should produce a speed match whenever Vp (standard) = Vp (test); whereas when they compare and intrinsic test with a vertical test, they should produce a speed match whenever average (Vt standard, Vp standard) = average (Vt test,vp test). But the latter condition is true whenever Vt (standard) = Vt (test) = 1.4 pixel/s and Vp (standard) = Vp (test) = 1 pixel/s. Hence, the predicted pattern of results is exactly the same as that predicted by the capture/suppression model. Conversely, in the crossed set, when observers compare an extrinsic standard with a vertical test, they should produce a speed match whenever Vp (standard) = average (Vt test, Vp test). For this condition to be true, then the Vt(test) speed which we plotted in our graphs must be greater than 1 pixel/s. For instance, if the extrinsic standard moves perpendicularly with speed = 1 pixel/s, the average (Vt test, Vp test) equals 1 when Vt(test) = 1.2 and Vp(test) = 0.8. By

How fast is the barberpole? 27 the same logic, when observers compare an intrinsic standard with a perpendicular test, they should produce a speed match whenever average (Vt standard, Vp standard) = Vp (test). For this condition to be true, then the Vp(test) speed which we plotted in our graphs must be smaller than 1.4 pixel/s. For instance, if the intrinsic standard moves (in a direction intermediate between vertical and perpendicular) with speed equal to average (Vt standard, Vp standard) = 1.2 pixel/s, this speed will match a Vp(test) = 1.2. Hence, in the crossed set data we should expect approximately the same matching speeds for both intrinsic and extrinsic terminator conditions. We conclude that the results of experiments 2 and 3 fully support an effect of terminator type on motion integration. In addition, we suggest that the nature of this effect can be captured by an averaging/suppression model in these conditions. Extrinsic terminators are suppressed, whereas intrinsic terminators compete with perpendicular components. Experiment 4 To further test the hypothesis that speed matches are influenced by perceived depth and therefore by the classification of contour terminators as intrinsic or extrinsic, we performed a final experiment. Experiment 4 was a replication of the matched-set conditions of experiment 3, except for the orientation of the rectangular frame. In experiment 3, as in the previous experiments, the rectangular frame was vertical. In

How fast is the barberpole? 28 experiment 4, we used a horizontal frame. This manipulation is interesting, because the use of a horizontal frame removes from the display one potential source of binocular information about depth order: the lack of binocular correspondence between small areas that are visibles by one eye, but not by the other ("Da Vinci" stereopsis, sometimes also called "half occlusions"). In a previous paper, Castet, Dufour & Bonnet (1999) reported that the barberpole effect was no longer abolished by extrinsic terminators when the barberpole configuration was horizontal rather than vertical (see also Anderson, 1999). This finding has been interpreted as evidence that retinal disparity is not sufficient, in itself, to cause the exclusion of Vt components from motion integration process. This is so because, when a horizontal frame is displaced binocularly relative to a line that abuts the horizontal contours of the frame, all parts of this line remain fully visible to each eye and therefore no "Da Vinci" stereopsis is present in the display. Conversely, when a vertical frame is subjected to an equivalent displacement relative to a line that abuts the vertical contours of the frame, parts of this line become visible to the left eye but remain invisible to the right eye, and other parts become visible to the right eye but remain invisible to the left eye. However, our informal observations of the barberpole displays tested in experiments 1-3 after rotating the rectangular frame to a horizontal orientation indicated that the abolition of the barberpole effect can be obtained even in these conditions, provided that one maintains fixation in the center of the frame during the motion. To

How fast is the barberpole? 29 corroborate this observation with more objective evidence, we measured speed matches as we did for vertical frames in the previous experiments. Methods Observers. Three observers participated. One of them (F.M.) was the first author. The other two (M.M. and C.F.) were unpaid members of the University of Trieste community and were naïve to the purpose of the study. All observers had normal or corrected-tonormal acuity and normal stereoscopic vision. Standard Stimuli. Standard stimuli were the same as those of the matched set used in experiment 3, except for the orientation of the rectangular frame and therefore the direction of the line presented within this frame. Given the orientation of the frame, the standard line moved with a Vt component in the horizontal direction. The Vp component of the standard line was exactly the same as that of all previous experiments. Test Stimuli. Test stimuli were same as those of the matched set used in experiment 3, except for the direction of their motion. Given that the standard stimuli were presented in horizontal frame in this experiment, the Vt component of the test stimuli was now a horizontal translation instead of vertical. The Vp component of the test stimuli was exactly the same as that of all previous experiments.

How fast is the barberpole? 30 Procedure and Analysis. They were the same as those of experiment 3. Results Mean observer matching speeds and standard deviations in the intrinsic and extrinsic conditions are presented individually in Figure 9. Speed matches exhibited a clear difference as a function of terminator type. Visual inspection of the suggested that these were quite close to the theoretical expectations based on Vt and Vp for the first two observers (F.M. and M.M.), whereas they were considerably higher than those expectations for the third. Confidence intervals around individual regression slopes confirmed this visual impression (see Table 4). Even for observer C.F., however, the difference in angular coefficients was quite close to the expected one (7 deg difference between the arctangents of the observed slopes, against 10 deg expected). Statistical analysis of this pattern confirmed that the matching speeds were linear functions of the standard speed with different slopes but equal intercepts. As in experiments 2 and 3, matches varied linearly with the Vp component speed of the standard, F (1, 2) = 23.1, p < 0.04. The interaction between Vp component and disparity was significant, F (1, 2) = 21.2, p < 0.05, and the main effect of disparity was not, F (1, 2) = 4.8, p > 0.1. Also consistent with the previous experiments, there were individual differences in mean matches, F (2, 6) = 0.4, p > 0.6, as well as individual slopes as tested by the two-way interaction, F (2, 6) = 27.7, p < 0.001.

How fast is the barberpole? 31 --Figure 9-- Discussion Given that the rotating the frame to a horizontal orientation removed "Da Vinci" stereopsis from these displays, the present results confirm that retinal disparity is sufficient, in itself, to produce a change in speed matches as a function of terminator type. Second, the effect of binocular disparity is present even in horizontal barberpoles. This finding is not consistent with reports by Castet, Dufour & Bonnet (1999) and Anderson (1999). These authors collected direction judgments and found that the barberpole effect was not abolished with extrinsic terminators and horizontal orientations of the rectangular frame. They interpeted this result as evidence that the crucial factor in determining the abolition is «Da Vinci» stereopsis, not retinal disparity. In our data, however, we found a strong effect of binocular disparity even in horizontal barberpoles, where «Da Vinci» stereopsis was not present. General Discussion We have developed and tested a speed matching paradigm aimed at investigating the effect of binocular disparity for depth on motion integration. Our results are in good general agreement with previous reports of such effects on barberpole displays (Shimojo,

How fast is the barberpole? 32 Silverman & Nakayama, 1989). This agreement validates the method and provides further support for the hypothesis that binocular disparity supports a form of perceptual classification of edge terminators, which in turn affects the relative importance of Vp and Vt components in the integration of motion components. Although our results are partly a replication of previous findings with a different methodology, they provide important evidence supporting the idea that directional judgements of relatively long-lasting complex displays may confound effects due to terminator classification with effects that have to do with where an observers is fixating, or with where and how the eyes move. That eye movements are an additional source of information for motion perception has been argued by several investigators (Beutter, Lorenceau & Stone, 1996; Beutter & Stone, 1997; Buetter & Stone, 1998; Wallach, 1982). Given that the systems involved in pursuit eye movements and in the perception of motion direction are localized both in MT and MST cortical areas, it is extremely plausible that these two functions are related. In particular, Buetter & Stone (1998) have showed similar perceptual and oculomotor biases with elongated apertures, suggesting that pursuit and perception share a critical motion processing stage. The importance of carefully controlling for fixation and eye movements along with figure/ground segregation is also demonstrated by the elegant study of Vallortigara & Bressan (1991). Vallortigara & Bressan investigated barberpole patterns presented with the addition of external prolongations, such as those in Figure 1c. They found that when the

How fast is the barberpole? 33 frame was narrower than the lines, then the Vp component of the external edges tended to capture the motion of the edge inside the rectangular window, abolishing the barberpole effect. This outcome is consistent with an effect of figure/ground segregation based on relative widths, promoting a classification of the terminators as extrinsic (see also Trueswell & Hayhoe, 1993). However, when frame and lines had equal widths, the prevalent direction was vertical, as in the standard effect, but only when observers fixated the central part of the display. When they distributed their attention on the whole configuration, the barberpole effect was again abolished. The experiments presented here controlled for fixation and eye movements in two ways. First, we asked observers to perform an initial depth adjustment task to force them to fixate at a target square, positioned in the center of the barberpole stimulus. Second, we measured speed matches instead of directional judgments, which allowed us to employ stimulus durations that were sufficiently brief to minimize the possibility of pursuit eye movements, or of conscious attempts to estimate the direction of motion. In addition, we used only movements such that both line terminators were always along the longer sides of the rectangle. This feature of our displays avoided the need to consider potential integrations of terminator components in different directions. Using this paradigm, we found evidence for an averaging/suppression model of motion integration (experiments 2-3) and for a role of binocular disparity in controlling the suppression effect (experiment 4). These findings are not consistent with other reports

How fast is the barberpole? 34 suggesting directional bistability with extrinsic terminators and a crucial role of "Da Vinci" stereopsis, rather than binocular disparity, in modulating the terminator effect (see Anderson, 1999; Castet, Charton, & Dufour, 1999). Rather, they suggest that motion integration obeys a simple coplanarity rule: components that are placed on the same depth plane by disparity information are integrated (via averaging); components that are placed on a different plane from that of a target object are excluded from the computation of that object's speed (via suppression). These findings also differ from reports that claimed bistability of barberpole displays having extrinsic terminators (Castet, Charton, & Dufour, 1999). In all our speed matching experiments, estimates of match variability were about the same with extrinsic and extrinsic terminators. Although many questions are still open about the process of motion integration in complex displays, we stress that further studies will have to pay greater attention to the potential effect of fixation and eye movements, especially when relatively long stimulus durations are employed.

How fast is the barberpole? 35 Author Note The present results were reported in part at the 1998 Meeting of the Association for Research on Vision and Ophtalmology (Ft. Lauderdale, FL, May 10-15 1998) and at the 1999 European Conference on Visual Perception (Trieste, Italy, 22-26 August 1999). Supported by the University of Trieste and by MURST grant n. 9911333852 to the second author.

How fast is the barberpole? 36 Footnotes 1. In a pilot experiment, speed matches were collected for intrinsic or extrinsic standards containing a set of several lines that were compared with test stimuli consisting of a circular aperture containing again several lines. Although all observers yielded slightly higher matches in the intrinsic condition relative to the extrinsic one, the difference between the two conditions was small and the statistical analysis failed to detect the expected difference in velocity matches as a function of terminator condition. Given that using several lines in the displays may produce spatiotemporal summation of motion signals and therefore floor effects, we decided to use single lines in all experiments.

How fast is the barberpole? 37 Figure Captions Figure 1. (a) The «aperture» problem: When a homogeneus contour moves inside a circular aperture its direction is ambiguous. (b) The «barberpole» effect: when a homogeneus line is moved inside an aperture, it tends to move in the direction of the aperture s longer side. (c) Effects of surrounding contours, fixation, and figure/ground segregation on the barberpole effect. In the left configuration, when attending to the inside of the rectangle one perceives vertical motion; conversely, when attending to the whole configuration one perceives perpendicular motion. In the right configuration, the rectangular frames is perceived behind the bars and only perpendicular motion is seen (from Vallortigara & Bressan, 1991). Figure 2. First experiment. Proportion of vertical judgments in extrinsic and intrinsic terminators. Figure 3. Perpendicular (Vp) and terminator (Vt) motion components for a single line translating within a rectangular aperture; their relation for a contour oriented at 45 degrees relative to the longer side of the aperture. Figure 4. Example of typical psychometric function in extrinsic (open diamonds) and in intrinsic (fill square) terminators. As is possible to observe that the intrinsic sigmoid is in

How fast is the barberpole? 38 advantage position with respect extrinsic sigmoid. Figure 5. Schematics of experimental trials. Each trial began with a static presentation of the standard plus a small green square on the same depth plane as the surrounding circle. Observers manipulated the disparity of this square probe until it appeared at the same depth plane of the rectangular frame. Next, they pressed the console spacebar to initiate the matching trial. The square disappeared, and the presentation of the standard motion began (204 ms). Finally, the test bar motion was presented (204 ms). The response was provided by pressing the left- (standard faster) or right (test faster) mouse buttons. Figure 6. Second experiment. Top: matching speeds (points of subjective equality) as a function of the Vp component in the standard bars (filled squares: crossed disparity rectangular frame in front of the bars; open circles: uncrossed disparity rectangular frame behind the bars; dashes: theoretical Vp (matching speeds = Vp standard speed) and Vt (matching speeds = Vp standard speed 2) matches. Error bars represent 95% confidence intervals. Bottom: standard deviations of the judgments. Figure 7. Thirth experiment. Top: matching speeds (points of subjective equality) as a function of the Vp component in the standard bars (filled squares: crossed disparity rectangular frame in front of the bars; open circles: uncrossed disparity rectangular frame behind the bars) matches for terminators type. Error bars represent 95% confidence intervals. Bottom: matching speeds (points of subjective equality) as a function of the Vp

How fast is the barberpole? 39 component in the standard bars (filled squares: vertical test moving; open circles: perpendicular test moving) matches for test motion type. Figure 8a. Third experiment matched-set. Top: matching speeds (points of subjective equality) as a function of the Vp component in the standard bars (filled squares: crossed disparity rectangular frame in front of the bars; open circles: uncrossed disparity rectangular frame behind the bars; dashes: theoretical Vp (matching speeds = Vp standard speed) and Vt (matching speeds = Vp standard speed 2) matches. Error bars represent 95% confidence intervals. Bottom: standard deviations of the judgments. Figure 8b. Third experiment crossed-set. Figure 9. Fourth experiment. Top: matching speeds (points of subjective equality) as a function of the Vp component in the standard bars (filled squares: crossed disparity rectangular frame in front of the bars; open circles: uncrossed disparity rectangular frame behind the bars; dashes: theoretical Vp (matching speeds = Vp standard speed) and Vt (matching speeds = Vp standard speed 2) matches. Error bars represent 95% confidence intervals. Bottom: standard deviations of the judgments. Tab 1. First experiment: individual slopes ± 2SE. Tab 2. Second experiment: individual slopes ± 2 SE.

How fast is the barberpole? 40 Tab 3. Third experiment: individual slopes ± 2 SE. Table 4. Fourth experiment: individual slopes ± 2 SE.

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Figure 1. (a) How fast is the barberpole? 46 (c) (b)