We investigated the influence of motion context on tactile localization, using a paradigm similar to the cutaneous rabbit or sensory saltation (Geldard FA, Sherrick CE. Science 178: 178–179, 1972). In one of its forms, the rabbit stimulus consists of a tap in one location quickly followed by another tap elsewhere, creating the illusion that the two taps are near each other. Instead of taps, we used position of a halted brush and instead of distance judgment, localization responses. The brush moved across the skin of the left forearm, creating a clear motion signal before and after a rabbitlike leap of 10 cm (at 100 cm/s). Three before-and-after velocities (7.5, 15, or 30 cm/s) were used. Participants (n = 13) pointed with their right arm at the felt location of the brush when it halted either 1 cm before or after the leap. These stops were 12 cm apart, but distances computed from localization responses were only 5.4, 6.5, and 7.5 cm for the three velocities, respectively (F[2,11] = 15.19, P = 0.001). Thus the leap resulted in compressive position shift, as described previously for sensory saltation, but modulated by motion velocity before the leap: the slower the motion, the greater the shift opposite to motion direction. No gap in stimulation was perceived. We propose that velocity extrapolation causes the position shift: extrapolated motion does not have enough time to bridge the real spatial gap and thus assigns a closer location to the skin on the opposite side of the gap.
- somatosensory space
- motion interpolation
- position shift
- local sign
a number of illusions reveal interdependence between perceptions of space and time. Temporal aspects of the stimulus may affect perception of its spatial properties, and vice versa. A well-known tactile illusion of the first kind is sensory saltation (cutaneous rabbit; Geldard and Sherrick 1972), also shown to occur in vision (Geldard 1976) and audition (Getzmann 2009). In the “utterly reduced rabbit” version of the illusion (Geldard 1975; Trojan et al. 2010), two spatially separated taps delivered at a temporal interval of 100–200 ms are perceived as much closer together than they really are. Normally, illusory motion is also perceived as if the same moving object caused both taps on the skin (for review and detailed investigation of the quality of apparent motion in touch, see Cholewiak 1999; Cholewiak and Collins 2000). Continuous motion is subject to a similar spatial distortion: brushed regions of the forearm seem increasingly short as the stimulus velocity increases beyond 15 cm/s (Whitsel et al. 1986). At 100 cm/s, the perceived path of the moving brush is approximately half that at 10 cm/s (Fig. 4, Whitsel et al. 1986). This dependence of perceived distance on time in perception of motion suggests there are limits on the “allowed” velocities, i.e., that very high speeds will not be perceived. Instead, a bias in the perception of distance traveled (or time) will occur to reduce perceived speed. Such a low-velocity prior was proposed for both tactile and visual motion (see Goldreich 2007; Stocker and Simoncelli 2006; Weiss et al. 2002).
The utterly reduced rabbit consisting of two taps is an utterly impoverished stimulus and cannot offer many clues about the way we process natural motion stimuli. The original form of the rabbit is slightly richer: multiple taps are applied to one skin site, followed by a tap at another. The resulting sensation is that of multiple taps distributed along a motion trajectory, as if a rabbit is hopping along the skin (Geldard and Sherrick 1972). The roughly uniform spatial distribution of the perceived taps mirrors the equal temporal intervals between them. Perceived spatial intervals also mirror time intervals in paradigms not involving motion (the tau effect, Helson and King 1931). A reverse bias also exists, i.e., the judgment of temporal intervals is strongly influenced by the spatial separation between successive stimuli (the kappa effect, Cohen et al. 1953). The cutaneous rabbit, tau, and kappa effects all suggest an underlying bias toward perceiving that objects move at constant velocity, an idea considered in the older psychological literature (see Collyer 1977; Jones and Huang 1982). Jones and Huang propose that “the functional relations between distance, duration and velocity provide a natural context for distance and duration judgments” (p. 128).
A related idea underpins our approach. We think that motion across the receptor surface, being the most ubiquitous form of natural stimulation, is a powerful organizing principle for spatial maps, i.e., the neural representations of the skin's surface that underpin our spatial abilities (see Hiramoto and Cline 2014; Seizova-Cajic and Taylor 2014; Wiemer et al. 2000). Statistical regularities of physical motion are therefore a “natural context” not only for relational judgments but also for perception of the location of individual stimuli.
Thus the aim of the present study was to test whether a constant-velocity constraint, or perceptual tendency to minimize deviations from constant velocity, influences localization of tactile stimuli. Specifically, we tested the idea that when a position on the skin is arrived at through constant-velocity motion, its perceived location is susceptible to a constant-velocity bias. This has not been formally tested, as past research has utilized mostly simple stimuli from which it would be difficult to extrapolate velocity.
The stimulus used to test our proposal—called the Abridging stimulus—places a discontinuous motion signal, similar to the cutaneous rabbit, in the context of continuous motion. It was used for the first time in our previous study (Seizova-Cajic and Taylor 2014). A brush moved up and down the forearm, from a location near the wrist to a location near the elbow, providing a reliable estimate of object velocity. We introduced uncertainty into the motion signal by taking the brush quickly (at 100 cm/s) across an artificial tactile scotoma in the middle of the forearm (an area that remained unstimulated while we brushed the surrounding parts of the skin; see Fig. 1). This stimulation results in compressive mislocalization of positions bordering the scotoma, abridging the space (Seizova-Cajic and Taylor 2014). The segment of the Abridging stimulus that crosses the scotoma provides a signal similar to the cutaneous rabbit. A touch on one side of the scotoma is quickly followed by a touch on the other side, and these positions are felt to be closer together than they really are. However, an important difference in comparison to the classical, discrete rabbit stimulus is the motion context.
In the present study, our critical manipulation was to vary the velocity of the brush before and after it crossed the scotoma. The question of interest was whether the speed outside the scotoma would modulate the amount of compression. Because a slow velocity would move the brush a shorter distance than a fast velocity in the brief time taken to cross the scotoma, we hypothesized that a constant-velocity constraint on perception would lead to greater compression in the context of slower velocity. If speed outside the scotoma did not modulate compression, then this would provide evidence against a constant-velocity constraint. On the other hand, the presence of any compression would be consistent with a low-velocity constraint. Note that the two constraints are not mutually exclusive.
Three different velocities were used on three different days to brush the skin of the forearm from the wrist to the elbow and back, across a 10-cm tactile occluder (scotoma) in the middle of the forearm. The outcome of greatest interest was perceived terminal position of the brush after it crossed the occluder and briefly halted. Blindfolded participants also reported on the sensations felt on the forearm during repetitive back-and-forth brushing.
The study was approved by the University of Sydney ethics committee. Participants provided their written informed consent to participate in the study, according to the procedure approved by the committee. Thirteen participants (6 women, 7 men; age 21–48 yr) each attended on 3 days to complete the experiment. Ten subjects were naive and were paid for their participation.
Apparatus and Setup
Participants were seated with their left forearm pronated and supported on an armrest placed perpendicular to the seat back (see Fig. 1A). This arm was hidden from view by a 12 × 18-in. Wacom graphics tablet sitting vertically upright between the participant's arms, parallel to the length of the forearm. The participant held a graphics tablet stylus in the right hand. During all stimulation, participants were blindfolded and wore headphones playing white noise.
The left forearm was fitted with a leather sleeve that had two rectangular 6 × 5-cm windows over the dorsum of the forearm. These were separated by a 10-cm metal-covered occluder, which was centered on the forearm. Thus when the dorsum of the forearm was brushed from one end to the other there were two ∼5-cm areas of stimulation separated by a 10-cm gap (artificial tactile scotoma). Two brushes (1 cm thick and 4 cm wide) were mounted on a single carrier, which was driven parallel to the forearm by a computer-controlled stepper motor (Excitron Au Controllercoder model Au57-40M). The distance between the brushes was set to achieve a 100-ms traverse time over the occluder and was thus different in the three different speed conditions. Only one of the brushes was in contact with the skin at any given time (see Fig. 1A, C, and D). When the carrier moved distally, the proximal brush swept the skin from the elbow toward the occluder as the distal brush moved along the occluder. The proximal brush then moved onto the occluder, where for ∼100 ms both brushes were located. This was followed by the distal brush stepping off the occluder and moving along the skin until it stopped near the wrist (while the proximal brush moved along the occluder). This constituted a single sweep. When followed with a sweep in the other direction (wrist to elbow) this constituted an up-and-down sweep.
The across-the-occluder time is approximate because 1-cm-thick brushes were manually adjusted to the appropriate height for each participant, resulting in small variations in the degree to which the hairs splayed. The two brushes were also manually adjusted to the appropriate separation for each speed, and their position could vary by 1 or 2 mm.
There were four targets at which the brush could stop, labeled A, B, D, and E starting from a proximal location (near the elbow; see Fig. 1B). Separation between the two proximal targets, A and B, was ∼3.6 cm, with the same separation for distal targets D and E. Targets B and D were 12.0 cm apart. In Baseline conditions, an additional target (C) was located halfway between B and D. This location was underneath the occluder in all other conditions. The purpose of using this additional target in Baseline trials only was to suggest to participants that stimulation could occur anywhere along the forearm.
The experiment had a 3 (velocity) × 2 (duration of exposure to brushing, hereafter simply “exposure”) × 2 (direction of approach) design. The dependent variables were localization by pointing and phenomenological report. In the report, participants indicated where on the arm they felt the brushing and how intense it was.
The main independent variable was velocity on either side of the occluder (Slow: 7.5 cm/s, Medium: 15 cm/s, or Fast: 30 cm/s). The three velocity conditions were presented in separate sessions on separate days, counterbalanced across participants. The gap in stimulation was 100 ms in all three conditions. We also manipulated exposure (Short and Long) and direction of approach (Proximal or Distal).
In each session the participants completed a “Short” run followed by a “Long” run of brushing. In Short the brushes made one or two up-and-down sweeps before stopping at each target location. Between Short and Long runs the brush made 100 nonstop up-and-down sweeps. In Long there were six or seven up-and-down sweeps between stops. The order of runs was fixed to test for any immediate illusion (observable in Short) and any cumulative effects (observable during Long).
The targets near the occluder (B and D) could be approached from two directions. We refer to the approach from the wrist toward the elbow as the Proximal direction and the approach from the elbow toward the wrist as the Distal direction. Targets A and E were at end points of brushing motion and could only be approached from one direction (A with proximal motion and E with distal motion).
In each run the brush stopped 24 times at the locations on either side of the occluder (B and D). Half of the 24 stops were approached during Proximal motion, while the other half were during Distal motion. Locations A and E were stopped at only six times each, and their main purpose was to suggest to the participant that the brush might stop at any location along the arm. Each time the brush stopped, a computer-generated sound alerted the participant to point to the current location of the brush, which remained stationary on the skin for the duration of the pointing response. Pointing comprised moving the right hand holding the stylus from the rest position (at the right of the table) to touch the stylus to the graphics tablet, as if pointing at the site of the brush on the skin. After a period of 4 s from the moment it stopped, the brush resumed moving. In each velocity condition, participants completed a total of 60 pointing trials per Short and Long runs or 120 trials overall [48 trials each for targets B and D (2 directions × 2 exposures × 12 repeats) and 12 trials each for targets A and E (2 exposures × 6 repeats)]. Targets were presented randomly with the constraint that all targets were presented twice before any could be presented again.
Basic localization ability was determined at the beginning (“Baseline pretest”) and end (“Baseline posttest”) of each session. For each trial, the experimenter brushed the participant's arm at one of five target locations (A–E) with the direction of brush motion orthogonal to the long axis of the forearm (Fig. 1B; in other conditions, the brush moved along the long axis of the forearm). Participants responded by pointing to the location with the stylus. Each location was brushed six times in a random order with the same constraint as the other conditions (all targets were presented twice before any were presented again) for a total of 30 trials.
Participants attended on 3 days. On each day, they completed four runs comprising Baseline pretest, Short, Long, and Baseline posttest in that order. In a single session, the brushing on either side of the occluder used in the Short and Long runs were of the same velocity. The duration of each session differed for the Slow, Medium, and Fast conditions, taking ∼75 min, 60 min, and 45 min, respectively. Participants provided phenomenological reports after Short and Long runs or at the end of the session. They were asked to indicate where on the arm they felt the brushing and how intense it was by drawing on outlines of an arm. If they felt changes over time, they made multiple drawings. Other comments regarding the sensations they had noticed during the brushing were also encouraged.
Participants indicated where along the arm they had felt brushing, and their reports were classified in the following categories indicating the degree of motion completion across the gap, i.e., closing of the gap: 1) two separate areas of brushing (no completion) with no changes over time; 2) two separate areas of brushing (no completion) but gap decreased during the session; 3) no gap in brushed area (completion) for part of the time; 4) no gap in brushed area (completion) for the whole time.
If participants reported different percepts in Short and Long runs in a single session, the corresponding ratings were averaged so that each participant contributed three ratings in total, one for each velocity. Categories 1–4 thus indicate increasing degree of completion and were analyzed with Friedman's ANOVA to determine whether motion completion was affected by velocity.
Raw data were localization responses to targets A–E expressed as x coordinates of the graphics tablet in millimeters, with 0 at the proximal corner of the tablet. Target A was near the elbow crease and target E near the wrist. Responses of individual participants were checked for outliers, using as the criterion the variability of their 6 (in Baseline) or 12 (other conditions) responses to a single target. Variability expressed as the standard deviation (SD) was computed for each individual and each target. The mean and SD were then computed for the set of those values (across all participants for any given combination of velocity and exposure), and limits for deviation from the mean were established with the 2.5 SD criterion. If an individual SD for any target exceeded this limit, then the participant's responses to that target were investigated for outliers and up to two responses were removed. Approximately 0.9% of pointing trials were excluded on this basis, with relatively even spread across experimental conditions.
We computed position uncertainty for our brush stimulus as a median variable error, i.e., one-half of the interquartile range (IQR) for a given set of responses: 12 responses of the same participant to the same target (B or D) in the same experimental condition (e.g., target B, Distal motion, Short exposure) or 6 responses for Baseline conditions. A four-way ANOVA was conducted to compare the brushing conditions, with factors 1) location (B, D), 2) velocity (Slow, Medium, Fast), 3) brush localization Before vs. After it crossed the gap, and 4) exposure (Short, Long).
Of most interest to us were responses to the brush halted at targets B and D, adjacent to the occluder (thus no statistical analysis is presented for targets A and E, for which we collected a quarter of the responses as for B and D). Distal motion took the brush across target B to target D, while Proximal motion took it across target D to target B. Thus, to compute our final measure (referred to as the “computed B–D distance”) for each individual participant for each direction separately, the mean response to B was subtracted from the mean response to D. This computation accounted for the potential dependence of perceived distance across the skin on velocity (Whitsel et al. 1986), due to which the perceived starting point of the brush crossing the occluder would not be equal for different velocities. We were only interested in localization of the brush after it crossed the occluder and how it depended on the outside velocity (not in how velocity influenced perceived extent of the brushed skin).
A three-way repeated-measures ANOVA (velocity × exposure × direction of approach) was used to compare computed B–D distance across conditions and a two-way repeated-measures ANOVA (velocity × pre/post) to compare computed B–D distance for the Baseline data collected at the beginning and end of each of the three sessions.
Error bars in Figs. 3 and 4 were computed with the method suitable for repeated-measures designs that removes irrelevant overall intersubject variability (see Cousineau 2005). Here, the removed component of variance was the tendency for individuals to reach closer or further overall when pointing. The error bars thus reflect the intersubject variability in the response pattern, i.e., in the differences between conditions, which is of interest to us. Confidence intervals (CIs) reported in text were computed with BCa bootstrap procedure in SPSS.
Although 10 cm of the skin was never brushed, participants indicated that the brushing stimulus felt continuous along the forearm for at least part of the time in 35 of 39 responses across all three velocities. Results broken down by velocity show that 6, 8, and 7 of 13 participants (46%, 62%, and 54%) experienced full motion completion throughout the brushing session in Slow, Medium, and Fast conditions, respectively. Median (IQR) scores for the three velocities, shown in Fig. 2, were 3.5 (3.0–4.0), 4.0 (3.5–4.0), and 4.0 (3.0–4.0). Friedman's ANOVA shows that the difference between the velocities was not significant (χ2 = 3.36, P = 0.186).
A timeline of pointing responses within each session is shown in Fig. 3. For this illustration, each participant's responses were binned such that their first three pointing responses to a target within a run were averaged to create the first bin. The next bin contained the next three pointing responses to that target location, and so on. Figure 3 shows that immediately after Baseline there is a large compressive effect: separation between the blue lines (Distal motion), as well as between the green lines (Proximal motion), is smaller than B–D separation in Baseline pretest at all three velocities. Shift of proximal targets (A and B) toward the opposite side is very pronounced for all velocities. Further analysis was carried out on the computed distances (“blue” B–D distance and “green” B–D distance) calculated for each velocity, exposure, and direction of approach. The actual distance between targets B and D was 12 cm, including the 10-cm gap plus 2 cm of brushed skin, 1 cm on each side of the occluder. Note that a smaller computed B–D distance means greater mislocalization of positions B and D.
A critical finding was that computed distance increased with the velocity of the brush. The results are shown in Fig. 4. The means were 53.9, 65.5, and 75.1 mm in the Slow, Medium, and Fast conditions, respectively. The mean difference (95% CI) between Medium and Slow was 11.6 mm (4.4–20.7) and between Fast and Medium was 9.7 mm (1.6–17.1). These differences are comparable to the differences of 7.5 and 15 mm predicted from constant velocity assumption, although they do not increase with velocity. (The prediction was derived as follows: at Slow velocity of 75 mm/s distance traveled in 100 ms would be 7.5 mm, at Medium velocity of 150 mm/s it would be 15 mm, and at Fast velocity of 300 mm/s it would be 30 mm. Each value is corrected by adding a constant of 20 mm to account for the accurate perception of extent of brush motion when traveling across the skin between the occluder and targets B and D. Thus, should localization be based on extrapolated motion alone, the predicted values for the computed distance would be 27.5, 35.0, and 50.0 mm for Slow, Medium, and Fast velocities, respectively.) Perceived B–D distances, however, are greater than the predicted values (thick dashed line in Fig. 4).
A three-way repeated-measures ANOVA (velocity × exposure × direction of approach) showed a significant main effect of velocity (F[2,11] = 13.841, P < 0.001). Repeated contrast analysis compared Slow to Medium velocity conditions, finding a significant difference (F[1,12] = 6.164, P = 0.029, r = 0.58), and Medium to Fast, also significant (F[1,12] = 7.528, P = 0.018, r = 0.62). The main effect of exposure was not significant (F[1,12] = 2.422, P = 0.146). However, one interaction term involving exposure and velocity approached significance (F[1,12] = 4.653, P = 0.052): the computed B–D distance in Fast decreased from 80.5 mm in Short to 69.8 mm in Long, while for Medium velocity it barely changed (66.0 vs. 65.0 mm). The main effect for direction of approach was significant (F[1,12] = 6.327, P = 0.027, r = 0.59), with 6.3 mm smaller computed distance in Distal than Proximal approach (95% CI: 2.4–10.3). There were no statistically significant interactions involving direction.
Baseline was analyzed to determine whether brushing resulted in a change in perceived locations in posttest depending on velocity. Computed B–D distance in Baseline posttest across all velocities was 99.9 mm, much smaller than the 119.9 mm in the pretest. The mean differences for Slow, Medium, and Fast were 15.6 mm (95% CI: 1.9–28.7), 25.5 mm (15.9–35.2), and 18.9 mm (8.8–30.5), respectively. A 3 (velocity) × 2 (pretest, posttest) ANOVA showed that the difference between pretest and posttest was highly significant (F[1,12] = 34.45, P < 0.0001), but there was no interaction with velocity (F[2,24] = 0.640, P = 0.536).
As can be seen in Fig. 3, distribution of responses shifted distally after Baseline pretest. We quantified this shift for responses B and D using their center (average), which was positioned at 153.4 ± 9.2 mm (mean ± SE) in Baseline pretest. One-way ANOVA showed no significant difference in the amount of shift between the three velocity conditions (F[2,24] = 1.276, P = 0.297). However, their combined 28.5 ± 12.8-mm displacement from Baseline pretest was statistically significant (t = 2.228, P = 0.046). In Baseline posttest the center of B and D responses shifted back to 141.0 ± 9.8 mm.
In Baseline pretest, position uncertainty measured as median variable error was on average 9.0 (±0.6 SE) mm for target B, not significantly different from 11.3 (±1.1) mm for target D (t = 1.733, P = 0.09). Brushing conditions produced more uncertainty, with 14.4 mm average across both targets (meaning that ∼50% of all responses to any single target would have fallen within a 30-mm range). The four-way ANOVA showed no significant difference between proximal target B (14.7 ± 0.8 mm) and distal target D (14.2 ± 0.8 mm) (F[1,12] = 0.17, P = 0.69). Position error decreased with velocity and was 15.5, 14.8, and 13.0 mm for Slow, Medium, and Fast, respectively [linear trend approached significance (F[1,12] = 4.04, P = 0.07)]. Exposure to brushing increased the error from 13.3 (±0.4) in Short to 15.6 (±0.4) in Long brushing condition (F[1,12] = 4.76, P = 0.05). The most pronounced and highly significant difference was between the variable error for location targeted before the brush crossed the gap (12.8 ± 0.8 mm) vs. after it crossed the gap (16.0 ± 0.9 mm), regardless of whether the location was B or D (F[1,12] = 15.55, P = 0.002). None of the two-way or three-way interactions was statistically significant.
Our results strongly support the hypothesis that perceived terminal position of a moving object is susceptible to a constant-velocity bias. Here, the velocity of the brush motion before the gap modulated its perceived position after the gap, such that slower before-the-gap motion resulted in a shorter apparent leap than faster motion. In other words, how far the cutaneous rabbit jumps depends on how fast it is running before making the leap. Velocity modulation came on top of a large inward position shift of the two targets. The third main finding is that the 10-cm physical gap in stimulation was perceptually completed, such that in most cases motion felt continuous. The latter two findings, the Abridging effect and motion completion, confirm the results from our previous study (Seizova-Cajic and Taylor 2014).
Findings secondary to our main aims included a change in Baseline localization after brushing, with 20-mm inward shift of points on either side of the gap (Fig. 4B). This effect was not modulated by velocity. Previously we found a similar compression not only when the gap was stitched in time but also when the brush had a long traverse time over the gap (see Fig. 4A, Seizova-Cajic and Taylor 2014) and thus cannot interpret it as the carryover (learned) effect of compressive mislocalization. It is not clear what causes it. There was also an effect of direction: distal brush motion resulted in a smaller apparent leap (greater mislocalization) than proximal. Our estimates of position uncertainty were similar for proximal and distal locations (B and D), so the result is unlikely to be due to this potential factor. Our final finding that has no obvious explanation is that the distribution of responses to the brushing stimuli shifted distally soon after the brushing began (relative to the responses in Baseline pretest). It is possible that some aspect of the setup that differed between Baseline and brushing runs caused distal attention shift, which in turn affected localization. Manipulation of attention caused position shift of a sensory saltation stimulus pair in a study by Kilgard and Merzenich (1995). Their stimulus location and parameters were similar to ours, and the mean difference between the perceived locations under proximal and distal instructions was 3.1 ± 0.5 cm, comparable to our 2.8 ± 1.3 cm mean distal shift for the center of the B and D pair.
Our main results can be summarized as 1) motion interpolation (by which we mean filling in of any spatiotemporal discontinuity with motion signal from the surround) and 2) velocity-dependent compressive mislocalization (position shift). We discuss each in turn, examining their potential mechanisms and interrelationship.
Our motion stimulus, a brush, paused briefly at times when the localization response was required but otherwise moved up and down along the forearm. The brushed areas that provided a clear motion signal and speed estimate therefore flanked the gap, creating an artificial scotoma and conditions for motion interpolation when the object was “hidden” by the occluder. Participants anecdotally reported that they could not always clearly feel the position of the halted brush, which might have reinforced a motion tracking strategy.
Vision research has shown that small spatiotemporal interruptions in a motion path (e.g., 13 ms, 0.16° presented in peripheral vision) go unnoticed if sufficient time has passed between the motion onset and the interruption, as this allows for the motion percept to stabilize (Kanai et al. 2007). Smooth motion interpolation can also be achieved through attentive tracking of moving objects in the presence of an ambiguous motion signal, crossing much larger gaps (Shiori et al. 2000). These and similar findings (e.g., Chun and Cavanagh 1997) suggest that, once established, the motion percept plays a role in the “retention of spatiotemporal continuity of an object” (p. 944, Kanai et al. 2007), i.e., an object constancy assumption.
Consistent with this idea, as well as the gestalt principles of grouping by motion (Todorovic 2011; Wertheimer 1923) and completion (Pessoa et al. 1998), most of our participants reported perceiving a single object moving up and down their forearm with no gaps in stimulation, although in reality there were two brushes straddling a very large (10 cm) gap. Anecdotal reports and lighter brushing in the middle of the forearm reported in drawings suggest that other stimulus features, such as the bristliness of the brush, were not necessarily interpolated, only the motion. We also know that there are time limits on completion—when the temporal gap in our previous study was ∼660 ms, completion normally did not occur (Seizova-Cajic and Taylor 2014).
It is important to note that phenomenological experiences of motion continuity can occur in response to very different spatiotemporal patterns. Two such patterns are shown in Fig. 5, A and B. Figure 5A mimics a real-world experience of occlusion: it shows constant-velocity motion with a spatiotemporal gap that allows (the perceived) motion to continue unchanged throughout the gap until the physical stimulus reappears. Figure 5B shows our Abridging stimulus, with a highly incongruent spatiotemporal gap (also illustrated in Fig. 1D, right): any object undergoing interpolated motion would need to suddenly accelerate in order to connect to the position where the physical stimulus reappears.
Velocity-Dependent Compressive Mislocalization (Position Shift)
Position shift of the two targets bordering the scotoma brought them 54 mm closer to each other relative to their 119-mm distance in Baseline pretest (averaged across all 3 velocities). This combined position shift exceeds the combined position uncertainty of the two targets, which we estimated to be ∼30 mm. Illusory position shifts in the presence of motion have been richly documented and debated in the vision literature (see reviews by Eagleman and Sejnowski 2007; Whitney 2002), but in most cases they are in the direction of motion: motion stimuli appear to be displaced forward compared with briefly presented stationary stimuli (flash-lag effect, Nijhawan 1994) or when their last location is reproduced from memory (representational momentum; for review see Hubbard 2005); stationary stimuli enclosing areas filled with motion seem to be displaced in the direction of motion (Ramachandran and Anstis 1983), as do stationary objects placed in the vicinity of motion (Whitney and Cavanagh 2000). This forward bias is opposite to the compressive illusory shift we report, which is backward, toward the motion origin.
So why did position shifts occur in our study? As indicated above, the large spatial and negligible temporal gap in our stimulus would require a single moving object to speed up dramatically (see Fig. 1D and Fig. 5B). We have previously proposed that the observed compressive mislocalization, or perceptual shortening of the gap, in these circumstances is driven by perception that the stimulus is delivered by a single brush (consistent with an object constancy assumption), combined with a bias against unusual perceived accelerations (Seizova-Cajic and Taylor 2014). However, unequivocal evidence that motion is at least partly responsible for the position shifts was lacking until now. The fact that localization error is correlated with the surround velocity removes any doubt. Nevertheless, we do not rule out minor contributions from other sources, such as the enlargement of receptive fields devoid of input when they are surrounded by active neurons, shown in vision to result in small position shifts (Kapadia et al. 1994; Pettet and Gilbert 1992).
Pure extrapolation of motion velocity predicts a greater compressive mislocalization than observed, and thus cannot be its sole explanation (compare thin dashed arrows in Fig. 5C to actual localization responses). It is likely that the position signal from the halted brush also affected localization. A formal model of length compression developed by Goldreich (2007) and Goldreich and Tong (2013) for briefly presented tap stimuli—including the cutaneous rabbit—combines a current position signal (“measured” position) with a constraint (prior) to predict perception of intertap distance. Our results are consistent with this general approach. These authors also implement the idea that subsequent positions of a moving object influence perception of its previous positions (“postdictive” inference, Eagleman and Sejnowski 2000) in their model. Applied to our paradigm, it means that the perceived brush position before the gap (which we measured with the brush halted in position) would feel different in retrospect, after the brush crossed the gap; it would be drawn toward subsequent brush positions, as shown in cutaneous rabbit studies. In other words, the postdictive element of the illusion would likely result in an even smaller measurement of gap size. However, the continuous brush motion as well as perceptual completion in the present paradigm make individual target positions indistinguishable. This makes it difficult to assess the degree of postdictive inference.
Mechanisms Responsible for Position Shift
Our findings suggest that both motion and local position signals contributed to the assignment of terminal location of the moving brush. They support the idea that spatiotemporal mechanisms are used and rule out some of the alternative theories proposed in vision that focus on separable temporal or spatial mechanisms (for review see Whitney 2002). One is the temporal integration (or temporal pooling) hypothesis, according to which the position of a moving target is integrated over a fixed time window (Lappe and Krekelberg 1998). It predicts greater bias toward the origin of motion for the faster-moving objects in the present study—opposite to our findings. Another proposition is that a spatial bias in perception of moving objects compensates for neural latency (see Whitney 2002). Such a bias could also be velocity dependent, but again in the direction of motion, opposite to our findings.
Our spatiotemporal account needs to explain the origin of the observed bias against sudden accelerations. Its possible origin is experience with moving objects accumulated through evolutionary and personal experience. How accumulated knowledge is built into perception has been a subject of much theorizing and variously labeled unconscious inference, perceptual constraints, expectations, biases, priors, etc. (see Kubovy et al. 2013). As mentioned in the introduction, two plausible constraints have been proposed for perception of moving objects that come into contact with our skin: a low-speed constraint, according to which objects move at relatively low speeds, and a constant-velocity or low-acceleration constraint, according to which they rarely undergo sudden changes in speed. Either of these constraints would influence perception more when the motion signal is less clear, but only the latter (low acceleration) constraint can take advantage of motion context in the surround of the area with the poor motion signal. A clear motion signal in the surround allows velocity to be interpolated into areas where the signal is less clear (as described in vision by Kanai et al. 2007; Nowlan and Sejnowski 1995). Note that an untested notion of constant-acceleration constraint might be the most general and most adequate formulation of constraints on our motion perception, given that statistical regularities of physical motion also include accelerations and decelerations, which could also be interpolated.
A low-acceleration prior in touch was formalized in a Bayesian model by Goldreich and Tong (2013) and pitted against their low-speed prior to determine which of the two better predicts Helson and King's (1931) tau effect and Geldard's (1982) multitap rabbit sequence. The low-speed prior won (see their Figs. 10–12). With sufficiently dense sampling, tap stimuli modeled by Goldreich and Tong approach our continuous brushing stimulus. If a low-speed constraint were superior in predicting the above experimental results, could it also explain ours? The answer is negative: a low-speed prior predicts greater contraction for higher before-the-leap speed (see appendix for details; predictions based on the low-speed prior were computed with the Leaping Lagomorphs application, Goldreich and Tong 2013), a pattern opposite to both our results and predictions of the low-acceleration constraint. It is of interest to consider why the low-acceleration constraint did not predict the tau and multitap rabbit patterns as well as the low-speed constraint, as described above. We think the reason is the absence of a clear velocity signal in those patterns, which did not allow the low-acceleration constraint to be given a fair test.
We thus propose that motion, i.e., velocity interpolation, causes position shift. What neural mechanisms might be responsible? Motion provides context for perception of spatial position, and two prime candidates for context-sensitive neural mechanisms are feedback from higher-level motion neurons with large receptive fields to the neurons with more accurate representation of spatial position, and lateral connections between neurons at various levels (Bouecke et al. 2011; Khuu et al. 2010; Muckli et al. 2005; Neumann 2003; Nishida and Johnston 1999). The basic architecture of such a neural model, and how it would process our stimulus, is shown in Fig. 6. Its feedback and horizontal connections impose contextual “meaning” on the individual neurons through selective excitation and inhibition. Note that neurons represented as gray filled circles receive only feedback and horizontal signals when the Abridging stimulus is applied, but this is sufficient, without direct sensory input, to account for perception of motion in the nonstimulated area. The model also needs to explain the position shift. We propose that motion neurons, in addition to direction and speed, also signal motion extent and bias perceived absolute position of the local neurons via feedback connections. Support for this idea comes from the Kilgard and Merzenich (1995) study mentioned above, which shows a relative independence of the perceived separation between two stimuli delivered in very quick succession and their perceived absolute position (see their Fig. 1c). It suggests that the mechanism signaling separation or extent is partially separable from that signaling position. We believe that our proposed neural model is also consistent with the Bayesian model by Goldreich and Tong (2013; see their Fig. 8 and related discussion) who explain the same (Kilgard and Merzenich 1995) finding as the change in uncertainty about position of taps under the influence of attention. Their model postulates a low-speed prior, which modulates perceived position and perceived separation, distorting the original position signal (“measured” position). Implementation of a low-speed prior would presumably involve higher-order tactile motion neurons, which would distort the position signal and determine perception of extent, as we propose (for comparison, Stocker and Simoncelli 2006 propose that the population response of neurons in visual area MT reflects the influence of the visual low-velocity prior).
Applied to our stimulus, the model described above would “hook” the end point of extrapolated motion (the rightmost gray square in Fig. 5B) to the next available signal about stimulus position (black square on the other side of the gap). The instantaneous effect of this would be a compromise between a position signal from the end point of a motion vector and a local position signal, resulting in the velocity-dependent stimulus mislocalization (backward position shift). Should a similar stimulation pattern be repeated many times, mimicking surgical extraction of a patch of skin or a tactile “scotoma,” longer-term changes might occur such as a change in the neural signature (local sign) in the local position neuron.
We answer in the affirmative to Whitney (2002), who asked whether tactile motion information influences the apparent position of a tactile target (p. 215). The velocity of surround motion biases perceived position of skin patches bordering an artificial scotoma in the direction opposite to the direction of motion, unlike previously described motion-induced position shifts. Our artificial tactile scotoma simulates loss of input from an area of the receptor surface but is only temporary. Permanent scotomas create a need for lasting, plastic change of the sensory apparatus. Motion interpolation or completion can thus be viewed as only the beginning of a more lasting plastic change that will occur if the conditions of stimulation last (Pessoa and De Weerd 2003). Cortical plasticity studies (Merzenich and Jenkins 1993) show that such plastic changes occur in sensory neurons. A possible neural mechanism that involves motion neurons signaling extent would support this function of motion.
This work was supported by Australian Research Council Discovery Project DP110104691 to T. Seizova-Cajic. J. L. Taylor was supported by a fellowship from the National Health and Medical Research Council of Australia.
No conflicts of interest, financial or otherwise, are declared by the author(s).
Author contributions: E.H.L.N., J.L.T., and T.S.-C. conception and design of research; E.H.L.N. and J.B. performed experiments; E.H.L.N. and T.S.-C. analyzed data; E.H.L.N., J.L.T., J.B., and T.S.-C. interpreted results of experiments; E.H.L.N. and T.S.-C. prepared figures; E.H.L.N. and T.S.-C. drafted manuscript; E.H.L.N., J.L.T., J.B., and T.S.-C. edited and revised manuscript; E.H.L.N., J.L.T., J.B., and T.S.-C. approved final version of manuscript.
We thank David Menardo for constructing the apparatus.
Predictions based on a low-speed prior (Goldreich 2007; Goldreich and Tong 2013) were computed with Goldreich and Tong's (2013) Leaping Lagomorphs application (http://psych.mcmaster.ca/goldreich-lab/LL/Leaping_Lagomorphs.html). Percepts for the three brushing conditions were simulated to estimate expected gap sizes for the three brushing conditions. Densely spaced taps were used to approximately simulate our continuous motion stimulus (see Table A1 for parameter values: Sigma-s in the table represents spatial uncertainty, and sigma-v is dispersion around the zero-speed expectation; smaller values of sigma-v indicate stronger low-speed expectation).
To estimate the leap distances for the three velocity conditions, two separate simulations were performed within each condition (see Fig. A1)—one to find the perceived position of location B before the brush moved over the gap (Fig. A1, left: Bbefore) and another to simulate the response to location D after the brush had just traversed the gap (Fig. A1, center: Dafter). The perceived locations of B and D were then used to compute a gap size (Fig. A1, right). This simulated how computed B–D gap size was derived in our experiment (subtracting the response to the location before the leap from the response to the location after the leap).
The observer's spatial uncertainties (sigma-s) for each stimulation location were taken from our position uncertainty results for B and D in Baseline pretest (see Position Uncertainty).
Predictions based on these parameters gave computed B–D distances of 10.58 cm for Slow, 10.01 cm for Medium, and 9.85 cm for Fast, demonstrating a trend of greater compression at faster velocities (opposite to that found in our study). We also ran the simulations using position uncertainty values of B and D during brushing conditions (when there is greater uncertainty), which resulted in the same (but stronger) trend as that reported here.
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