**4. Problems with measuring perceived slant with haptic matching tasks**

One current controversy in the study of slant perception concerns a popular method of assessing perceived slant. Proffitt et al. (1995) developed a method of assessing perceived slant that they initially referred to as a haptic measure, but also (e.g., Bhalla & Proffitt, 1999) described as an action measure. The measure consists of using one's hand to adjust the orientation of a "palm board" so as to match the perceived slant of a surface. The palm board was originally developed by Gibson (1950) as a non-verbal measure of perceived slant. In their studies of hills, Proffitt et al. (1995) placed the palm board at waist level so that it was at the edge of the field of view of the observer. They found that unlike verbal measures, which overestimated hill orientations, the palm board measure was relatively accurate. Bhalla and Proffitt interpreted the relative accuracy of the palm board measure as evidence of an accurate underlying perceptual representation "for action." However, some simple control experiments carried out by Durgin, Hajnal, Li, Tonge and Stigliani (2010) suggested that that palm boards were only accidentally accurate.

Durgin, Hajnal, Li, Tonge and Stigliani (2010) reasoned that if palm boards were assessing accurate motor representations of space, then they ought to be particularly accurate for

This analysis provided by Li and Durgin (2010) shows how the apparent discrepancy between the perceived slants of hills and of near surfaces may be due to differences in viewing distance. However, the model does not explain why haptic slant perception of ramps underfoot has such a high gain. The most intriguing observation we can make about this concerns the discrepancy between the haptically perceived slant of the 16° ramp (~35°) and the visually perceived slant of that same ramp (~23°). Because the ramp was viewed at a near viewing distance, with head declined, the resulting exaggerated scaling in vision ought to be by about 1.5 times, and it was. In contrast, if a 16° hill were viewed with gaze forward, the horizontal distance to the surface would be 5.6 m away, and the model prediction would be a perceived slant of 32.6°, which is quite close to the haptically-perceived slant of the 16° ramp. In contrast, for a 6° ramp, the estimates given haptically and from visual estimates of the ramp were in close agreement with one another (~11°, Hajnal et al., 2011). Although these were both far lower than (i.e., about half) what would be expected for forward viewing of a 6° hill, a value of ~11° is consistent with predictions of the one-parameter model for the actual viewing distance of about 1.8 m. Thus, the data of Hajnal et al. suggest that there is indeed *some* calibration between pedal and visual estimates of slant for common slants (of 10° or less) of near surfaces, as Kinsella-Shaw et al. (1992) suggested. However, Hajnal et al. (2011) have emphasized that the biomechanics of placing the foot upon a locomotor surface allow for rapid accommodation of the foot to the surface and may not require a very precise visual estimate of surface orientation in order for stepping to be successful. It is probably surprising to many that using hand gestures to try to match the slant of the surface on which one stands produces as much error as it does. This seems strong confirmation that the perceptual experience of the slants underfoot really is quite exaggerated. Because of the limited range of upward flexion of the foot, the extreme scaling of pedal slant is consistent with the idea of sensory scaling of perceived ramp orientation partly representing the biomechanical range of flexion. The evidence that a similar magnitude of perceptual exaggeration is present in participants who are congenitally blind lends support to this interpretation, by indicating that calibration is not the source of the

haptic distortion. It seems unlikely that the visual distortion derives from the haptic.

**4. Problems with measuring perceived slant with haptic matching tasks** 

suggested that that palm boards were only accidentally accurate.

One current controversy in the study of slant perception concerns a popular method of assessing perceived slant. Proffitt et al. (1995) developed a method of assessing perceived slant that they initially referred to as a haptic measure, but also (e.g., Bhalla & Proffitt, 1999) described as an action measure. The measure consists of using one's hand to adjust the orientation of a "palm board" so as to match the perceived slant of a surface. The palm board was originally developed by Gibson (1950) as a non-verbal measure of perceived slant. In their studies of hills, Proffitt et al. (1995) placed the palm board at waist level so that it was at the edge of the field of view of the observer. They found that unlike verbal measures, which overestimated hill orientations, the palm board measure was relatively accurate. Bhalla and Proffitt interpreted the relative accuracy of the palm board measure as evidence of an accurate underlying perceptual representation "for action." However, some simple control experiments carried out by Durgin, Hajnal, Li, Tonge and Stigliani (2010)

Durgin, Hajnal, Li, Tonge and Stigliani (2010) reasoned that if palm boards were assessing accurate motor representations of space, then they ought to be particularly accurate for matching near surfaces with which the hand could actually interact. That is, Durgin et al. presented full-cue wooden surfaces within reach and had people try to match their orientations using a palm board. Rather than being accurate, as the action theory predicted, palm board settings were much too low. Durgin et al. interpreted this as a haptic/proprioceptive error due to inaccurate scaling of wrist flexion. Durgin et al. showed that people overestimated the flexion of their wrist with about the same gain as they overestimated far surfaces. Li and Durgin (2011a) showed that when verbal estimates of near surfaces (similar to those shown in Figure 1) were used to predict palm board matches to those surfaces the function relating the two measures was identical to the function that related verbal estimates of hills to palm board matches to those hills. In other words, the perceived orientation of the palm board was exaggerated in a way that (imperfectly) approximated the exaggeration of hills viewed at a distance. Palm board measures were not tapping into a separate motor representation, but rather were differently-scaled outputs tapping into the same distorted representation as verbal reports. When the distortion in vision was approximately cancelled by the distortions in proprioception/haptics, the illusion of accuracy resulted.

Fig. 6. Contrasting the gain of a palm board measure (i.e. 0.62) with the gain of a free-hand gesture for matching full-cue surfaces within reach (i.e., ~1.0). The hand was occluded from vision in all cases. The visual surfaces were wooden surfaces within reach of the hand.

Strikingly, Durgin, Hajnal, Li, Tonge and Stigliani (2010, 2011) also showed that proprioceptive performance for near surfaces was greatly improved if the palm board were simply removed and people were allowed to gesture freely with their hand (with the hand hidden behind an occluding barrier). Some of their data are shown in Figure 6. As in the study of the haptic perception of ramps underfoot, free-hand gestures for far hills were found to grossly overestimate the slants of those hills (roughly consistent with verbal reports), but free-hand gestures for surfaces in near space were quite precise and accurate. The main difference between free-hand gestures and palm board matches were that palm boards prevented the use of the elbow as a primary axis of hand rotation. Because the axis of the palm board was near the wrist, the wrist had to be the principal joint for adjusting the palm board. Moreover, Durgin, Li and Hajnal (2010) showed that the perceived orientation of a fairly steep palm board was even higher than haptic perception of a rigid surface of the

Spatial Biases and the Haptic Experience of Surface Orientation 85

the lowest three plot points deviate from the typical curvature we have observed elsewhere. We therefore sought to replicate their dynamic touch result. We chose to use a real physical

Fig. 7. Hajnal et al.'s (2011) dynamic touch data with two different fit lines. In the left panel, the linear fit line originally plotted by Hajnal et al. is shown. In the right panel, a cubic

The main question of the present experiment is whether the haptic perception of surface orientation (geographical slant in the pitch axis relative to the observer) by dynamic touch will show the same kinds of spatial bias documented in vision by Durgin, Li and Hajnal (2010). Whereas Durgin, Li and Hajnal reported evidence of similar bias in perceived surface orientation based on static contact with the palm of the hand, Hajnal et al. (2011) have argued that there is very little bias evident in dynamic touch. However, as noted above, it is not clear that the linear fit they plotted is better justified by their data than a cubic fit, like that shown in Figure 7. Moreover, examination of the raw data of Hajnal et al. suggested that participants relied nearly exclusively on angular estimates that were multiples of 5. This may have contributed to distorting the lower end of the range. Finally, because Hajnal et al. did not constrain their participants' exploratory strategies, it is possible that the observed function was less exaggerated in some places because of a tendency for oblique paths of travel along the slanted surface. In the present study we used real surfaces and provided a ridge along the main axis of the surface to ensure that the steepest direction of inclination was felt. In addition we asked that participants be as precise as possible in their responses.

All experimental procedures were conducted in accord with the ethical standards of the American Psychological Association and approved by a local institutional review board. The general method is similar to those employed by Hajnal et al. (2011) and by Durgin, Li and Hajnal (2010). Participants made numeric estimates of the slant of surfaces explored

**5. Experiment 1: Numeric estimation of real surface orientation in depth** 

**assessed by dynamic touch with the tip of the index finger** 

function with an intercept of (0, 0) was fit to the data.

surface instead of a virtual one.

**5.1 Method** 

haptically.

same orientation – perhaps because of the additional forces used to maintain the tilted orientation of the palm board.

In summary, haptic matching tasks have proven to be very difficult to interpret for at least three reasons. First, evidence of surprising accuracy between palm board matches and hills has turned out to be spurious. Palm boards simply feel much steeper than they are because they require flexing the wrist more than is customary in normal circumstances. Second, the perceptual gain of haptic surface perception is generally unknown. If people see a visual surface as 45° when it is only 34° and they feel that a haptic surface is 45° when it is only 34°, they may seem to be correctly matching a 34° surface when they think they are matching a 45° surface. Finally, the fact that passive contact with a rigid surface dissociates from active rotation of a palm board suggests that haptic measures can be contaminated by active control of the surface's orientation.
