**3.2 Proprioceptive bias in the perceived orientation of locomotor surfaces**

Proprioceptive error in the perceived declination of gaze was first reported in a study of downhill slant perception: Li and Durgin (2009) observed that standing back from the edge of an outdoor downhill surface made it appear steeper than when standing closer to the

Spatial Biases and the Haptic Experience of Surface Orientation 81

gain of only 1.5, then why does a hill of 5° appear to be 20° rather than, say, 7.5°? And why is the perceptual gain for outdoor hills, as illustrated in Figure 3, limited to a factor of about 1.2? Following up on the observations of Bridgeman and Hoover (2008), Li and Durgin (2010) noted that viewing outdoor hills from the base of the hill with gaze forward means that geographical slant is confounded with viewing distance to the hill surface. For example, for a typical eye-height of 1.6 m, a 5° hill is viewed at a horizontal distance of 18 m, whereas

Fig. 5. Predictions of outdoor visual data from Proffitt et al. (1995) based on a model with only one free parameter. With the overall intercept set to 0°, and the slant gain fixed at 1.5,

horizontal viewing distance from the base of the hill (assuming an eye height of 1.6 m),

Using a high quality virtual environment, Li and Durgin (2010) decoupled viewing distance and geographical slant by presenting large full-cue binocular surfaces at 6 orientations in the linear range of 6-36° at 5 distances in the logarithmic range of 1 to 16 m. Viewing was horizontal. They found that at each viewing distance the gain of perceived slant was about 1.5, but that the intercept of the slant function increased with the log of distance. Thus, the 30 combinations of orientation and distance could be fit with a three-parameter model including an overall intercept, a constant multiplied by log distance and a slant gain of about 1.5). Despite the many potential differences between virtual environments and real ones, Li and Durgin showed that a 3-parameter model derived from their verbal report data in the virtual environment provided an excellent fit to Proffitt et al.'s (1995) outdoor hill data when the viewing distance required for each hill was taken into account. By setting the slant gain to 1.5 and assuming an overall intercept of 0°, we can reduce the model to a single free parameter, based on the multiplier of log viewing distance. The predictions of such a model are shown in Figure 5 alongside each of the observed mean estimates from Proffitt et al. The success of this model in fitting the outdoor data shows that, once viewing distance is taken into account, the underlying slant gain for outdoor hills as for small surfaces seems to be 1.5.

*p* = 1.5

*<sup>p</sup>* denotes perceived slant; the one free parameter, *k*, equals 5.

+ *k*log(*D*), where *D* denotes the

the perceived slant model depicted here is simply

denotes actual slant and

a 30° embankment would be viewed at a horizontal distance of less than 3 m.

edge. Indeed, for a steep hill, the maximum perceived orientation seemed to occur when standing far enough back from the edge of the hill that one's line of gaze was nearly coincident with the surface of the hill. Using a virtual environment in which viewing position was manipulated orthogonally to the steepness of the incline, Li and Durgin found that the functions relating simulated optical slant to perceived optical slant only lined up with one another at the two viewpoints if it was assumed that the change in perceived declination of gaze was exaggerated with a gain of about 1.5.

Fig. 4. Verbal and proprioceptive (hand gesture) estimates of the haptically-perceived orientation of a ramp while standing on it, blindfolded (from Hajnal et al., 2011). Hand gesture data has been recomputed to represent the main orientation of the hand rather than the orientation of the palm, which is about 6.5° steeper (see Durgin, Li & Hajnal, 2010). Proprioceptive points are displaced to show the SEMs. Fit line is to verbal data.

Deducing from these observations that the perceived direction of gaze might itself be distorted Li and Durgin (2009) tested this directly by asking people to look at targets at various declinations out of upper-floor windows and estimate the downward pitch of their gaze. Again, a gain of 1.5 was found. Later studies confirmed that the gain of perceived gaze declination is about 1.5 even for objects in near space and along a locomotor surface (Durgin et al., 2011), as discussed in Section 2.

#### **3.3 Continuity between visual biases for near and far surfaces**

Across a number of studies, Li and Durgin (2009, 2010; Durgin & Li, 2011a) have found systematic evidence suggesting that the visual perception of slant also has a gain of 1.5 in the low end of the geographical slant range. But this led to a puzzle. If perceived slant has a

edge. Indeed, for a steep hill, the maximum perceived orientation seemed to occur when standing far enough back from the edge of the hill that one's line of gaze was nearly coincident with the surface of the hill. Using a virtual environment in which viewing position was manipulated orthogonally to the steepness of the incline, Li and Durgin found that the functions relating simulated optical slant to perceived optical slant only lined up with one another at the two viewpoints if it was assumed that the change in perceived

Fig. 4. Verbal and proprioceptive (hand gesture) estimates of the haptically-perceived orientation of a ramp while standing on it, blindfolded (from Hajnal et al., 2011). Hand gesture data has been recomputed to represent the main orientation of the hand rather than the orientation of the palm, which is about 6.5° steeper (see Durgin, Li & Hajnal, 2010). Proprioceptive points are displaced to show the SEMs. Fit line is to verbal data.

et al., 2011), as discussed in Section 2.

**3.3 Continuity between visual biases for near and far surfaces** 

Deducing from these observations that the perceived direction of gaze might itself be distorted Li and Durgin (2009) tested this directly by asking people to look at targets at various declinations out of upper-floor windows and estimate the downward pitch of their gaze. Again, a gain of 1.5 was found. Later studies confirmed that the gain of perceived gaze declination is about 1.5 even for objects in near space and along a locomotor surface (Durgin

Across a number of studies, Li and Durgin (2009, 2010; Durgin & Li, 2011a) have found systematic evidence suggesting that the visual perception of slant also has a gain of 1.5 in the low end of the geographical slant range. But this led to a puzzle. If perceived slant has a

declination of gaze was exaggerated with a gain of about 1.5.

gain of only 1.5, then why does a hill of 5° appear to be 20° rather than, say, 7.5°? And why is the perceptual gain for outdoor hills, as illustrated in Figure 3, limited to a factor of about 1.2? Following up on the observations of Bridgeman and Hoover (2008), Li and Durgin (2010) noted that viewing outdoor hills from the base of the hill with gaze forward means that geographical slant is confounded with viewing distance to the hill surface. For example, for a typical eye-height of 1.6 m, a 5° hill is viewed at a horizontal distance of 18 m, whereas a 30° embankment would be viewed at a horizontal distance of less than 3 m.

Fig. 5. Predictions of outdoor visual data from Proffitt et al. (1995) based on a model with only one free parameter. With the overall intercept set to 0°, and the slant gain fixed at 1.5, the perceived slant model depicted here is simply *p* = 1.5 + *k*log(*D*), where *D* denotes the horizontal viewing distance from the base of the hill (assuming an eye height of 1.6 m), denotes actual slant and *<sup>p</sup>* denotes perceived slant; the one free parameter, *k*, equals 5.

Using a high quality virtual environment, Li and Durgin (2010) decoupled viewing distance and geographical slant by presenting large full-cue binocular surfaces at 6 orientations in the linear range of 6-36° at 5 distances in the logarithmic range of 1 to 16 m. Viewing was horizontal. They found that at each viewing distance the gain of perceived slant was about 1.5, but that the intercept of the slant function increased with the log of distance. Thus, the 30 combinations of orientation and distance could be fit with a three-parameter model including an overall intercept, a constant multiplied by log distance and a slant gain of about 1.5). Despite the many potential differences between virtual environments and real ones, Li and Durgin showed that a 3-parameter model derived from their verbal report data in the virtual environment provided an excellent fit to Proffitt et al.'s (1995) outdoor hill data when the viewing distance required for each hill was taken into account. By setting the slant gain to 1.5 and assuming an overall intercept of 0°, we can reduce the model to a single free parameter, based on the multiplier of log viewing distance. The predictions of such a model are shown in Figure 5 alongside each of the observed mean estimates from Proffitt et al. The success of this model in fitting the outdoor data shows that, once viewing distance is taken into account, the underlying slant gain for outdoor hills as for small surfaces seems to be 1.5.

Spatial Biases and the Haptic Experience of Surface Orientation 83

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

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

illusion of accuracy resulted.

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.
