**2. Spatial bias in the perception of orientation: Surfaces within manual reach**

What is meant by a spatial bias in the perception of surface orientation? Durgin, Li and Hajnal (2010) reported a series of studies of a bias they called the "vertical tendency" in slant

Spatial Biases and the Haptic Experience of Surface Orientation 77

Moreover, to emphasize that these biases did not depend on generating verbal estimates, Durgin, Li and Hajnal (2010) asked a fourth set of participants to judge whether various oriented planar surfaces were closer to horizontal or to vertical. They fit a psychometric function to the resulting choice data and found that a surface slanted by only 34.3° from horizontal was, on average, visually perceived to be equidistant from vertical and

This spatial bias function for near surfaces closely matches the observed proprioceptive function for the perceived declination of gaze. That is, when people are asked to report the pitch of their gaze, verbal reports provide evidence of an exaggerated deviation from horizontal that closely matches the bias function shown above for perceived surface slant (Durgin & Li, 2011a; Li & Durgin, 2009). Thus, it appears that several different perceptual representations of pitch contain a bias that expands the scale of differences near horizontal

Fig. 2. Surface orientation estimates for surfaces (0-48°) felt with the palm of the hand

In the haptic domain and in the proprioception of gaze, the perceptual scale of the bias function for perceived pitch has mostly only been measured for orientations within about 50° from horizontal (e.g., Durgin, Li & Hajnal, 2010). In this range the scaling of pitch tends to closely approximate a linear scale with a gain of 1.5 (Durgin & Li, 2011a). For example the haptic data of Durgin, Li and Hajnal are shown in Figure 2. These data are based on numeric estimates of orientation in deg (relative to horizontal) made based on placing the palm of the hand on various real slanted surfaces while blindfolded. Durgin and Li have reported a very similar function for explicit estimates of the pitch of gaze over a similar range. Durgin and Li (like Durgin, Li & Hajnal) supplemented their verbal estimation data with a horizontal-vertical bisection task and again found that a rather shallow gaze declination of about 30° from horizontal was perceived as the bisection point

(Durgin, Li & Hajnal, 2010, Experiment 4). Error bars indicate ±1 SEM.

horizontal.

while compressing the scale near vertical.

between vertical and horizontal gaze.

perception. Specifically, they found that small, irregularly-shaped wooden surfaces appeared steeper than they actually were both when viewed visually and when experienced haptically while blindfolded. The term "vertical tendency" was used to distinguish the observed effect from what has been called "frontal tendency" in the literature (Gibson, 1950). For many years it has been argued that surfaces viewed visually, appear compressed along the depth axis of visual regard and thus appear more frontal to gaze than they are. However, when Durgin, Li and Hajnal asked participants to make estimates of the geographical slants of wooden surfaces within reach, they found that that they got approximately the same bias function whether the surfaces were at eye level (so that "frontal" and vertical coincided) or viewed with gaze declined by about 40°. Moreover, the same kinds of bias were found when surfaces were experienced haptically by placing the palm of the hand on them, though their measurements of this were limited to the angle of 0- 45°. The typical bias function for vision is shown in Figure 1.

Fig. 1. Surface orientation estimates for near visual surfaces presented within reach of the hand (Durgin, Li & Hajnal, 2010, Experiment 1). Symbol size approximates SEM.

The estimates shown in Figure 1 are based on verbal/numeric estimates of orientation relative to horizontal, but the bias observed cannot be due to verbal coding. Essentially the same spatial function was found if participants instead estimated orientation relative to vertical and their responses were then subtracted from 90° in order to express them relative to horizontal. Thus for example, a surface that was actually at a 42° orientation from horizontal (and thus 48° from vertical), was estimated as being about 60° from horizontal by one group of participants and about 30° from vertical by another. Clearly both groups saw it as much steeper than its actual slant. When the same 42° surface was explored, haptically, by a third group of participants by each placing the palm of the right hand against it while blindfolded, it was also judged to be 60° from horizontal (Durgin, Li & Hajnal, 2010, Experiment 4).

perception. Specifically, they found that small, irregularly-shaped wooden surfaces appeared steeper than they actually were both when viewed visually and when experienced haptically while blindfolded. The term "vertical tendency" was used to distinguish the observed effect from what has been called "frontal tendency" in the literature (Gibson, 1950). For many years it has been argued that surfaces viewed visually, appear compressed along the depth axis of visual regard and thus appear more frontal to gaze than they are. However, when Durgin, Li and Hajnal asked participants to make estimates of the geographical slants of wooden surfaces within reach, they found that that they got approximately the same bias function whether the surfaces were at eye level (so that "frontal" and vertical coincided) or viewed with gaze declined by about 40°. Moreover, the same kinds of bias were found when surfaces were experienced haptically by placing the palm of the hand on them, though their measurements of this were limited to the angle of 0-

Fig. 1. Surface orientation estimates for near visual surfaces presented within reach of the

The estimates shown in Figure 1 are based on verbal/numeric estimates of orientation relative to horizontal, but the bias observed cannot be due to verbal coding. Essentially the same spatial function was found if participants instead estimated orientation relative to vertical and their responses were then subtracted from 90° in order to express them relative to horizontal. Thus for example, a surface that was actually at a 42° orientation from horizontal (and thus 48° from vertical), was estimated as being about 60° from horizontal by one group of participants and about 30° from vertical by another. Clearly both groups saw it as much steeper than its actual slant. When the same 42° surface was explored, haptically, by a third group of participants by each placing the palm of the right hand against it while blindfolded, it was also judged to be 60° from horizontal (Durgin, Li & Hajnal, 2010,

hand (Durgin, Li & Hajnal, 2010, Experiment 1). Symbol size approximates SEM.

Experiment 4).

45°. The typical bias function for vision is shown in Figure 1.

Moreover, to emphasize that these biases did not depend on generating verbal estimates, Durgin, Li and Hajnal (2010) asked a fourth set of participants to judge whether various oriented planar surfaces were closer to horizontal or to vertical. They fit a psychometric function to the resulting choice data and found that a surface slanted by only 34.3° from horizontal was, on average, visually perceived to be equidistant from vertical and horizontal.

This spatial bias function for near surfaces closely matches the observed proprioceptive function for the perceived declination of gaze. That is, when people are asked to report the pitch of their gaze, verbal reports provide evidence of an exaggerated deviation from horizontal that closely matches the bias function shown above for perceived surface slant (Durgin & Li, 2011a; Li & Durgin, 2009). Thus, it appears that several different perceptual representations of pitch contain a bias that expands the scale of differences near horizontal while compressing the scale near vertical.

Fig. 2. Surface orientation estimates for surfaces (0-48°) felt with the palm of the hand (Durgin, Li & Hajnal, 2010, Experiment 4). Error bars indicate ±1 SEM.

In the haptic domain and in the proprioception of gaze, the perceptual scale of the bias function for perceived pitch has mostly only been measured for orientations within about 50° from horizontal (e.g., Durgin, Li & Hajnal, 2010). In this range the scaling of pitch tends to closely approximate a linear scale with a gain of 1.5 (Durgin & Li, 2011a). For example the haptic data of Durgin, Li and Hajnal are shown in Figure 2. These data are based on numeric estimates of orientation in deg (relative to horizontal) made based on placing the palm of the hand on various real slanted surfaces while blindfolded. Durgin and Li have reported a very similar function for explicit estimates of the pitch of gaze over a similar range. Durgin and Li (like Durgin, Li & Hajnal) supplemented their verbal estimation data with a horizontal-vertical bisection task and again found that a rather shallow gaze declination of about 30° from horizontal was perceived as the bisection point between vertical and horizontal gaze.

Spatial Biases and the Haptic Experience of Surface Orientation 79

and energetic costs and thus to inform decisions about route selection during locomotion in the wild. A difficulty with this view is that perceived hill orientation decreases as one approaches a hill (Li & Durgin, 2010), and nearer portions of hills appear shallower than farther portions (Bridgeman & Hoover, 2008). In fact, as we will discuss below, there is continuity between orientation biases we have measured for small, near surfaces and those

Proffitt further proposed that physical actions, such as stepping, were controlled by an *unbiased* perceptual representation (vision for action) that was contrasted with the exaggerated representation available for long-range cognitive planning. This view has since

Hajnal et al. (2011) asked participants to step onto ramps that they could not see. (They were either wearing a blindfold or an occluding collar that blocked their view of the floor.) The ramps varied in orientation from 4° to 16°. Participants were asked to provide either verbal estimates of the surface orientation or to gesture the orientation with the their hand, which was measured using digital photography. The data are reproduced in Figure 4, along with a photograph of the experimental situation. Both forms of measurement documented surprisingly-large perceptual exaggerations of haptic slant. For somewhat steep ramps, the haptic exaggeration of perceived slant was even greater than the visual exaggeration observed when the same participants judged the orientations of the ramps when looking at them afterward. For example, Hajnal et al. found that participants standing on a 16° ramp judged it to be about 35-40° (both verbally, and as measured by hand gesture) based on their haptic experience, whereas when looking down at a 16° ramp (while standing on a level surface at the base of the ramp) they judged it to be only about 22-24°. The same pattern (higher estimates based on haptic perception) was found for a 14.5° ramp by Durgin et al.

been challenged by studies of the haptic perception of locomotor inclines.

(2009) who collected visual estimates before having people step onto the ramp.

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

control of action.

Haptic evaluations of the surface under one's feet are more valuable for immediate motor planning than for distal route planning. Hajnal et al. (2011) therefore suggested that these distortions might be the perceptual consequence of dense coding of orientations near horizontal that led to functionally exaggerated perceived orientation for the more precise

Kinsella-Shaw et al. (1992) had previously reported that participants were good at matching haptic inclines underfoot to visual inclines. To rule out the possibility that the haptic exaggerations were learned from calibrating haptic experience to visual experience, Hajnal et al. (2011) also tested a population of four congenitally blind individuals using verbal report. The blind individuals' estimates were quite similar to those of the sighted participants, though they were slightly higher. This indicates that the haptic exaggeration of the apparent inclination of surfaces on which one stands exists even in the absence of visual experience.

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

**3.1 Haptic bias in the perceived orientation of locomotor surfaces** 

measured by Proffitt et al. for hills (Li & Durgin, 2010).

These observations are particularly relevant to the present discussion because they emphasize that the form of the perceptual bias may not be a "vertical tendency." Rather, the linear gain of about 1.5 found in various measurements of perceived pitch between 0° and 45° from horizontal suggests that deviations from horizontal are being exaggerated and therefore that it is the horizontal that is special. Durgin and Li (2011a) have hypothesized that the expanded scaling (near horizontal) of the perceived pitch of gaze direction serves to expand the most highly utilized portion of the angular range for purpose of maintaining greater cognitive precision. Across a variety of contexts, they proposed that a gain of about 1.5 may provide efficient scaling for retaining greater precision in this lower half of the range when sending neural pitch signals upstream to cognitive and motor areas.
