Many previous studies have used noise tolerance to quantify sensitivity to point-light walkers heading ±90° from straight-ahead. Here we measured the smallest deviations from straight-ahead that observers could detect (azimuth thresholds) in the absence of noise. Thresholds were measured at a range of stimulus sizes and eccentricities for (1) upright and (2) inverted walkers, (3) intact walkers, those without feet and those with only feet, and (4) in the presence and absence of a second, attention-absorbing task. At large stimulus sizes azimuth thresholds were very small (between 1 and 2°) except in the case of inverted walkers. Size scaling generally compensated for eccentricity dependent sensitivity loss, however in the case of inverted walkers the data were quite noisy. At large sizes walkers without feet elicited higher thresholds than those with only feet, suggesting a special role for the feet even when walkers are not viewed side-on. Unlike others, we found no evidence that competing tasks affected performance. We argue that the value of our modified direction-discrimination task lies in its focus on the limits of discrimination within the domain of interest, rather than the amount of noise needed to impair discrimination of widely separated stimulus values.

*scrambled walker noise,*which comprises many moving dots drawn from the population defining the action in question, with positions and phases randomized to eliminate any sense of coherent motion (Aaen-Stockdale et al., 2008; Bertenthal & Pinto, 1994; Thompson et al., 2007; Thurman & Grossman, 2008). So strong is the right–left walker signal, for example, that scores of scrambled walker noise dots are required to bring performance off the ceiling (Thompson et al., 2007). Given the subtlety of the information conveyed by point-light walker stimuli (e.g., sex, age, mental states, actions, and intentions) the standard walker direction discrimination task and the action vs. scrambled action task are decidedly unsubtle tools for studying biological motion.

*θ*deg) from straight ahead. Rightward heading walkers can move in any direction from 0 to 90 deg from straight-ahead and leftward heading walkers can move in any direction from 0 to −90 deg from straight-ahead. Therefore, azimuth thresholds represent the azimuth (i.e., direction difference) eliciting 81% correct performance in a two alternative forced choice discrimination task. An adaptive threshold procedure is used to determine azimuth thresholds. We use this paradigm, in a variety of tasks, to investigate sensitivity to biological motion across the visual field.

*F*

_{E}) at each eccentricity (

*E*) required to elicit performance equivalent to a foveal standard. The free parameter

*E*

_{2}indicates the eccentricity (in degrees visual angle, °) at which stimulus size must double to elicit equivalent-to-foveal performance. (It should be noted that

*E*

_{2}is inversely related to the rate at which the required stimulus magnification increases with eccentricity; therefore, small

*E*

_{2}values reflect rapid eccentricity dependent sensitivity loss.)

*E*

_{2}of 3.5° was sufficient to compensate for eccentricity-dependent sensitivity loss (N = 4, estimated

*SEM*= .147, 95% confidence interval = 3.03 to 3.97) and for walkers heading ±4° an average

*E*

_{2}of .87 (estimated

*SEM*= .136; 95% confidence interval = .53 to 1.22) compensated for eccentricity-dependent sensitivity loss.

*E*

_{2}is task dependent such that finer direction differences elicit a faster loss of sensitivity with increasing eccentricity. However, because both Gurnsey et al. (2008) and Gibson et al. (2005) employed fixed direction differences it is unclear (i) whether the limits of walker direction discrimination change with eccentricity and (ii) what

*E*

_{2}value would be obtained at the limits of performance. It might be that the

*E*

_{2}required to equate performance across the visual field at the limits of discrimination sensitivity is less than previously found.

*E*

_{2}values associated with this compensation will be similar to, or less than, those reported by Gurnsey et al. (2008) when walker direction was fixed at ±4° from straight-ahead. Experiment 2 was identical in all respects to Experiment 1 except that walkers were inverted. We expected sensitivity to walker direction to be lower for inverted than upright walkers, however, it was unclear how sensitivity would change with eccentricity relative to the upright condition. In Experiment 3 we examined sensitivity to walker direction for (i) intact walkers, (ii) feet-only walkers (all but the two dots representing the feet were removed) and (iii) walkers with no feet. The purpose of this experiment was to clarify the role of the feet in the walker direction discrimination task when walker direction differences are smaller than the standard ±90°. In Experiments 4 and 5 subjects performed a walker direction discrimination task alone (single task) or simultaneously with an attention demanding second task (dual task). The question was whether direction discrimination thresholds would be inflated in the presence of a competing task and, if so, how such changes in thresholds might vary with eccentricity.

*E*

_{2}values compare to those found in previous studies.

*α*) of 20 numbers representing the weights on the first 20 principle components. If all elements of

*α*are set to zero then a neutral, average walker is generated representing the origin of “walker space.” Any other vector can be viewed as a direction through walker space and the length of the vector determines how different the walker is from the average walker. The three-dimensional (x,y,z) coordinates for each of 15 points were generated and projected (orthographically) to the display screen.

*α*were drawn from a standard normal distribution to create a novel walker. The resulting walker could be made to move to the left or right by rotating it about the vertical axis by an angle ±Δ

*θ*deg. The objective of the experiment was to find thresholds for a range of stimulus sizes at a range of eccentricities. At each eccentricity nine logarithmically spaced stimulus sizes were chosen such that Δ

*θ*thresholds ranged from asymptotically low, at large sizes, to roughly 30 to 70 deg at small sizes. For all stimuli the walker dot diameters were always 1/36 of the stimulus height; in other words, dot size scaled with stimulus size. Stimulus size was manipulated by varying viewing distance and/or stimulus size on the monitor. Viewing distances were varied from 57 to 456 cm and were chosen to satisfy the twin constraints of (i) keeping the fixation dot and stimulus on the screen and (ii) maximizing the number of pixels per dot. For example, stimuli presented at fixation were always viewed from 456 cm and those presented at 16° were viewed from 57 cm.

*θ*deg at each stimulus size and eccentricity. Prior to data collection subjects received sufficient practice to become familiar with the task. Two thresholds were determined for each combination of size and eccentricity and then averaged.

*F*(5, 15) = .703,

*p*= .603,

*η*

_{ p}

^{2}= .19.

*σ*) increases Δ

*θ*thresholds decrease until they reach an asymptotically small value (Δ

*θ*

_{min}). Therefore, at each eccentricity we can fit the data with a predicted threshold (Δ

*θ*′) at each size (

*σ*) using the following negatively accelerated curve

*a*and

*b*are free parameters. Because the curves in Figure 2 (top) are shifted versions of each other this suggests that determining

*F*= 1 +

*E*/

*E*

_{2}would allow us to collapse all data in to a single curve

*σ*/

*F*

_{ E}represents

*scaled*stimulus size.

*θ*

_{min},

*a*,

*b*and

*E*

_{2}that minimize the deviation of the data from the parametric curve. The quality of the fit is reported as

*r*

^{2}to express the proportion of variability in the data explained by the fit; the correlation was formed between log(Δ

*θ*) and log(Δ

*θ*′), which are the actual and predicted thresholds respectively. The data were fit using the error minimization routine (fminsearch) provided in MATLAB (Mathworks Ltd.). The scaled data are shown in the bottom panels of Figure 2 (panels E to H). The average

*E*

_{2}value was .95 (estimated

*SEM*= .051, 95% confidence interval = .79 to 1.11). This range of

*E*

_{2}values is consistent with the results of Gurnsey et al. (2008) for walkers heading ±4° from straight ahead; average

*E*

_{2}value was .87 (estimated

*SEM*= .136; 95% confidence interval = .53 to 1.22). Therefore it seems that the two tasks are subject to very similar eccentricity dependent limitations.

*E*

_{2}of about .95, which is in good agreement with a previous estimate of .87 determined with Δ

*θ*fixed at ±4° (Gurnsey et al., 2008).

*F*(5, 15) = 1.69,

*p*= .197,

*η*

_{ p}

^{2}= .36. In particular, the linear trend was not statistically significant,

*F*(1, 3) = .024,

*p*= .887,

*η*

_{ p}

^{2}= .008, meaning there was no statistically significant increase in minimum Δ

*θ*with eccentricity.

*E*

_{2}value was 1.15 (estimated

*SEM*= .153, 95% confidence interval = .66 to 1.64). Clearly the

*E*

_{2}values were more variable for inverted than upright walkers. However, we note that three of the subjects show relatively large

*E*

_{2}values (mean = 1.29) and the fourth (GR) a very small

*E*

_{2}of .71. This seems to be because her data were shifted somewhat further leftward at fixation and somewhat further rightward at 16°. In other words, she was a little better at fixation and a little worse in the periphery.

*r*

^{2}value for upright walkers was .90 (N = 4; estimated

*SEM*= .015; 95% confidence interval = .85 to .95) and .80 (N = 4; estimated

*SEM*= .037; 95% confidence interval = .68 to .91) for the inverted walkers. The inability to extract precise heading information from inverted walkers (resulting in highly variable thresholds) may be a consequence of lack of familiarity/practice with such stimuli or a more fundamental encoding limitation; perhaps because the inverted walkers produce movements inconsistent with the effect of gravity on bodies (Shipley, 2003).

*θ*) to log(

*Scaled Size*) for all subjects in both conditions. The average slopes for the upright conditions were −1.40 (N = 4; estimated

*SEM*= .035; 95% confidence interval = −1.29 to −1.51), and −1.05 (N = 4; estimated

*SEM*= .105; 95% confidence interval = −.72 to −1.38) for the inverted condition. Therefore, there was a more gradual decrease in thresholds with stimulus size for the inverted walkers than the upright walkers.

*SEM*= .205; 95% confidence interval = .92 to 2.22) were much lower than those obtained in the inverted condition (6.52 deg; N = 4; estimated

*SEM*= 1.14; 95% confidence interval = 2.89 to 10.15). (Again, these minimum thresholds were determined from the average Δ

*θ*thresholds at the two largest sizes for each eccentricity.) This is one of the most consistent differences between the two conditions. It's not clear to what extent this deficit could be overcome with practice.

_{ E}) represents a rough measure of the magnitude of the inversion effect. We submitted the

_{ E}scores to a within-subjects ANOVA and found no statistically significant effect of eccentricity,

*F*(5,15) = .606,

*p*= .69,

*η*

_{ p}

^{2}= .168. Therefore, there is no evidence that the magnitude of the inversion effect changes with eccentricity.

*E*

_{2}values associated with each of the three conditions. The

*E*

_{2}values were submitted to a one-factor, within-subjects ANOVA and the omnibus F was not statistically significant,

*F*(2, 6) = 2.94,

*p*= .163,

*η*

_{ p}

^{2}= .454. For the intact walkers the mean

*E*

_{2}value was .87 (N = 4, estimated

*SEM*= .033, 95% confidence interval = .76 to .97); for the feet-only walkers the mean

*E*

_{2}value was .94 (N = 4, estimated

*SEM*= .102, 95% confidence interval = .61 to 1.26); for the no-feet walkers the mean

*E*

_{2}value was 1.14 (N = 4, estimated

*SEM*= .092, 95% confidence interval = .85 to 1.43). Therefore, the eccentricity dependent shifts of the 16° presentations relative to the 0° presentations do not differ in the three conditions.

*θ*

_{ fo}/Δ

*θ*

_{ i}) and the ratio of the no-feet to intact walker thresholds (Δ

*θ*

_{ nf}/Δ

*θ*

_{ i}). The ratios were computed at each size and eccentricity for each subject and then averaged. The results (excluding the two smallest sizes) are presented in Figure 6.

*SEM*= .341, 95% confidence interval = .742 to 2.912) for the intact walkers, 1.086 (N = 4, estimated

*SEM*= .108, 95% confidence interval = .743 to 1.430) for the feet-only walkers and 2.898 (N = 4, estimated

*SEM*= .458, 95% confidence interval = 1.442 to 4.353) for the no-feet walkers. We refer to mean thresholds at the two largest sizes as

*minimum thresholds*.

*g*(

*g*= (

_{1}−

_{2})/

*s*

_{ p}) was computed for all pairs of minimum thresholds (averaged over eccentricity) as a measure of effect size. The results were

*g*

_{ intact,feet-only}= 2.07,

*g*

_{ intact,no-feet}= 1.88 and

*g*

_{ feet-only,no-feet}= 3.85. The corresponding

*t*-tests (uncorrected) for paired samples were

*t*

_{ intact,feet-only}= 2.729,

*p*= .072,

*t*

_{ intact,no-feet}= −3.016,

*p*= .057 and

*t*

_{ feet-only,no-feet}= −4.882,

*p*= .016. For completeness we computed effect sizes and t scores for the eccentricity effect within each of the three conditions. The results are as follows: intact walkers,

*g*= .155, t = .246,

*p*= .882; feet-only walkers,

*g*= 1.955, t = 2.596,

*p*= .081; no-feet walkers,

*g*= .861, t = −1.383,

*p*= .261. Therefore, there was a modest effect of eccentricity on minimum thresholds for the feet-only condition but not the other two.

*E*

_{2}value in each condition. However, the functions relating size to threshold are not identical in the three conditions. Thresholds in the no-feet condition are generally higher than those in the intact condition. Thresholds in the feet-only condition are higher than those in the intact condition at small sizes but lower at large sizes. Note that a 1 deg feet-only stimulus was derived from the 1 deg intact walker by just deleting all dots but the feet. Consequently, a 1 deg feet-only display subtends only about 0.2 degrees of visual angle. If we were to define stimulus size in terms of the vertical extent, the curves representing the feet only condition in Figure 6 would shift 0.7 log units to the left and differences between the feet-only and the no-feet conditions would be even more pronounced.

*ɛ*); raising the red gun and lowering the green gun produced a reddish walker and the opposite change produced a greenish walker. In the dual task condition an adaptive procedure was used to find threshold Δ

*ɛ*while a second adaptive procedure simultaneously varied Δ

*θ*. Subjects were instructed to give priority to the color discrimination task and to report walker color before reporting walker direction. A threshold run was terminated only when both adaptive procedures reached the criterion for threshold. The logic of the experiment is to measure walker direction thresholds in a context in which the color task difficulty was maintained at a constant level; i.e., the color contrast was always at QUEST's best estimate of threshold.

*θ*thresholds are shown in blue and the dual task Δ

*θ*thresholds are shown in green. Within each panel the data from 0° are to the left and those from 16° are to the right. It is clear that for both subjects the single and dual task curves superimpose almost perfectly. There is no evidence that asymptotic thresholds fall to different levels in the single and dual-task conditions and the computed

*E*

_{2}values are essentially identical in both tasks for the two subjects. Therefore, there is no evidence that Δ

*θ*thresholds are impaired when obtained in the presence of a competing color discrimination task.

*θ*thresholds would be affected when attention is divided between the walker and a stimulus that surrounds that walker.

*θ*is defined as:

*r*

_{0}is the average radius of the pattern,

*ϖ*is radial frequency (in this case either 3 or 4),

*ϕ*is the phase of the sinusoidal modulation, which was randomized on each trial, and

*A*is the amplitude of the radial frequency modulation, which ranged from 0 to 1. The cross section of the radial frequency pattern was Gaussian and a static frame of one stimulus is shown in Figure 8. On each trial the radial frequency pattern appeared and disappeared simultaneously with the walker. Subjects first judged radial frequency then walker direction.

*A*) of the radial frequency pattern and walker direction (Δ

*θ*) were controlled by independent adaptive procedures. As in Experiment 4, a threshold run terminated only when both of the procedures achieved termination conditions. In one of the single task conditions subjects judged the walker direction while ignoring variations in the radial frequency pattern; to make the conditions of the single task comparable to those of the dual task the amplitude (

*A*) of the radial frequency pattern varied in proportion to Δ

*θ*. To avoid interference with the walker,

*A*was capped at 10%. In the second single task condition, subjects judged radial frequency while ignoring walker direction. To make the conditions of the single task comparable to those of the dual task walker direction varied in proportion to

*A*.

*E*

_{2}for walker direction in the single task was 1.31 and in the dual task it was 1.37. Therefore, there is little, on average, to distinguish single task and dual task performance. However, we note that subject P5 showed lower asymptotic thresholds in the single task than in the dual task at 0°. This is consistent with the idea that the radial frequency task and the walker direction discrimination task compete for resources. However, this effect was not seen for P5 at 16° or any of the other subjects at either eccentricity. Therefore, the weight of evidence suggests no cost to walker direction discrimination in the dual task.

*E*

_{2}is so large as to be meaningless; an

*E*

_{2}of 158 (see Figure 9, panel G) means that peripherally presented stimuli have to be moved 158° from fixation before stimulus size has to double to elicit equivalent to foveal performance. Therefore, the data do not permit a meaningful fit.

*E*

_{2}values (see Figure 9). These data suggest that failing to attend to the radial frequency task cannot explain similarity of the single and dual task results for the walker discrimination data ( Figure 9, panels A to D). Therefore, we conclude that the walker direction discrimination task does not compete for resources with the radial frequency task.

*E*

_{2}values in the walker direction discrimination task tend to be smaller than in the radial frequency task. The average

*E*

_{2}in the walker discrimination task was 1.34 and in the radial frequency task (excepting the

*E*

_{2}of 158 in Figure 9, panel G) was 2.78. This corresponds to an effect size of

*g*= 3.079. When the data were subjected to a paired samples

*t*-test the difference was statistically significant,

*t*(3) = 3.373,

*p*= .047. This difference means that there is a faster loss of sensitivity with eccentricity for the walker direction discrimination task than for the radial frequency task.

*θ*) across the visual field and if so how the needed magnification relates to previously reported results. Experiment 1 showed that size scaling was indeed sufficient to compensate for eccentricity dependent sensitivity loss. The azimuth-vs.-size curves were very similar at all eccentricities and so dividing actual stimulus size by

*F*= 1 +

*E*/

*E*

_{2}collapsed data from all eccentricities onto a single curve. The fits were generally very good and explained about 90% of the variability in the data on average. The average

*E*

_{2}in Experiment 1 was .95, which is consistent with the average

*E*

_{2}value of .87 reported by Gurnsey et al. (2008) for walkers heading ±4° from straight-ahead. Furthermore, the minimum thresholds at the largest stimulus sizes did not change with eccentricity. Therefore, we conclude that the eccentricity dependent magnification required at the limits of walker direction discrimination is not different from that at a fixed difference of ±4° from straight-ahead.

*E*

_{2}value associated with a task would identify the anatomical locus (e.g., retinal or cortical) of the eccentricity dependent limitation (Wilson, Levi, Maffei, Rovamo, & DeValois, 1990). This hope has dimmed in recent years, in part because estimates of

*E*

_{2}can be quite variable and in part because manipulations of contrast, for example, can alter the

*E*

_{2}recovered in a particular task (Sally & Gurnsey, 2007), suggesting an effect on physiological mechanisms rather than the anatomical locus of the limitation. On the other hand, there is evidence that associations can be made between known structural properties of the visual system and

*E*

_{2}. For example, it has been shown that for color discrimination the

*E*

_{2}associated with L/M contrast detection is much smaller than that required for S/LM discrimination, which is consistent with the distributions of L, M and S cones in the retina (Vakrou, Whitaker, McGraw, & McKeefry, 2005). The

*E*

_{2}values reported here are generally in the neighborhood of 1, which traditionally suggests a cortical limitation because resolution limits imposed by the retina increase at a much lower rate (

*cf*. Drasdo, 1991). Therefore, it seems reasonable to assume that the limitation in the present task does not reflect difficulty resolving the presence of the stimulus itself but with extracting the information required to infer direction.

*vertical*eccentricities meaning that less informative dots are closer to fixation than the feet. Nevertheless, the present evidence is consistent with a special role for the feet even in cases in which walkers are not moving ±90° from straight-ahead. On the other hand, there is no advantage of the feet–only condition at smaller sizes. Under these conditions thresholds increase and walkers are seen more in profile, as in the usual walker direction discrimination task.

^{2}), placing it close to, if not in, the mesopic range. This latter point may explain the difficulty subjects had with the task. For upright walkers at 4° eccentricity and 4° in height our subjects achieved discrimination thresholds of about 3°. Although we did not measure reaction time it's clear that our subjects would have found ±90° walkers trivially easy to discriminate under conditions that subjects in the Cavanagh et al. study found very difficult. Therefore, it would be worth redoing their experiment at higher luminance levels. Note as well that Grossman and Blake (1999) found a reduced sensitivity to biological motion under low luminance conditions, although their stimuli were degraded with noise, whereas those of Cavanagh et al. were not.