Figure 2a plots discrimination thresholds for three observers' judgment of overall direction (clockwise or anti-clockwise of reference) as a function of the range of directions present in the stimulus, and for two reference directions (vertical and 45°). At low levels of directional variability observers are consistently worse at judging the direction of stimuli moving in near-oblique directions— this is the OEM. However, performance converges, and the OEM effectively disappears at high levels of directional variance. The fits from the EN analysis, shown by the solid lines, provide a good account of performance in both conditions. Parameters from the fits (shown in the legends of
Figure 2a) reveal that this pattern of performance is consistent with observers pooling a constant number of local directions (
) in making their judgments of global direction but being approximately twice as uncertain about the direction of individual elements (
) moving in near-oblique directions than those moving in near-cardinal directions.
To determine if the OEM is generally reduced at high directional
SDs, we next measured direction discrimination for a range of reference directions “around the clock” either at a single low or a single high level of directional noise. Results are presented in
Figures 2b and
c for the low and high directional
SD conditions, respectively (note that there is no reflection of data in these plots). The pattern of thresholds around 360° produced “fat crosses” in
Figure 2b and indicates a robust oblique effect for all noncardinal directions tested (i.e., beyond 22.5° of the cardinals). In contrast, the oblique effect was greatly reduced when measured with a broad range of directions present in the stimulus (
Figure 2c). Results were not uniformly equal around the clock (e.g., PJB shows a general advantage for downwards motion), but given the degree of variability in threshold estimates (error bars indicate 95% confidence intervals) our findings are consistent with the results from the first part of the experiment: the OEM is attributable to observers being less precise at judging the direction of any one element (higher internal noise), rather than being poor at judging the direction of the field as a whole. Our findings are also consistent with an earlier report (in abstract form) of a general reduction in the extent of the oblique effect with the addition of directional noise (Flinn & Watamaniuk,
1997).
There is increasing consensus that the human visual system is optimized for characteristics of the natural visual environment (e.g., Field,
1987) and it is known that there is an overrepresentation of information on the cardinal axes in static images (Baddeley & Hancock,
1991; Betsch, Einhauser, Kording, & Konig,
2004; Coppola, Purves, McCoy, & Purves,
1998; Craven,
1993; Hancock, Baddeley, & Smith,
1992; Hansen, Essock, Zheng, & DeFord,
2003; Keil & Cristobal,
2000; Switkes, Mayer, & Sloan,
1978). The latter result led us to ask if the concentration of energy in cardinal directions would lead to anisotropies in local directional bandwidth measured in natural movies, which might in turn influence the tuning of local motion detectors in the visual system. To address this issue, we conducted an analysis of directional statistics within a natural movie stimulus.