In addition to the lateral bias and depth-direction confusions, other researchers have documented that motion trajectories towards the observer have some amount of “privileged” perceptual processing (
Lin, Franconeri, & Enns, 2008;
Lin, Murray, & Boynton, 2009;
Schiff, Caviness, & Gibson, 1962). Indeed, our prior work has shown a bias to report motion-in-depth stimuli as approaching rather than receding, or vice versa, depending on the specific appearance of the stimulus (
Cooper, van Ginkel, & Rokers, 2016;
Fulvio et al., 2015). These biases may be related to prior work which suggests that observers perceive lower contrast stimuli as farther away than high-contrast stimuli (
Dosher, Sperling, & Wurst, 1986;
Farnè, 1977;
O'Shea, Blackburn, & Ono, 1994;
Schwartz & Sperling, 1983). However, given that the contrast of the stimuli in the motion-in-depth experiments did not vary within a given trial, the exact nature of this relationship remains to be explored.
Figure 9 illustrates how these approaching/receding biases manifest in the current set of experiments. Each panel shows the probability density of response directions, averaged over all participants from Experiment 1, for stimuli that moved toward four different quadrants: rightward (red), leftward (yellow), approaching (green), and receding (blue).
Figure 9A shows the responses for the high-contrast (100%) smaller viewing distance (45 cm): The reported motion directions tended to generally fall within the stimulus quadrant, but some motion-in-depth direction confusions are clearly evident.
Figure 9B and
9C shows the responses for two conditions in which participants, on average, were biased to report that motion was receding (B) and approaching (C). The current Bayesian model does not predict approaching or receding biases because the prior for motion is always centered on 0 in both
x′ and
z′. That is, although the sampling distribution of the MAP extends into reversed directions (
Figure 7A), the average of this distribution is always in the same direction as the stimulus. Prior studies directly comparing a Bayesian ideal observer to 3-D motion perception either did not present both approaching and receding motion or disregarded direction confusions (
Lages, 2006;
Welchman et al., 2008), and thus this additional bias was not observed. However, there are several ways in which existing Bayesian models, including the one presented here, may be elaborated to account for these effects. For example, extensions to our model might incorporate a prior that is not centered on zero motion for some stimuli, a cost function that reflects the different behavioral consequences of misperceiving approaching and receding motion, or the impact of attentional effects. Of particular interest would be the exploration of a statistical relationship between stimulus contrast and motion direction in natural scenes.