Abstract
Two Bayesian models are proposed that extend existing models of 3-D motion encoding. The first model uses velocity constraints in the left and right eye to recover trajectory angle and velocity of a target stimulus moving in x-z space. The prior of this model is defined in velocity space and favours slow motion in 3-D. Uncertainty in velocity encoding produces blurred velocity constraint lines in the left and right eye. Applying a decision rule to a posterior distribution results in biased estimates of trajectory angle and velocity (cf. Weiss, Simoncellli & Adelson, 2002). The second model is based on changing binocular disparity and spatial position with disparity encoding as the primary source of uncertainty. The prior in this model favours zero disparity. A posterior is derived from integration of estimated target positions over time also resulting in biased estimates of trajectory angle and velocity.
Predictions from both models were tested in an experiment where binocular disparity and interocular velocity difference served as main depth cues. Stimuli were presented to the left and right eye on a flat CRT screen with a refresh rate of 120 Hz using a split-screen Wheatstone configuration. On each trial Ss verged on a fixation-cross flanked by nonius lines at 114 cm before a Gaussian dot of approximately 3 arcmin moved in depth with constant velocity. Trajectory angle (0 to 360 deg) and distance travelled in depth varied in randomly intermixed trials and between conditions. After each presentation Ss indicated trajectory angle and distance travelled by adjusting markers on screen. The results show that under these conditions Ss systematically overestimate trajectory angle (Harris & Dean, 2003) and underestimate velocity of motion towards the observer. A similar bias was found for trajectories away from the observer supporting a stereo-motion system that encodes disparity first. Additional testing may help to clearly distinguish between the two statistical models.