Second-order reversed phi

In a first-order reversed-phi motion stimulus (Anstis, 1970), the black-white contrast of successive frames is reversed, and the direction of apparent motion may, under some conditions, appear to be reversed. It is demonstrated here that, for many classes of stimuli, this reversal is a mathematical property of the stimuli themselves, and the real problem is in perceiving forward motion, which involves the second- or third-order motion systems or both. Three classes of novel second-order reversed-phi stimuli (contrast, spatial frequency, and flicker modulation) that are invisible to first-order motion analysis were constructed. In these stimuli, the salient stimulus features move in the forward (feature displacement) direction, but the second-order motion energy model predicts motion in the reversed direction. In peripheral vision, for all stimulus types and all temporal frequencies, all the observers saw only the reversed-phi direction of motion. In central vision, the observers also perceived reversed motion at temporal frequencies above about 4 Hz, but they perceived movement in the forward direction at lower temporal frequencies. Since all of these stimuli are invisible to first-order motion, these results indicate that the second-order reversed-phi stimuli activate two subsequent competing motion mechanisms, both of which involve an initial stage of texture grabbing (spatiotemporal filtering, followed by fullwave rectification). The second-order motion system then applies a Reichardt detector (or equivalently, motion energy analysis) directly to this signal and arrives at the reversed-phi direction. The third-order system marks the location of features that differ from the background (the figure) in a salience map and computes motion in the forward direction from the changes in the spatiotemporal location of these marks. The second-order system's report of reversed movement dominates in peripheral vision and in central vision at higher temporal frequencies, because it has better spatial and temporal resolution than the third-order system, which has a cutoff frequency of 3-4 Hz (Lu & Sperling, 1995b). In central vision, below 3-4 Hz, the third-order system's report of resolvable forward movement of something salient (the figure) dominates the second-order system's report of texture contrast movement.