Second-order reversed phi

Abstract

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 theforward (feature displacement) direction, but the second-order motion energy model predicts motion in the reoersed 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 oftexture 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 thirdorder 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 spatiotemporallocation 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.There is mounting evidence that there are three parallel streams of visual motion computation-first-and second-order systems that are primarily monocular and a third-order binocular system (Lu & Sperling, 1995a, 1995b, 1996c. The first-order system extracts motion from drifting luminance modulations, and the secondorder system extracts motion from drifting texture contrast modulations. These primarily monocular systems use motion energy analyses (Adelson & Bergen, 1985) or, equivalently, elaborated Reichardt detectors (van Santen & Sperling, 1984. Both primarily monocular systems are fast (temporal cutoff frequency at 10-12 Hz) and approximately equally sensitive to a wide range of spatial -Accepted by previous editor, My...

Evidence and Counterevidence in Motion Perception

“…Two reasons for the indifference toward reverse-phi may be that several motion models claim to readily explain the illusion (Reichardt 1961;Adelson and Bergen 1985;van Santen and Sperling 1985;Johnston and Clifford 1995), or that there is nothing to explain (Lu and Sperling 1999). We believe these reasons to be incomplete or incorrect, respectively.…”

“…We believe these reasons to be incomplete or incorrect, respectively. To address the latter point first, Lu and Sperling (1999) present the example of a sinewave grating that steps 90 degrees per frame. Inverting the contrast of such a grating results, of course, in a display that is physically identical to a constant-contrast grating stepping in the opposite direction.…”

“…Such stimuli, however, provide a mixture of inverted-contrast correlations (between one frame and any odd number of frames later) and constant-contrast correlations (between frames separated by any even number of frames). As a consequence, such stimuli cannot fully isolate same and opposite-contrast motion signals and leave open a number of trivial explanations of the reversephi illusion (Lu and Sperling 1999).…”

“…Reverse-phi, however, is observed in a wide range of stimuli, not just in 90°stepping sine-wave gratings. Notably, our SSDL stimuli contain none of the motion signals that the model of Lu and Sperling (1999;their Fig. 4) uses to explain reverse-phi.…”

Spatial attention: Different mechanisms for central and peripheral temporal precues?

“…A special circuit (Pelli & Zhang, 1991) combined two 8-bit output channels of the video card to produce 6,144 distinct gray levels (12.6 bits). A psychophysical procedure (Lu & Sperling, 1999) was used to compute the gamma correction for the monitor. The background luminance was set at 27 cd/m 2 , with a dynamic range from 1 cd/m 2 to 53 cd/m 2 .…”