Two theories are considered to account for the perception of motion of depth-defined objects in random-dot stereograms (stereomotion). In the Lu–Sperling three-motion-systems theory [J. Opt. Soc. Am. A 18, 2331 (2001)], stereomotion is perceived by the third-order motion system, which detects the motion of areas defined as figure (versus ground) in a salience map. Alternatively, in his comment [J. Opt. Soc. Am. A 19, 2142 (2002)], Patterson proposes a low-level motion-energy system dedicated to stereo depth. The critical difference between these theories is the preprocessing (figure–ground based on depth and other cues versus simply stereo depth) rather than the motion-detection algorithm itself (because the motion-extraction algorithm for third-order motion is undetermined). Furthermore, the ability of observers to perceive motion in alternating feature displays in which stereo depth alternates with other features such as texture orientation indicates that the third-order motion system can perceive stereomotion. This reduces the stereomotion question to “Is it third-order alone or third-order plus dedicated depth-motion processing?” Two new experiments intended to support the dedicated depth-motion processing theory are shown here to be perfectly accounted for by third-order motion, as are many older experiments that have previously been shown to be consistent with third-order motion. Cyclopean and rivalry images are shown to be a likely confound in stereomotion studies, rivalry motion being as strong as stereomotion. The phase dependence of superimposed same-direction stereomotion stimuli, rivalry stimuli, and isoluminant color stimuli indicates that these stimuli are processed in the same (third-order) motion system. The phase-dependence paradigm [Lu and Sperling, Vision Res. 35, 2697 (1995)] ultimately can resolve the question of which types of signals share a single motion detector. All the evidence accumulated so far is consistent with the three-motion-systems theory.
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