Transparent Motion Perception as Detection of Unbalanced Motion 
        Signals III: Modeling 
Ning Qian, Richard A. Andersen and Edward H. Adelson
Published in
Journal of Neuroscience, vol. 14, pp. 7381-7392 (1994).
In the preceding two companion articles we studied the conditions 
under which transparent motion perception occurs through psychophysical 
experiments, and investigated the underlining neural mechanisms through 
physiological recordings. The main finding of our perceptual experiments 
was that whenever a display has finely balanced motion signals in all 
local areas, it is perceptually nontransparent, and that transparent 
displays always contain motion signals in different directions that are 
either spatially unbalanced, or unbalanced in their disparity or spatial 
frequency contents. In the physiological experiments, we found two 
stages in the processing of transparent stimuli. The first stage is 
located primarily in area V1. At this stage motion measurements are made 
and V1 cells respond well to both the balanced, nontransparent stimuli 
and the unbalanced, perceptually transparent stimuli. The second stage 
is located primarily in area MT. MT cells show strong suppression 
between opposite directions of motion. The suppression for the 
unbalanced, transparent stimuli is significantly less than that for the 
balanced, nontransparent stimuli. Therefore, the activity in the second, 
MT stage correlates better with the perception of motion transparency 
than the first, V1 stage, which does not distinguish reliably between 
transparent and nontransparent motion.
The above experiments suggest a  two-stage model of motion perception 
with a motion measurement stage in V1 and an opponent-direction 
suppression stage in area MT. In this article we explicitly test this 
model through analysis and computer simulations, and compare the 
response of the model to the perceptual and physiological results using 
the same balanced and unbalanced stimuli we used in the experiments. In 
the first stage of the computational model, motion energies in different 
spatial frequency and disparity ranges are extracted from each local 
region. Similar to V1, this stage does not distinguish between the 
balanced and unbalanced stimuli. In the subsequent stage motion energies 
of opposite directions but with same spatial frequency  and  
disparity contents suppress each other using subtractive or divisive 
inhibition. This stage responds significantly better to the transparent 
stimuli than to the nontransparent ones, in agreement with MT activity.