Transparent motion perception as detection of unbalanced motion signals. III. Modeling

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.