Visual responses to vorticity and the neural analysis of optic flow

While an observer is moving forward, his retinal image of the outside world contains a flow field. This optical flow field carries information both about external objects and about where the observer is going relative to these objects. Mathematically, the flow pattern can be analyzed into elements that include the curl of local velocity (i.e., vorticity), and it has been suggested that the visual pathway might contain independent neural mechanisms sensitive to these mathematical elements [H. C. Longuet-Higgins and K. Prazdny, Proc. R. Soc. London Ser. B 208, 385-397 (1980)]. To test this suggestion we compared visual responses to two circular areas of random dots, A and B. These two stimuli were identical in that all dots oscillated along a straight line in one of two possible directions. However, the relative phases of dot oscillations were different for A and B, causing A to have a rotary component of motion that B did not have. We found that rotary motion thresholds for a rotary test stimulus were more elevated after adapting to A than after adapting to B, a difference that cannot be explained in terms of visual responses to linear motion, since linear motion components were the same for A and B. This finding is consistent with the idea of a neural mechanism sensitive to the curl of velocity (i.e., vorticity). Adding this to previous evidence for a mechanism specifically sensitive to the divergence of velocity (i.e., dilatation), we suggest that one role of these postulated mechanisms might be to parallel vector calculus by analyzing each small patch of the visual flow field into neural representations of the mathematically independent quantities curl and divergence of velocity.