Temporal covariance model of human motion perception.

We propose a model of direction-sensitive units in human vision. It is a modified and elaborated version of a model by Reichardt [Z. Naturforsch . Teil B 12, 447 (1957)]. The model is applied to threshold experiments in which subjects view adjacent vertical bars with independently (typically sinusoidally), temporally modulated luminances. The subject must report whether the patterns moved to the left or to the right. According to the model, a basic motion-detecting unit consists of two subunits tuned to opposite directions. Each performs a spatial and temporal linear filtering of its input; outputs of the filters are multiplied, and the multiplied output is integrated (for a time that is long relative to the modulation period). The model's output consists of the difference between the subunit outputs. Direction of movement is indicated by the sign of the model output. Mathematical analysis of the model yielded several predictions that were confirmed experimentally. Specifically, we found that (1) performance with complex patterns can be predicted by spatiotemporal Fourier analysis that results in the segregation and linear addition in the output for different temporal frequencies; (2) under special conditions, performance depends on the product of adjacent bar amplitudes, offering strong support for the multiplication principle; (3) performance is unaffected by addition of stationary patterns; and (4) addition of homogeneous flicker normally produces no effect but under special conditions reverses perceived direction. These and other results confirm our model and reject several other models, including Reichardt 's original model.