Figure 5.

Models for motion estimation. (a) A correlator model of motion estimation, also known as a Hassenstein Reichardt correlator (Hassenstein & Reichardt 1956). Intensity or contrast signals from neighboring points in space are multiplied after one signal is delayed in time. This operation amplifies signals when the delayed and nondelayed signals coincide at the multiplicative step. The output of the model is the difference between two mirror-symmetric multipliers. (b) A motion energy model (Adelson & Bergen 1985). An oriented spatiotemporal filter amplifies signals in a preferred direction compared to the null direction, after which the filtered signal is squared. The linear operation alone does not create a direction-selective signal, since both preferred and null-direction signals have the same mean. (c) A biophysical model for motion estimation (Mo & Koch 2003, Zavatone-Veth et al. 2020) can be expanded into a Volterra series that approximates its operations at different polynomial orders of the input (Poggio & Reichardt 1973, Potters & Bialek 1994). The first three non-direction-selective terms each contain a nonlinearity, N. The lowest-order directional terms multiply pairs of inputs: These terms are approximated by correlator and motion energy models. The last term is an example third-order term, which multiplies three signals from two points in space. Other third- and higher-order terms are not shown, and we omit signs and scale factors for simplicity. V_m represents membrane voltage in the model.