One of the criticisms often leveled at models using differential operations is that they will be particularly sensitive to noise in the input image. In particular our model uses higher order derivatives to condition the speed ratios, which could therefore make our model even more susceptible to noise. Here we display the results for our model in the presence of two levels of additive static noise on a translating sine grating. While the temporal differentiation may remove the effect of static noise in the time domain, the effect of the noise will remain in the spatial direction. The ratio of spatial to temporal differential is taken to recover speed, so we might still expect a poor performance of gradient based models in the presence of noise. This is not the case for the model architecture we use, as can be seen in the figures below. The details of why our model is insensitive to the effects of static noise can be found in
Johnston A, McOwan P W & Benton C, Robust velocity computation from a biologically motivated model of motion perception Proc. Royal Soc. Lond. B 266 (1999) pp509-518
Upwards translating sine grating, model recovers uniform speed (0.5 deg/sec) and correct direction
Upwards translating sine grating with 25% static noise added, model recovers uniform speed (average 0.49 deg/sec) and correct direction
Upwards translating sine grating with 100% static noise added, model recovers fairly uniform speed (average 0.48 deg/sec) and correct direction.