White noise analysis for the correlation-type elementary motion detectors with half-wave rectifiers

The motion detection mechanism of insects has been attracted attention of many researchers. Several motion-detection models have been proposed on the basis of insect visual system studies. Here, we examine two models, the Hassenstein-Reichardt (HR) model and the two-detector (2D) model. We analytically obtain the mean and variance of the stationary responses of the HR and the 2D models to white noise, and we derive the signal-to-fluctuation-noise ratio (SFNR) to evaluate encoding abilities of the two models. Especially when analyzing the 2D model, we calculate higher-order cumulants of a rectified Gaussian. The results show that the 2D model robustly works almost as well as the HR model in several sets of parameters estimated on the basis of experimental data.