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

Abstract

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.

Keywords: Hassenstein–Reichardt model; Motion detection; Neural coding; Two-detector model; White-noise analysis.