Contributed Talks I: The role of fixational drift in the Vernier task

We develop a simple one-dimensional continuum model of the Vernier discrimination task to study the impact of Gaussian blur, fixational drift, receptor noise, and retinal adaptation on an ideal observer's Vernier performance. Two rectangular stimuli with a prescribed width and relative offset are subjected to a Gaussian blur. Fixational drift shifts the resulting signal with time. The perceived signal is the weighted average over the history of local stimulation encoded by an adaptation kernel. We model this kernel as a difference of two exponentials, introducing two timescales describing initial integration and eventual recovery of a receptor. Ultimately, Gaussian white noise is added to capture random receptor fluctuations. Based on the Bayesian estimation of location and relative offset of both stimuli, we can study Vernier performance through numerical simulation as well as through analytical approximation for different eye movements. Analyzing diffusive motion in particular, we extract the diffusion constant that optimizes stimulus localization for long observation times. This optimal diffusion constant is inversely proportional to an average of the two timescales describing adaptation and proportional to the square of the larger of stimulus size or blurring width, giving rise to two separate regimes. We generalize our analysis to optimize discrimination and extend the class of eye motions considered beyond purely diffusive drift, e.g. with the inclusion of persistence.