Pitching in for optimal (yaw) estimation

The fly visual system can estimate motion with an accuracy close to the limits set by the physical properties of the input signals. This requires the fly's brain to use specific algorithms that balance systematic and random errors; the structure of these algorithms can be predicted if we know the statistical structure of the relevant signals. The FlEye camera is a custom-designed device that mimics optical sampling by the fly visual system, but at higher SNR, and we can use this instrument to sample the joint distribution of movies and motion in natural environments. Here we report on the use of these data to construct the optimal local estimator of yaw velocity from the spatial and temporal gradients of the image. Naively, yaw velocity should be related to spatial gradients along the azimuthal axis. When the orthogonal (pitch) gradients are small, the optimal mapping from azimuthal and temporal gradients to yaw velocity is similar to what we see if we ignore pitch entirely. But as pitch gradients increase, estimation becomes less reliable and contours of constant estimated velocity shift toward larger spatial and temporal derivatives. These contours form cone-like structures in the full gradient space, because larger pitch gradients effectively introduce extra noise into yaw estimation. This noise-like effect mirrors previous findings from wide-field motion-sensitive neurons in the blowfly visual system, and we explore how these algorithms might be embedded in the circuitry of motion-sensitive neurons.