As an animal moves through the world, the array of its photoreceptors typically receives a complicated, fluctuating spatiotemporal pattern of stimuli, which is corrupted by photon shot noise, and blurred by the optics. It is the brain’s job to make sense of this complex high-dimensional data stream. We are interested in how the fly’s brain performs this job, and, more specifically, in the design principles underlying its computations. With motion estimation as an example of a neural computation I will present two approaches to this question:

1)  Using a simple custom-built camera coupled to a rotation sensor, we sample the joint statistics of rotational motion and visual input during a walk in a natural environment. From these data we obtain directly the conditional probability distribution describing the distribution of rotational velocities conditional on visual input. The conditional mean of that distribution defines an optimal velocity estimator for natural visual input signals. This estimator is biased: For example, it underestimates velocity if visual contrast is low. We compare its predictions to responses of H1, a motion sensitive neuron in the blowfly visual system. In laboratory experiments we find that H1 gives a biased readout of velocity very reminiscent of the bias in the optimal estimator.

2)  We quantify how accurately H1 represents motion in natural conditions by recording from this cell with the fly spinning on a motor outdoors. For behaviorally relevant visual stimuli, H1 increases the precision of motion estimation if the statistical quality of the visual input improves: For example, at noon the neural response is much more reproducible than around sunset. Even a relatively small decrease in light intensity produces a measurable decrease in information transmission, suggesting that H1’s precision is limited by photon shot noise.

Both these findings indicate that motion estimation by the fly’s brain approaches an optimal strategy within the context of real world visual statistics. This interpretation unifies two disparate models of motion estimation, namely the Reichardt correlator model and the gradient model. These models should be seen as extremes on a continuum, the first being optimal at low, the second at high signal to noise ratio of the visual input.