Correlation versus gradient type motion detectors: the pros and cons

Abstract

Visual motion contains a wealth of information about self-motion as well as the three-dimensional structure of the environment. Therefore, it is of utmost importance for any organism with eyes. However, visual motion information is not explicitly represented at the photoreceptor level, but rather has to be computed by the nervous system from the changing retinal images as one of the first processing steps. Two prominent models have been proposed to account for this neural computation: the Reichardt detector and the gradient detector. While the Reichardt detector correlates the luminance levels derived from two adjacent image points, the gradient detector provides an estimate of the local retinal image velocity by dividing the spatial and the temporal luminance gradient. As a consequence of their different internal processing structure, both the models differ in a number of functional aspects such as their dependence on the spatial-pattern structure as well as their sensitivity to photon noise. These different properties lead to the proposal that an ideal motion detector should be of Reichardt type at low luminance levels, but of gradient type at high luminance levels. However, experiments on the fly visual systems provided unambiguous evidence in favour of the Reichardt detector under all luminance conditions. Does this mean that the fly nervous system uses suboptimal computations, or is there a functional aspect missing in the optimality criterion? In the following, I will argue in favour of the latter, showing that Reichardt detectors have an automatic gain control allowing them to dynamically adjust their input-output relationships to the statistical range of velocities presented, while gradient detectors do not have this property. As a consequence, Reichardt detectors, but not gradient detectors, always provide a maximum amount of information about stimulus velocity over a large range of velocities. This important property might explain why Reichardt type of computations have been demonstrated to underlie the extraction of motion information in the fly visual system under all luminance levels.

Figure 1

Two competing mechanisms proposed to underlie direction selectivity in fly motion detection. (a) Reichardt detector. It consists of two mirror-symmetrical subunits. In each subunit, the luminance values as measured in two adjacent image locations become multiplied (M) with each other after one of them is delayed by a low-pass filter with time constant τ. The resulting output signals of the multipliers become finally subtracted. (b) Gradient detector. The temporal luminance gradient as measured after one photoreceptor (δI/δt, to the left) is divided by the spatial luminance gradient (δI/δx).

Figure 2

Steady-state velocity dependence of (a) Reichardt and (b) gradient detectors in response to moving sine gratings (spatial wavelength λ as indicated). The Reichardt detector shows a peaked velocity dependence. For velocities higher than the optimal velocity, the response gradually returns to 0. Furthermore, the optimal velocity is different for different pattern wavelengths. In contrast, the response of the gradient detector follows the pattern velocity in a linear way and is independent of the pattern wavelength.

Figure 3

Signal-to-noise ratios of Reichardt and gradient detector responses at low luminance levels. A sine grating of 100% contrast was moved with a Gaussian velocity fluctuation at a luminance level corrupted by photon noise corresponding to 1 cd m⁻². The velocity waveform was created by a white-noise signal with an autocorrelation time constant of 100 ms and a standard deviation σ of 5 Hz. The resulting signal and noise spectra at the output of the detector arrays are shown for both types of detectors. Reichardt detectors perform much better than gradient detectors under such conditions, resulting in high information rates for Reichardt detectors and negligible ones for gradient detectors.

Figure 4

Dynamic gain control in Reichardt detectors. Using a white-noise velocity stimulus with three different amplitudes (indicated in temporal frequencies corresponding to the number of periods passing one image location per second), the Reichardt detector can be seen to adapt its velocity gain to the stimulus statistics (a). Owing to this adaptive gain control, the information rate rises only by a small amount with increasing stimulus amplitude (c). The same phenomenon is observed in the fly motion-sensitive neuron H1 (b, d; data from Brenner et al. 2000). Note that in this simulation, in order to compare the model and experimental data in a one-to-one fashion and to use identical software to evaluate responses from both sources, the output of the Reichardt detector array was used to drive a leaky integrate-and-fire neuron, resulting in a spike output of the model too. Information was calculated from the spike output according to the method as outlined in de Ruyter et al. (1997) and Borst (2003).

Figure 5

Gradient detectors do not show adaptive gain control: when stimulated by white-noise velocity fluctuations with three different amplitudes, identical stimulus–response curves are obtained.

Figure 6

Response histograms of Reichardt and gradient detectors stimulated by white-noise velocity fluctuations with three different amplitudes. Whereas Reichardt detectors exhibit similar response distributions, gradient detector response distributions simply follow the corresponding stimulus distributions.