Dynamic response properties of movement detectors: Theoretical analysis and electrophysiological investigation in the visual system of the fly

Abstract

Dynamic aspects of the computation of visual motion information are analysed both theoretically and experimentally. The theoretical analysis is based on the type of movement detector which has been proposed to be realized in the visual system of insects (e.g. Hassenstein and Reichardt 1956; Reichardt 1957, 1961; Buchner 1984), but also of man (e.g. van Doorn and Koenderink 1982a, b; van Santen and Sperling 1984; Wilson 1985). The output of both a single movement detector and a one-dimensional array of detectors is formulated mathematically as a function of time. The resulting movement detector theory can be applied to a much wider range of moving stimuli than has been possible on the basis of previous formulations of the detector output. These stimuli comprise one-dimensional “smooth” detector input functions, i.e. functions which can be expanded into a time-dependent convergent Taylor series for any value of the spatial coordinate.

The movement detector response can be represented by a power series. Each term of this series consists of one exclusively time-dependent component and of another component that depends, in addition, on the properties of the pattern. Even the exclusively time-dependent components of the movement detector output are not solely determined by the stimulus velocity. They rather depend in a non-linear way on the weighted sum of the instantaneous velocity and all its higher order time derivatives. The latter point represents another reason — not discussed so far in the literature — that movement detectors of the type analysed here do not represent pure velocity sensors.

The significance of this movement detector theory is established for the visual system of the fly. This is done by comparing the spatially integrated movement detector response with the functional properties of the directionally-selective motion-sensitive. Horizontal Cells of the third visual ganglion of the fly's brain.

These integrate local motion information over large parts of the visual field. The time course of the spatially integrated movement detector response is about proportional to the velocity of the stimulus pattern only as long as the pattern velocity and its time derivatives are sufficiently small. For large velocities and velocity changes of the stimulus pattern characteristic deviations of the response profiles from being proportional to pattern velocity are predicted on the basis of the detector theory developed here. These deviations are clearly reflected in the response of the wide-field Horizontal Cells, thus, providing very specific evidence that the movement detector theory developed here can be applied to motion detection in the fly. The characteristic dynamic features of the theoretically predicted and the experimentally determined cellular responses are exploited to estimate the time constant of the movement detector filter.