Notes: 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.

Notes: Abstract The performance of the fly's movement detection system is analysed using the visually induced yaw torque generated during tethered flight as a behavioural indicator. In earlier studies usually large parts of the visual field were exposed to the movement stimuli; the fly's response, therefore, represented the spatially pooled output signals of a large number of local movement detectors. Here we examined the responses of individual movement detectors. The stimulus pattern was presented to the fly via small vertical slits, thus, nearly avoiding spatial integration of local movement information along the horizontal axis of the eye. The stimulus consisted of a vertically oriented sine-wave grating which was moved with a constant velocity either clockwise or counterclockwise. In agreement with the theory of movement detectors of the correlation type, the time-course of the detector signal is modulated with the spatial phase of the stimulus pattern. It can even assume negative values for some time during the response cycle and thus signal the wrong direction of motion. By spatially integrating the response over sufficiently large arrays of movement detectors these response modulations disappear. Finally, one obtains a signal of the movement detection system which is constant while the pattern moves in one direction and only changes its sign when the pattern reverses its direction of motion. Spatial integration thus represents a simple means to obtain a meaningful representations of motion information.

Notes: Abstract The local extraction of motion information from brightness patterns by individual movement detectors of the correlation-type is considered in the first part of the paper. A two-dimensional field theory of movement detection is developed by treating the distance between two adjacent photoreceptors as a differential. In the first approximation of the theory we only consider linear terms of the time interval between the reception of a contrast element and its delayed representation by the detector and linear terms of the spatial distances between adjacent photoreceptors. As a result we may neglect terms of higher order than quadratic in a Taylor series development of the brightness pattern. The responses of pairs of individual movement detectors are combined to a local response vector. In the first approximation of the detector field theory the response vector is proportional to the instantaneous pattern velocity vector and linearly dependent on local properties of the moving pattern. The linear dependence on pattern properties is represented by a two by two tensor consisting of elements which are nonlinear, local functional of the moving pattern. Some of the properties of the tensor elements are treated in detail. So, for instance, it is shown that the off-diagonal elements of the tensor disappear when the moving pattern consists of x- and y-dependent separable components. In the second part of the paper the tensor relation leading to the output of a movement detector pair is spatially integrated. The result of the integration is an approximation to a summation of the outputs of an array of detector pairs. The spatially integrated detector tensor relates the translatory motion vector to the resultant output vector. It is shown that the angle between the motion vector and the resultant output vector is always smaller than ±90° whereas the angle between the motion vector and local response vectors, elicited by detector pairs, may cover the entire angular range. In the discussion of the paper the limits of the field theory for motion computation as well as its higher approximations are pointed out in some detail. In a special chapter the dependence of the detector response on the pattern properties is treated and in another chapter questions connected with the so called aperture problem are discussed. Furthermore, properties for compensation of the pattern dependent deviation angle by spatial physiological integration are mentioned in the discussion.

Notes: Abstract This paper investigates the problem of spontaneous pattern discrimination by the visual system of the fly. The indicator for discrimination and attractivity of a pattern is the yaw torque of a test fly. It is shown that the pattern discrimination process may be treated as a special (“degenerate”) case of figureground discrimination which has been described in detail in earlier publications. Decisive for the discrimination process is the fact that pattern discrimination by the fly is mediated by motion detectors which respond not only a pattern velocity but also to structural properties of pattern contrast. This is demonstrated by the transition from the existing twodimensional array of motion detectors to a continuous detector field which enabled us to calculate instantaneous detector responses to instationary pattern motion. The new approach, together with the special theory for figure-ground discrimination, is then applied to predict spontaneous discriminations of onedimensional periodic patterns. It is shown that predictions and experimental results are in good agreement. The second set of discrimination experiments deals with two dimensional dot patterns for which a quantitative theory is not yet available. However, it is shown that the attractivity of a dot pattern crucially depends on both the orientation and the direction of motion relative to the fly's eyes. If the contrast of a moving dot elicits an event in a motion detector which through the detector's time constant leads to an interference with an event received by a preceeding dot, the attractivity of the dot pattern is diminished. In the discussion relations are drawn between the concepts of pattern discrimination in honey bees and the theoretical aspects of discrimination put forward in this paper. It is briefly discussed why a two-dimensional motion detector theory might become the key for an understanding of pattern categories like “figural intensity” and “figural quality”.

Notes: Abstract The visual system of the fly is able to extract different types of global retinal motion patterns as may be induced on the eyes during different flight maneuvers and to use this information to control visual orientation. The mechanisms underlying these tasks were analyzed by a combination of quantitative behavioral experiments on tethered flying flies (Musca domestica) and model simulations using different conditions of oscillatory large-field motion and relative motion of different segments of the stimulus pattern. Only torque responses about the vertical axis of the animal were determined. The stimulus patterns consisted of random dot textures (“Julesz patterns”) which could be moved either horizontally or vertically. Horizontal rotatory large-field motion leads to compensatory optomotor turning responses, which under natural conditions would tend to stabilize the retinal image. The response amplitude depends on the oscillation frequency: It is much larger at low oscillation frequencies than at high ones. When an object and its background move relative to each other, the object may, in principle, be discriminated and then induce turning responses of the fly towards the object. However, whether the object is distinguished by the fly depends not only on the phase relationship between object and background motion but also on the oscillation frequency. At all phase relations tested, the object is detected only at high oscillation frequencies. For the patterns used here, the turning responses are only affected by motion along the horizontal axis of the eye. No influences caused by vertical motion could be detected. The experimental data can be explained best by assuming two parallel control systems with different temporal and spatial integration properties: TheLF-system which is most sensitive to coherent rotatory large-field motion and mediates compensatory optomotor responses mainly at low oscillation frequencies. In contrast, theSF-system is tuned to small-field and relative motion and thus specialized to discriminate a moving object from its background; it mediates turning responses towards objects mainly at high oscillation frequencies. The principal organization of the neural networks underlying these control systems could be derived from the characteristic features of the responses to the different stimulus conditions. The input to the model circuits responsible for the characteristic sensitivity of the SF-system to small-field and relative motion is provided by retinotopic arrays of local movement detectors. The movement detectors are integrated by a large-field element, the output cell of the network. The synapses between the detectors and the output cells have nonlinear transmission characteristics. Another type of large-field elements (“pool cells”) which respond to motion in front of both eyes and have characteristic direction selectivities are assumed to interact with the local movement detector channels by inhibitory synapses of the shunting type, before the movement detectors are integrated by the output cells. The properties of the LF-system can be accounted for by similar model circuits which, however, differ with respect to the transmission characteristic of the synapses between the movement detectors and the output cell; moreover, their pool cells are only monocular. This type of network, however, is not necessary to account for the functional properties of the LF-system. Instead, intrinsic properties of single neurons may be sufficient. Computer simulations of the postulated mechanisms of the SF-and LF-system reveal that these can account for the specific features of the behavioral responses under quite different conditions of coherent large-field motion and relative motion of different pattern segments.