Motion: the long and short of it

Several authors have proposed that motion is analyzed by two separate processes: short-range and long-range. We claim that the differences between short-range and long-range motion phenomena are a direct consequence of the stimuli used in the two paradigms and are not evidence for the existence of two qualitatively different motion processes. We propose that a single style of motion analysis, similar to the well known Reichardt and Marr-Ullman motion detectors, underlies all motion phenomena. Although there are different detectors of this type specialized for different visual attributes (namely first-order and second-order stimuli), they all share the same mode of operation. We review the studies of second-order motion stimuli to show that they share the basic phenomena observed for first-order stimuli. The similarity across stimulus types suggests, not parallel streams of motion extraction, one short-range and passive and the other long-range and intelligent, but a concatenation of a common mode of initial motion extraction followed by a general inference process.     

Comments on Cavanagh and Mather (1989): coming up short (and long)

Cavanagh and Mather (1989) reviewed literature concerning the possible distinction between short- and long-range processes in motion perception and concluded that the distinction cannot be supported. Instead, they proposed that motion perception be considered on the basis of detectors for first-order (luminance, color) and second-order (first-order motion, texture, stereo) stimulus attributes. They supported their position with studies of motion based on second-order stimuli. The present paper contends that when experiments permitting the investigation of both processes in the same display are included and when criteria are examined in their totality rather than one-by-one, the original short-range/long-range distinction can be retained. Furthermore, it is argued that the first-order/second-order distinction does not represent a theoretical advancement and that studies of second-order motion can be interpreted in terms of the older distinction. It is concluded that the short-range/long-range distinction is useful and should not be abandoned.     

Ratios of template responses as the basis of semivision.

The template model starts with a layer of receptors that in the case of vision are leaky detectors or counters of photons. In many animals, the ratio of the responses of a few spectral types is the basis of colour vision irrespective of intensity. Ratios of template responses are now introduced as the basis of form discrimination. In insects, the second-order neurons on the visual pathway appear to detect temporal contrast at the spatial resolution of the retina. At the next level, in the optic medulla, we find a large number of small local neurons in a column on each visual axis. The template theory is a hypothesis about how the above system functions. All possible combinations of positive, indeterminate or negative temporal contrast are considered, at two adjacent visual axes at two successive instants, giving 81 possible local templates. These templates are therefore phasic detectors of all the possible spatiotemporal contrast combinations. Some of the template responses indicate polarity of edge, flicker, or direction of motion and other abstracted features of the stimulus pattern with the maximum spatial and temporal resolution. The ratios of numbers of template responses, in higher fields at a higher level, yield quantitative measures of the qualities of edges independently of the number of edges, but taking ratios causes a corresponding loss of the spatiotemporal resolution and the pattern within each field. Templates respond to transients without computation, are readily modified or selected in evolution and can be simulated in artificial vision.     

Motion detection, noise reduction, texture suppression, and contour enhancement by spatiotemporal Gabor filters with surround inhibition

We study the orientation and speed tuning properties of spatiotemporal three-dimensional (3D) Gabor and motion energy filters as models of time-dependent receptive fields of simple and complex cells in the primary visual cortex (V1). We augment the motion energy operator with surround suppression to model the inhibitory effect of stimuli outside the classical receptive field. We show that spatiotemporal integration and surround suppression lead to substantial noise reduction. We propose an effective and straightforward motion detection computation that uses the population code of a set of motion energy filters tuned to different velocities. We also show that surround inhibition leads to suppression of texture and thus improves the visibility of object contours and facilitates figure/ground segregation and the detection and recognition of objects.     

Mechanisms of dendritic integration underlying gain control in fly motion-sensitive interneurons

In the compensatory optomotor response of the fly the interesting phenomenon of gain control has been observed by Reichardt and colleagues (Reichardt et al., 1983): The amplitude of the response tends to saturate with increasing stimulus size, but different saturation plateaus are assumed with different velocities at which the stimulus is moving. This characteristic can already be found in the motion-sensitive large field neurons of the fly optic lobes that play a role in mediating this behavioral response (Hausen, 1982; Reichardt et al, 1983; Egelhaaf, 1985; Haag et al., 1992). To account for gain control a model was proposed involving shunting inhibition of these cells by another cell, the so-called pool cell (Reichardt et al., 1983), both cells sharing common input from an array of local motion detectors. This article describes an alternative model which only requires dendritic integration of the output signals of two types of local motion detectors with opposite polarity. The explanation of gain control relies on recent findings that these input elements are not perfectly directionally selective and that their direction selectivity is a function of pattern velocity. As a consequence, the resulting postsynaptic potential in the dendrite of the integrating cell saturates with increasing pattern size at a level between the excitatory and inhibitory reversal potentials. The exact value of saturation is then set by the activation ratio of excitatory and inhibitory input elements which in turn is a function of other stimulus parameters such as pattern velocity. Thus, the apparently complex phenomenon of gain control can be simply explained by the biophysics of dendritic integration in conjunction with the properties of the motion-sensitive input elements.     

A computational model of the analysis of some first-order and second-order motion patterns by simple and complex cells.

Although spatio-temporal gradient schemes are widely used in the computation of image motion, algorithms are ill conditioned for particular classes of input. This paper addresses this problem. Motion is computed as the space-time direction in which the difference in image illuminance from the local mean is conserved. This method can reliably detect motion in first-order and some second-order motion stimuli. Components of the model can be identified with directionally asymmetric and directionally selective simple cells. A stage in which we compute spatial and temporal derivatives of the difference between image illuminance and the local mean illuminance using a truncated Taylor series gives rise to a phase-invariant output reminiscent of the response of complex cells.     

Cellular basis for the response to second-order motion cues in Y retinal ganglion cells.

We perceive motion when presented with spatiotemporal changes in contrast (second-order cue). This requires linear signals to be rectified and then summed in temporal order to compute direction. Although both operations have been attributed to cortex, rectification might occur in retina, prior to the ganglion cell. Here we show that the Y ganglion cell does indeed respond to spatiotemporal contrast modulations of a second-order motion stimulus. Responses in an OFF ganglion cell are caused by an EPSP/IPSP sequence evoked from within the dendritic field; in ON cells inhibition is indirect. Inhibitory effects, which are blocked by tetrodotoxin, clamp the response near resting potential thus preventing saturation. Apparently the computation for second-order motion can be initiated by Y cells and completed by cortical cells that sum outputs of multiple Y cells in a directionally selective manner.     

一种感知视觉运动信息的简化脑模型

视觉运动信息的感知过程,包括从局域运动检测到对模式整体运动的感知过程.我们以蝇视觉系统的图形-背景相对运动分辨的神经回路网络为基本框架,采用初级运动检测器的六角形阵列作为输入层,构造了一种感知视觉运动信息的简化脑模型,模拟了运动信息应该神经计算模型各个层次上的处理.该模型对差分行为实验结果作出了正确预测.本文并对空间生理整合的神经机制作了讨论.     

Comparing internal models of the dynamics of the visual environment

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion.We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.     

Texture discrimination by Gabor functions

A 2D Gabor filter can be realized as a sinusoidal plane wave of some frequency and orientation within a two dimensional Gaussian envelope. Its spatial extent, frequency and orientation preferences as well as bandwidths are easily controlled by the parameters used in generating the filters. However, there is an uncertainty relation associated with linear filters which limits the resolution simultaneously attainable in space and frequency. Daugman (1985) has determined that 2D Gabor filters are members of a class of functions achieving optimal joint resolution in the 2D space and 2D frequency domains. They have also been found to be a good model for two dimensional receptive fields of simple cells in the striate cortex (Jones 1985; Jones et al. 1985).The characteristic of optimal joint resolution in both space and frequency suggests that these filters are appropriate operators for tasks requiring simultaneous measurement in these domains. Texture discrimination is such a task. Computer application of a set of Gabor filters to a variety of textures found to be preattentively discriminable produces results in which differently textured regions are distinguished by firstorder differences in the values measured by the filters. This ability to reduce the statistical complexity distinguishing differently textured region as well as the sensitivity of these filters to certain types of local features suggest that Gabor functions can act as detectors of certain texton types. The performance of the computer models suggests that cortical neurons with Gabor like receptive fields may be involved in preattentive texture discrimination.     

System analysis of Phycomyces light-growth response with gaussian white-noise test stimuli

The light-growth response of the Phycomyces sporangiophore is a transient change of elongation rate in response to changes in ambient blue-light intensity. The white-noise method of nonlinear system identification (Wiener-Lee-Schetzen theory) has been applied to this response, and the results have been interpreted by system analysis methods in the frequency domain. Experiments were performed on the Phycomyces tracking machine. Gaussian white-noise stimulus patterns were applied to the logarithm of the light intensity. The log-mean intensity of the broadband blue illumination was 0.1 W m^-2 and the standard deviation of the Gaussian white-noise was 0.58 decades. The results, in the form of temporal functions called Wiener kernels, represent the input-output relation of the light-growth response system. The transfer function, which was obtained as the Fourier transform of the first-order kernel, was analyzed in the frequency domain in terms of a dynamic model that consisted of a first-order high-pass filter, two secondorder low-pass filters, a delay element, and a gain factor. Parameters in the model (cutoff frequencies, damping coefficients, latency, and gain constant) were evaluated by nonlinear least-squares methods applied to the complex-valued transfer function. Analysis of the second-order kernel in the frequency domain suggests that the residual nonlinearity of the system lies close to the input.     

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.     

Dynamics of cockroach ocellar neurons

The incremental responses from the second-order neurons of the ocellus of the cockroach, Periplaneta americana, have been measured. The stimulus was a white-noise-modulated light with various mean illuminances. The kernels, obtained by cross-correlating the white-noise input against the resulting response, provided a measure of incremental sensitivity as well as of response dynamics. We found that the incremental sensitivity of the second-order neurons was an exact Weber-Fechner function; white-noise-evoked responses from second-order neurons were linear; the dynamics of second-order neurons remain unchanged over a mean illuminance range of 4 log units; the small nonlinearity in the response of the second-order neuron was a simple amplitude compression; and the correlation between the white-noise input and spike discharges of the second-order neurons produced a first-order kernel similar to that of the cell's slow potential. We conclude that signal processing in the cockroach ocellus is simple but different from that in other visual systems, including vertebrate retinas and insect compound eyes, in which the system's dynamics depend on the mean illuminance.     

Isometric force generated by locust skeletal muscle: responses to single stimuli

A mathematical model of the locust hind leg extensor muscle is described. The model accounts for the force response of the muscle to well-separated input stimuli under isometric conditions. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. In developing a model it was assumed that the response to a single isolated stimulus was linear. A linear model was found to fit well to the response to an isolated stimulus. No assumptions were made about the model order and models of various order were fitted to data in the frequency domain, using a least squares fit. The stimulus can be approximated as an impulse, with the response to each stimulus well described by a linear second-order system. Using a third-order model provided a better fit to data, but the improvement in fit was marginal and the model uses one extra parameter. A fourth-order model, which is often used to describe the behaviour of isometric muscle was found to overfit the data. Using a second-order model provides a simpler way of describing the behaviour of an isometric twitch.     

Analysis of the two-dimensional receptive fields learned by the Generalized Hebbian Algorithm in response to random input

The Generalized Hebbian Algorithm has been proposed for training linear feedforward neural networks and has been proven to cause the weights to converge to the eigenvectors of the input distribution (Sanger 1989a, b). For an input distribution given by 2D Gaussian smoothed white noise inside a Gaussian window, some of the masks learned by the Generalized Hebbian Algorithm resemble edge and bar detectors. Since these do not match the form of the actual eigenvectors of this distribution (Linsker 1987, 1990), we seek an explanation of the development of the masks prior to complete convergence to the correct solution. Analysis in the spatial and spatial frequency domains sheds light on this development, and shows that the masks which occur tend to be localized in the spatial frequency domain, reminiscent of one of the properties of 2D Gabor filters proposed by Daugman ( 1980, 1985) as a model for the receptive fields of cells in primate visual cortex.     

二阶运动条件下闪现滞后现象的研究

闪现滞后现象(flash—lag effect)是指运动物体旁闪现的物体在知觉中物体落后于运动物体的现象。对这个现象,有一种解释认为视网膜上对运动刺激的外推机制对闪现滞后现象有相当的贡献．用视网膜外推机制不再有效的二阶运动刺激取代前人实验中的一阶运动刺激来研究闪现滞后现象,发现在视网膜推断机制失效的情况下,闪现滞后现象并没有减小,而是和一阶运动刺激条件下的量相当。结果表明,视网膜上的加工机制并不是闪现滞后现象的主要原因,并提示闪现滞后现象的机制可能位于一、二阶运动加工通道的汇合阶段以上。     

Properties of individual movement detectors as derived from behavioural experiments on the visual system of the fly

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.     

Computational principles underlying the recognition of acoustic signals in insects

Many animals produce pulse-like signals during acoustic communication. These signals exhibit structure on two time scales: they consist of trains of pulses that are often broadcast in packets—so called chirps. Temporal parameters of the pulse and of the chirp are decisive for female preference. Despite these signals being produced by animals from many different taxa (e.g. frogs, grasshoppers, crickets, bushcrickets, flies), a general framework for their evaluation is still lacking. We propose such a framework, based on a simple and physiologically plausible model. The model consists of feature detectors, whose time-varying output is averaged over the signal and then linearly combined to yield the behavioral preference. We fitted this model to large data sets collected in two species of crickets and found that Gabor filters—known from visual and auditory physiology—explain the preference functions in these two species very well. We further explored the properties of Gabor filters and found a systematic relationship between parameters of the filters and the shape of preference functions. Although these Gabor filters were relatively short, they were also able to explain aspects of the preference for signal parameters on the longer time scale due to the integration step in our model. Our framework explains a wide range of phenomena associated with female preference for a widespread class of signals in an intuitive and physiologically plausible fashion. This approach thus constitutes a valuable tool to understand the functioning and evolution of communication systems in many species.     

Influence of Correspondence Noise and Spatial Scaling on the Upper Limit for Spatial Displacement in Fully-Coherent Random-Dot Kinematogram Stimuli

Correspondence noise is a major factor limiting direction discrimination performance in random-dot kinematograms [1]. In the current study we investigated the influence of correspondence noise on Dmax, which is the upper limit for the spatial displacement of the dots for which coherent motion is still perceived. Human direction discrimination performance was measured, using 2-frame kinematograms having leftward/rightward motion, over a 200-fold range of dot-densities and a four-fold range of dot displacements. From this data Dmax was estimated for the different dot densities tested. A model was proposed to evaluate the correspondence noise in the stimulus. This model summed the outputs of a set of elementary Reichardt-type local detectors that had receptive fields tiling the stimulus and were tuned to the two directions of motion in the stimulus. A key assumption of the model was that the local detectors would have the radius of their catchment areas scaled with the displacement that they were tuned to detect; the scaling factor k linking the radius to the displacement was the only free parameter in the model and a single value of k was used to fit all of the psychophysical data collected. This minimal, correspondence-noise based model was able to account for 91% of the variability in the human performance across all of the conditions tested. The results highlight the importance of correspondence noise in constraining the largest displacement that can be detected.     

Processing of figure and background motion in the visual system of the fly

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.