An astable multivibrator model of binocular rivalry

Perception, 1988, volume 17, pages 215-228

An astable multivibrator model of binocular rivalry

Sidney R Lehky Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, USA Received 8 June 1987; in revised form 14 March 1988

Abstract. The behavior of a neural network model for binocular rivalry is explored through the development of an analogy between it and an electronic astable multivibrator circuit. The model incorporates reciprocal feedback inhibition between signals from the left and the right eyes prior to binocular convergence. The strength of inhibitory coupling determines whether the system undergoes rivalrous oscillations or remains in stable fusion: strong coupling leads to oscillations, weak coupling to fusion. This implies that correlation between spatial patterns presented to the two eyes can affect the strength of binocular inhibition. Finally, computer simulations are presented which show that a reciprocal inhibition model can reproduce the stochastic behavior of rivalry. The model described is a counterexample to claims that reciprocal inhibition models as a class cannot exhibit many of the experimentally observed properties of rivalry. 1 Introduction When incompatible images are presented to the two eyes the visual system is thrown into oscillations, so that first the image from one eye is visible, and then that from the other, typically with a period of about 1 s. This is called binocular rivalry. The response is often provoked by presenting nonmatching contours to the two eyes, such as having one eye view horizontal stripes, and the other vertical stripes. In general, the entire visual field does not oscillate in unison, but rather forms a fluid patchwork in which constantly changing bits and pieces of the two images are visible. A reversal from suppression to dominance often appears to start as a local fluctuation, which then spreads outward to form a patch. However, if the rivalrous stimulus is kept small, within a diameter of about 1.0 deg visual angle, the entire stimulus will oscillate together. Two basic theories of binocular rivalry exist. The first is that rivalry is caused by shifts in attention between the two eyes, under conscious control. This was the point of view held by Helmholtz (1909/1962), among others. The second is that rivalry results from the operation of some sort of free-running oscillator. This has been the opinion of many researchers in recent years, and is the viewpoint taken here. (A comprehensive historical review of theories of binocular rivalry can be found in O'Shea 1983.) In adopting the 'free-running oscillator' hypothesis, however, one need not deny that there are significant attentional effects which modulate rivalry (see Lack 1978). The model I am proposing in this paper incorporates reciprocal feedback inhibition between signals from the two eyes (figure 1) to produce oscillations. In essence, reciprocal inhibition models work in the following way. Initially, the dominant side exerts a strong inhibitory influence on the opposite side, thereby suppressing it. Gradually, this inhibition adapts, or fatigues, downward. As inhibition weakens, a point is reached at which the suppressed side is released and becomes dominant, and the previously dominant side becomes suppressed. At this point the cycle restarts. In the simple form I have just outlined, reciprocal inhibition is among the more obvious models and has been around for some time. What I shall discuss here is a variant which will answer some objections that have been raised to reciprocal inhibition models in general. These objections have been outlined by, among others, Walker (1978), who favors an attentional theory of rivalry, and by Fox and Rasche (1969), who

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favor a different form of oscillator. My presentation of the model centers around an analogy between the binocular visual system and an electronic astable multivibrator circuit. I shall argue that the astable multivibrator is an example of an oscillator based on reciprocal inhibition which shows many properties of rivalry. I have previously (1983) presented a model of binocular brightness perception during fused binocular vision that involved reciprocal feedback inhibition of the sort shown in figure 1. That discussion is extended here to a consideration of reciprocal inhibition during rivalry.

Left

Right

Figure 1. Diagram of a neural network model. Peripheral inputs from the left and the right sides synapse onto neurons A and B. There is reciprocal feedback inhibition between the two sides prior to binocular convergence at neuron C. The black disks represent inhibitory neurons. [Lehky (1983) includes additional circuitry within the inhibitory feedback loop that acts as a gain control which allows the model to operate at different mean luminance levels. For the present purposes its presence is irrelevant, and so it is not depicted here.] 2 Background Prominent among early studies of binocular rivalry are those of Helmholtz (1909/1962) and Breese (1899). In recent years a large number of quantitative psychophysical studies have been conducted on the subject, and in this section I outline some data of particular relevance to the model. Of seminal importance has been the work of Levelt (1965). One interesting and important observation he made concerned the effects of stimulus strength on the durations for which each eye is dominant during rivalrous oscillations. He found that increasing the stimulus strength to one eye affected only the opposite eye, decreasing the durations that it was dominant, while not affecting durations of dominance of the ipsilateral eye. This curious effect has been confirmed by others (Fox and Rasche 1969; Blake 1977; Fahle 1982). Two consequences of this are that increasing the stimulus strength to one eye changes the duty cycle of the oscillation, and also increases the frequency of the oscillation. A major determinant of stimulus strength is contrast (Alexander and Bricker 1952; Levelt 1965; Fahle 1982), whereas changes in luminance have weaker effects. The presence of sharp contours also increases the effectiveness of a rivalrous stimulus (Levelt 1965, based on the data of Alexander 1951). During rivalry, thresholds, as measured by the detection of a test probe, are elevated for stimuli presented to the suppressed eye (Blake and Camisa 1978, 1979; Fox and Check 1972; Wales and Fox 1970; Makous and Sanders 1978). Threshold elevation is said to be about 0.5 log units (Wales and Fox 1970), but this is likely to be an underestimate, since flashing a test stimulus produces temporal transients that probably perturb the inhibitory mechanisms under study. Suppression magnitude is reported to be constant over the duration of a suppressed phase, ie the oscillations of binocular rivalry have a waveform that is more nearly rectangular than sinusoidal or sawtooth.

Model of binocular rivalry

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This was demonstrated by observing that the detectability of a test stimulus was reduced by a constant amount when measured at various times after the onset of the suppressed phase (Fox and Check 1972). 3 Stochastic properties of binocular rivalry Everything that I have said about durations of dominant and suppressed phases in binocular rivalry refers to averages taken over a large number of cycles. The duration of an individual phase is random. Stochastic properties of rivalry have been the subject of a number of studies (Levelt 1965; Fox and Herrmann 1967; Blake et al 1971; Fox et al 1975; Walker 1975), and these are of interest here because in the simulations I present below I shall attempt to reproduce their results. Typical statistical distributions for the durations of rivalrous phases are shown in figures 5b and 5c, and curves for a gamma distribution have been superimposed on these histograms. In the experimental literature, gamma distributions are commonly fit to the data, and they fit reasonably well. Nevertheless, it must be emphasized that the selection of a gamma distribution is empirical. Although it serves a useful descriptive role, there is no reason to believe that the equation describing the distribution or any of its associated parameters have any theoretical significance in relation to the physical mechanisms of rivalry. The equation for a gamma distribution is: fiaxa~lexp{-px) T(a)

'

Uj

where T{a) = (a-l)\. This distribution is generally thought of as representing the waiting time for the ath event when a single event has an exponential waiting time with parameter ft (ie a Poisson process). The parameters a and ft can be estimated from the data by the relations x2 a =— o

and

x f5 = — , a

(2)

where x is the mean and a2 the variance of measured phase durations. (These are not maximum likelihood estimates, but nevertheless produce reasonable results and are easy to compute.) To facilitate comparison of data taken from different subjects and different stimulus conditions, data are usually normalized by adjusting the mean to equal 1.0. Inspection of equation 2 shows that this normalization procedure makes both parameters of the gamma distribution a single number, which is the reciprocal of the variance of the normalized data. All the studies cited above agree that this number is about 4 (estimates range from 3 to 5). In other words, setting both parameters of the gamma distribution equal to 4 gives a good fit to the normalized data. Another statistical feature of binocular rivalry is that the durations of successive phases are uncorrelated. This can be seen in the autocorrelation function for phase durations shown in figure 6b (taken from Fox and Herrmann 1967). The autocorrelation function has also been calculated by Blake et al (1971), Fox et al (1975), and Walker (1975), all of whom also carried out the Lathrop test for sequential independence in a time series. In every case they found that successive durations are statistically independent. [Interestingly, the stochastic features of durations between reversals in the perception of ambiguous figures, such as the Necker cube or Schroeder staircase, are very similar to those of binocular rivalry (Borsellino et al 1972).] 4 Objections to a reciprocal inhibition model The first objection arises from observations, described above, in section 2, that increasing the stimulus strength to one eye has an asymmetric effect on phase durations.

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Mean durations of dominance of the contralateral eye are decreased, whereas those of the ipsilateral eye are unaffected. Fox and Rasche (1969) conjecture that this is incompatible with reciprocal inhibition. They argue that if reciprocal inhibition were occurring, an increase in duration of dominance of one eye necessarily entails a reciprocal decrease in duration of dominance of the other eye. The second objection arises from the observation that the strength of suppression during rivalry appears constant over the duration of a suppressed phase. Fox and Check (1972) believe that in a reciprocal inhibition model, strength of suppression should gradually decrease, so that the waveform of the oscillations should be roughly triangular (sawtooth) rather than rectangular. Finally, the third objection revolves around the statistical independence of the durations of successive dominant and suppressed phases in binocular rivalry. It has been suggested (eg by Walker 1978) that in a reciprocal inhibition model with adaptating inhibition, successive phase durations ought to be positively correlated. One version of this argument is the following. If a dominant phase is longer than average, then adaptation on the opposite (suppressed) side has more time to recover. Therefore, when the opposite side becomes dominant it too will have a longer-thanaverage duration. In the following sections, I shall answer these objections by presenting a reciprocal inhibition model which does conform to observed behaviors of rivalry. 5 The binocular visual system as an astable multivibrator The astable multivibrator circuit in figure 2 is presented here as a physical model of rivalry. It is meant to be analogous to the neural network in figure 1. Rather than discuss numerical solutions to a set of coupled nonlinear differential equations for model neurons, it is easier to visualize the behavior of this simple physical system. Both the neural model and its electronic analogue should be considered as 'equivalent circuits' which capture essential dynamical behaviors of a much more complex system. Each of the single 'neurons' may in fact represent populations of functionally similar neurons. Also, this model is intended to cover binocular responses from only a small isolated patch of the visual field. The multivibrator is a simple oscillating flip-flop circuit, discussed in many electronics texts and easily constructed. Attneave (1971) has proposed basically the same circuit in connection with alternations in the perception of ambiguous figures. Outputs of the two transistors Q L and Q R (points A and B in figure 2) correspond to the outputs of neurons A and B in figure 1. Summing circuitry between points A and B has been left out because it will not enter into the discussion, and so nothing in figure 2

Figure 2. Circuit diagram of an astable multivibrator. This circuit is meant to be a physical analogue of the neural network shown in figure 1, in which transistors Q L and Q R represent neurons A and B, resistors RFL and RFR control the strength of inhibitory coupling in the reciprocal feedback inhibition pathway, and capacitors C L and CR control the adaptation time constants of the inhibition. The subscripts L and R refer to the left and the right sides, respectively.


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corresponds to the binocular neuron in figure 1. The two transistors connect in a manner which may be considered as reciprocal inhibition. The 'inhibitory' pathway from Q L to Q R runs from point A through capacitor C L and resistor RFR to the base of QR, and an analogous pathway runs from point B to the base of Q L on the other side. If the collector voltage of Q L (voltage at point A) is high, that forces the collector voltage of Q R (voltage at point B) to be close to zero, and vice versa. As the circuit oscillates, the voltages at points A and B go high alternately, causing the light emitting diodes (LEDs) on each side to flash on and off. (The LEDs are there to visualize operation of the circuit and serve no functional role.) The slow charging of capacitors CL and CR can be thought of as 'adaptation' of inhibition, and this adaptation is necessary for the system to oscillate. When the voltage of capacitor C L on one side gradually charges up to the threshold of transistor Q R on the other side, the circuit flips over to the opposite state. At this point the whole process begins again with the other capacitor and transistor, and then so on, back and forth as the system oscillates. The output of this system, as monitored at points A and B, is a rectangular oscillation. The duration that one side is 'dominant' (ie the time that its LED is on) depends on the time constant for charging the capacitor on the opposite side. For example, if the time constant for charging a capacitor is decreased, the duration of dominance on the contralateral side decreases, whereas the duration of dominance on the ipsilateral side is unaffected. The properties of this circuit show several analogies with binocular rivalry. In both systems it is possible to manipulate the durations of dominance of each side independently of each other. Moreover, in both systems the duration of dominance on one side is controlled by changing a parameter on the opposite side. In the electronic model this parameter is the time constant for charging a capacitor, whereas in rivalry it is 'stimulus strength': 'decrease capacitor time constant' is equivalent to 'increase stimulus strength'. This last point suggests the following conjecture: the effect of increasing the stimulus strength during rivalry is to increase the rate of adaptation of binocular inhibition. One further similarity between the circuit and binocular rivalry is the production of rectangular oscillations. The parts of the multivibrator showing 'adaptation' are buried within the internal workings, hidden by nonlinearities, and not visible from the output, although the adapting components control the period of the oscillations. To summarize, an astable multivibrator can be interpreted as a device that shows reciprocal inhibition with adaptation. This device has the ability, first, to produce oscillations with a rectangular waveform, and second, to vary independently the durations of the 'left dominant' and 'right dominant' phases of a cycle, both properties that are observed in binocular rivalry. These characteristics of the multivibrator falsify by counterexample claims that a reciprocal inhibition model cannot show such behaviors. 6 Binocular fusion I shall suggest here that the difference between fusion and rivalry lies in the strength of the inhibitory coupling between the left and the right sides. Weak coupling leads to fusion, strong coupling to oscillations. In the electronic circuit, strength of inhibitory coupling is controlled by the variable resistors RFL and RFR in the reciprocal feedback paths between the transistors. In the preceding discussion of oscillations of the multivibrator, it was always assumed that these feedback resistances were sufficiently small. However, if one turns the knob of a potentiometer and increases them, a particular point is reached at which the oscillations suddenly stop. This is a bifurcation point in the language of dynamical systems theory, a point at which the qualitative behavior of the system changes discontinuously as a

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paranieter is varied continuously. Instead of the LEDs flashing on and off alternately, they are now both on simultaneously, but each shining only dimly as if there were a steady, partial, 'inhibition' between the left and the right sides. When the circuit ceases to oscillate, it can be thought of as passing from a state of 'rivalry' to a state of 'fusion'. Feedback resistances in the astable multivibrator are analogous to the strength of inhibitory coupling within the neural network. Small values for the resistances of RFL and RFR correspond to strong inhibitory coupling, and larger values to weaker coupling. By 'strength of inhibitory coupling' I mean the effective synaptic weight between an inhibitory neuron and its postsynaptic target. Matsuoka (1984) has studied the role of inhibitory coupling strength in the behavior of a pair of neurons with adapting reciprocal inhibition, and has set up the model as a system of nonlinear differential equations. He has analyzed this network using stability theory, and demonstrated that one condition necessary for it to oscillate is that inhibitory coupling must be sufficiently strong. This is the same property seen in the multivibrator when one interprets feedback resistance as corresponding to coupling strength. Matsuoka's analysis suggests that, in general, inhibitory coupling strength is a critical determinant of the dynamics of a system involving adapting reciprocal inhibition. It is not a peculiarity of the circuit presented here as an example of such a system. Under this model, the difference between fusion and rivalry is determined by a single parameter, inhibitory coupling, within a single mechanism. In this respect, it differs fundamentally from the models of Cogan (1987), Julesz and Tyler (1976), and Wolfe (1986), which postulate separate fusion and rivalry mechanisms. An implication here is that the degree of correlation between the spatial patterns presented to the two eyes must affect, in some unknown manner, the strength of binocular inhibition. Although inhibitory coupling is weaker for fusion than for rivalry, there still remains substantial (but nonoscillating) binocular inhibition during fusion. Fused binocular contours have already been considered in detail in Lehky (1983), where Levelt's (1965) equibrightness curves were fit with a model basically the same as that shown in figure 1. In essence, Levelt's data showed that binocular brightness was markedly less than would be expected from a simple summation of monocular stimuli. (An informal counterpart to Levelt's findings is the observation that the world does not appear twice as bright when viewed through two eyes compared to one.) This motivated a model in which binocular output is reduced by reciprocal feedback inhibition prior to summation. Rather than repeat the discussion in Lehky (1983), the predictions of the model are simply presented in figure 3a. This shows the responses of the network set out in figure 1 when matching contours are presented to both eyes, with parameters chosen to fit the equibrightness data of Levelt (1965). Responses of the monocular units in figure 3a are only 0.56 of what they would be in the absence of reciprocal inhibition, indicating that, according to the model, substantial inhibition remains during fusion. Figure 3b shows the situation hypothesized to occur during rivalry. One side is strongly suppressed, and the other released from the tonic inhibition of the fused condition. In reality, the situation is most likely not so extreme. Activity on the suppressed side probably does not reach zero, and the dominant side may not be completely relieved of inhibition. An expectation here is that release of the dominant side from the partial suppression of the fused state leads to dominant supersensitivity (ie the eye is more sensitive during dominance than during binocular fusion). This expectation is supported by the data of Cogan (1982), who found that detectability of a test probe was increased during monocular dominance relative to that seen during fusion (his experiment 3). Corroborating this was his observation that threshold contrast decreased during dominance relative to that seen during fusion (experiment 4).

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The data of Makous and Sanders (1978) also support the existence of dominant supersensitivity. They found that the psychometric function for detecting a test probe during fusion was intermediate to the psychometric functions measured during dominance and suppression (experiment 4 of that paper). Furthermore, the average psychometric function measured during rivalry (pooling together responses during dominant and suppressed phases) was approximately equal to that measured during fusion (experiment 5). This is again what is expected under the model, since the 0.56 activity during fusion is close to the average of the 0.0 and 1.0 activities seen during dominance and suppression. [In contradiction to the data interpreted here as showing dominant supersensitivity, and in contradiction to the model, Blake and Camisa (1978) found no difference in sensitivity during dominance and fusion. However, Sanders (1980) replicated their experiments and came to the opposite conclusion.] Finally, figure 3c reflects the observation made by Bolanowski (1987) that when Ganzfelder (contourless blank fields) are presented to both eyes there is complete binocular summation, so that the world does indeed appear twice as bright when viewed through two eyes. Bolanowski (1987) also confirmed Levelfs (1965) observation of incomplete binocular summation in the presence of fused contours. The finding that binocular summation is affected by whether or not contours are present supports the idea that the strength of binocular inhibitory coupling is some function of the spatial patterns presented to the two eyes. The interpretation placed here on these data is that, for Ganzfelder, binocular inhibitory coupling is zero, but in the presence of fused contours the coupling is increased (to about 0.5). In summary, I have suggested that the difference between the binocular system being in fusion or in rivalry is the strength of inhibitory coupling in a reciprocal feedback circuit that occurs prior to binocular convergence. Strong inhibitory coupling leads to oscillatory behavior (rivalry), and weak coupling to a steady state (fusion). Although binocular inhibition during fusion is weak relative to that during rivalry, it is still substantial. Under the interpretation of the data offered here, the strengths of inhibitory coupling for the three stimulus conditions in figure 3 are ordered as follows: uncorrected contours > correlated contours > Ganzfelder. Fusion

(a)

Rivalry

Ganzfeld

(b)

Figure 3. Activities in the neural network for three patterns of binocular input; (a) correlated contours (fusion), (b) uncorrelated contours (rivalry), and (c) no contours (Ganzfelder). Numbers indicate the relative levels of activity when inputs are arbitrarily set to 1.0. Differences in activities are explained by postulating that binocular spatial correlation affects the strength of inhibitory coupling between the left and the right sides.

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7 Simulation of stochastic properties of rivalry According to the third objection to reciprocal inhibition models outlined in section 4, in such a model successive durations of dominance and suppression ought to be positively correlated. However, the data show otherwise. In this section I describe computer simulations that deal with this problem. The computer simulations were conducted of a system meant to represent the behavior of a reciprocal inhibition network with adapting inhibition. This system captures the relevant dynamical features of the multivibrator described above, but is not the same in detail. It can be thought of as an idealized noisy astable multivibrator. Its behavior in the absence of noise is illustrated in figure 4a and with noise in figure 4b. Going back to figure 4a, the output of the system is indicated by the rectangular waveform. The 'high' and low' phases of this waveform indicate whether the left or right side is dominant. The quasitriangular curves at the bottom of the figure show adaptation and recovery from adaptation for inhibition on each side. Just as with the stable multivibrator, the adapting inhibition is entirely an internal process, and not reflected in the rectangular waveform of the outputs. The behavior of the system can be described as follows. The inhibitory effect of the dominant side upon the opposite, suppressed, side adapts downward with time. Simultaneously, the suppressed side recovers from adaptation. This continues until the dominant side adapts down to a particular threshold, at which point the system flips state. Adaptation follows an exponential time course, exp(—f/t), and recovery is expresses by 1 - exp( - t/x), where x was set arbitrarily to 1.0. The effect of adding random walk noise to the inhibition curves is shown in figure 4b. The noise was generated as follows. Time was divided into small intervals At. The value of the curve in a particular interval, v /+AM was calculated by combining two components. The first, reflecting exponential adaptation, was a deterministic component dependent on the value of the curve in the previous interval, yn and the second was a random component. (This is a discrete approximation to a diffusion process with drift, but this does not imply that anything is actually diffusing in the neural model, rather that the mathematical form is the same.) This can be described by the following equations: yt+At

= ayt + bb

yt+&t= ayt + (1.0 —a) + bb

(dominant side) (suppressed side),

Left dominant Right dominant Left inhibition threshold Right inhibition threshold Time Time Figure 4. Diagram of the dynamics of the model used to simulate the stochastic properties of rivalry. Axes are both on arbitrary scales, (a) Behavior in the absence of noise. The rectangular waveform shows output of the system and indicates whether the left or the right side is dominant. Without noise, the alternations of dominance are regular. The quasitriangular waveforms show adaptation and recovery from adaptation of binocular inhibition, (b) Behavior on addition of random walk noise to the system. The rectangular waveform shows that the durations of dominance are now random.

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where 5 = +1.0 or - 1 . 0 with probability 0.5; At = 0.002; a = exp(-Af) = 0.998; and b is set according to the amount of noise desired. The system reverses state when, on the dominant side, yt = threshold, which was set to 0.05. The amount of noise can be characterized by a diffusion coefficient D, defined as: D =

(4)

At'

with b and A* as indicated in equation 3. Increasing D corresponds to increasing the noise. The presence of noise makes the durations of dominance highly variable, as is apparent in figure 4b. Phase durations under this condition are shown in figure 5a, and a gamma distribution [equation (1)] with a = fi = 4.0 is superimposed. (The best-fit gamma parameter in the simulation was a power function of the diffusion coefficient Z), with D being a free parameter.) Figures 5b and 5c show experimental data. In all cases the data (experimental and simulated) have been normalized to a mean of 1.0 and fit with a gamma distribution having the same mean and variance, and which encloses the same area. The simulated and experimental histograms resemble each other closely, and are well approximated by gamma distributions. Nevertheless, the simulated data are not described exactly by a gamma distribution, and there is no reason to expect that the experimental data are either, or that a gamma distribution offers any theoretical insight into the mechanisms of rivalry. In particular, the histogram of the simulated data has a peak which overshoots the gamma distribution by a small but significant amount. In the

1.0 (c)

2.0 3.0 Relative duration

Figure 5. (a) Simulated data, showing distribution of dominance durations produced by the model system illustrated in figure 4b. The diffusion constant, which indicates the amount of noise used in the simulation, was 0.057. Experimental data for dominance durations are given in (b) (from Levelt 1965) and (c) (from Walker 1975). In all cases the data are normalized to a mean of 1.0, and a gamma distribution with both parameters set to 4.0 is superimposed.

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experimental data (not all of which are shown here), the histogram peak also usually overshoots the gamma distribution, but because of small sample sizes this is not always statistically significant. Sequential independence of phase durations in the simulated data was examined by calculating the autocorrelation function (figure 6a). This shows a weak correlation of about 0.20 between durations of a dominant phase and the succeeding suppressed phase. There were no significant longer-range correlations, and, in particular, no correlations between the durations of successive dominant phases. For comparison, the autocorrelation function for the experimental data is shown in figure 6b. The experimental and simulated autocorrelation functions are quite similar, and differences fall within the variability of the data. Overall, the simulations show that a reciprocal inhibition model can reproduce the observed stochastic properties of binocular rivalry.

o

Lag (a) (b) Figure 6. (a) Simulated and (b) experimental autocorrelation functions for dominance durations. Experimental data are from Fox and Herrmann (1967). 8 Adaptational aftereffects Another possible objection to the model is based on the relative strengths of adaptational aftereffects measured during conditions of either fusion or rivalry. Consideration here is limited to interocular transfer of adaptation, which is the most relevant measurement. Comparisons of interocular transfer of adaptation during rivalry and fusion have been conducted by Blake and Overton (1979; measuring threshold elevation to a grating) and O'Shea and Crassini (1981; measuring a motion aftereffect). These authors found no decrease in adaptation strength when the adapting stimulus was only intermittently visible during rivalry instead of continuously visible during fusion. These data have previously been interpreted in the following way. If the interocular transfer of adaptation is not weakened under rivalrous conditions, then the site of adaptation must come before the site of binocular inhibition (adaptation -»• inhibition), assuming some form of serial organization. And since the site of binocular convergence is located at or before the site of interocular transfer of adaptation (convergence -* adaptation), the following anatomical sequence is implied: convergence -* adaptation -• inhibition (ie the site of binocular inhibition occurs after the site of binocular convergence). Interpreted in this way, the adaptation data contradict the model presented here. In answering this objection, it should be pointed out that a serial organization in which binocular inhibition comes after binocular convergence is logically impossible. In a serial system, inhibition capable of selectively blocking signals from one eye can neither originate nor terminate at a point after the site of binocular convergence.


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Although serial organization is not possible, parallel organization of channels involved in rivalry and adaptation is in principle possible, although one must struggle with the question of why activity in the pathway not subject to rivalry is not continuously visible. In any case, this strategy of postulating separate parallel channels for each experimentally observed effect produces a cumbersome and unconvincing explanation of the data. As a more parsimonious explanation, consider the following. Although the adapting stimulus is present for a shorter duration during rivalry, it is present with greater strength, which compensates for the shorter duration. This is illustrated in figure 3, in which monocular activity during the dominant phase of rivalry is higher than during fusion. This explanation depends critically upon the existence of supersensitivity during the dominant phase of rivalry, evidence for which I presented earlier. Also, under this model, the rough equivalence of adaptation strength during fusion and rivalry depends on the coincidence that the predominance of rivalrous stimuli used experimentally, and the strength of inhibition postulated by the model during fusion, were both about 0.5. Averaging across time, this leads to the same exposure to the adapting stimulus during both rivalry and fusion. The prediction of this model is that the strength of adaptational aftereffects will increase as the predominance of the adapting stimulus increases. On the other hand, according to the explanation of Blake and Overton (1979), adaptation strength should remain the same whether the adapting stimulus is visible 1% or 99% of the time during rivalry. In this manner, the two viewpoints can be experimentally distinguished. 9 Discussion Basing my conclusions on a consideration of the psychophysical data, I propose that there is reciprocal feedback inhibition between signals from the two eyes prior to binocular convergence. Furthermore, the strength of inhibitory coupling determines the dynamical behavior of the binocular visual system. Strong inhibitory coupling leads to rivalrous oscillations, whereas weak coupling leads to stable fusion. I have presented an electronic astable multivibrator circuit as a physical example of a system possessing this behavior. Since the visual system oscillates when images to the two eyes are uncorrelated, the implication is that spatial pattern can affect the strength of binocular inhibitory coupling. How this occurs is not known. The model I have presented only considers binocular interactions within an isolated patch of visual field. In order to incorporate the postulated effects of spatial correlation on inhibitory coupling, the model would have to include lateral spatial interactions between large numbers of binocular inhibitory modules (of the sort illustrated in figure 1) organized into retinotopic sheets. A model of binocular interactions under fused conditions has recently been presented by Cogan (1987). Although rivalry is not a concern, he suggests in passing that there may be separate feedforward and feedback binocular inhibitory mechanisms to handle fusion and rivalry, respectively, instead of the one feedback mechanism proposed here. (As pointed out by Cogan, feedforward inhibition is not suitable for producing rivalry.) Another aspect of that model is that in addition to right and left visual channels it includes a third one, a purely binocular channel, active only if both stimuli are matched, and which summates with the other two channels to produce the binocular response. In contrast, I would suggest that facilitated responses for matched stimuli result from a weakening of inhibitory coupling between right and left channels, rather than from the activity of an additional channel. Wolfe (1986) has proposed that binocular processing involves four parallel channels: left and right monocular channels, a binocular OR channel, and a binocular AND channel. Again, mechanisms of rivalry are not the central concern of Wolfe's

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model, but several aspects of it still bear comment. The model is based chiefly on quantitative arguments related to the size of psychophysical adaptational aftereffects. Implicit in those arguments, however, is the assumption of a theory of the biophysics of neural adaptation. An important point is that interpretation of the psychophysical data can be radically altered depending on one's theory of neural adaptation. To give an example, for many stimuli the strength of adaptation measured in the unexposed eye is weaker (50-80%) than that in the adapting eye. In other words, there is incomplete interocular transfer of adaptation. Wolfe (1986), as well as Blake et al (1981) and Moulden (1980), offer this as evidence for left and right 'monocular only' channels operating in parallel to a binocular channel. Under this explanation, the degree of interocular transfer reflects the relative sizes of parallel binocular and monocular pools of neurons in the perceptual process. However, physiological data does not support the contention that incomplete interocular transfer of adaptation implies parallel channels. Marlin et al (1986) have shown incomplete transfer of motion aftereffects within individual binocular neurons of cat striate cortex. Even though the biophysics of adaptation underlying their observations is not known, it is easy to conceive of mechanisms that account for them. To give one example, suppose there is partial spatial segregation of monocular inputs within the dendritic tree of a binocular neuron, and also suppose that adaptation involves some localized change around a synapse. This would then lead to incomplete interocular transfer without the need for parallel monocular and binocular channels. A variety of other mechanisms that do the same can be imagined. The purpose here is not to defend any particular model of neural adaptation, but merely to emphasize that the interpretation placed on psychophysical adaptation data can depend on one's concept of the biophysics of adaptation. In this light then, it should be kept in mind that the data discussed by Wolfe (1986) can be understood in ways other than that presented in his theory. Let us now consider the neurophysiological correlates of rivalry. Some studies indicate that it may occur quite early, and perhaps involve the lateral geniculate nucleus (LGN) (as was suggested by Blakemore et al 1972). Varela and Singer (1987) have found strong orientation-specific binocular inhibition in cat LGN whose strength was dependent on the correlation between the two input patterns, although no oscillations were observed in the anesthetized animal. The inhibition was eliminated upon disruption of corticofugal inputs to the LGN. Binocular suppression developed with a latency of hundreds of milliseconds. [Psychophysical observations indicate that rivalry starts after comparable latencies (Kaufmann 1963; Wolfe 1983).] It would be impossible to explain this slow time-course in terms of conduction times and synaptic delays. Rather, it may reflect the time needed for the organization of large-scale cooperative interactions within the nervous system. Also, oscillations in neural activity associated with binocular rivalry have been observed in the superficial layers of the primary visual cortex of owl monkey (John Allman, personal communication). The activities of cells switched on and off in synchrony with behavioral indications of eye dominance in the alert monkey. The findings of Allman and of Varela and Singer (1987) point out the complexity of binocular activity that occurs early in visual pathways. Poggio et aFs (1985) observations of cells in monkey VI cortex responsive to disparities in random-dot stereograms again emphasize the sophistication of binocular processing early in the visual pathway. In this context, the suggestions of Blakemore et al (1972) and of Varela and Singer (1987) that the LGN makes significant contributions to binocular processing becomes attractive. Although the focus of interest here has been the role of binocular reciprocal inhibition in producing rivalry and affecting binocular summation, it is likely that this inhibition is most important in the matching of left and right images during


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stereopsis. Nevertheless, aspects of binocular vision other than stereopsis have been emphasized here, not only because of their intrinsic interest, but also in the expectation that a greater knowledge of them will provide clues and constraints in constructing an understanding of stereopsis. Acknowledgements. Computer simulations were conducted in the laboratory of Hugh Wilson at the Department of Biophysics and Theoretical Biology, University of Chicago, and presented at the 1984 annual meeting of the Optical Society of America. This paper has benefited from discussions with Randolph Blake, Terrence Sejnowski, and Hugh Wilson. The author was supported by a grant from the Sloan Foundation to Terrence Sejnowski and Gian Poggio during preparation of the manuscript. References Alexander L, 1951 "The influence of figure - ground relationships in binocular rivalry" Journal of Experimental Psychology 41 37'6 - 381 Alexander L, Bricker P D, 1952 "Figure-ground contrast and binocular rivalry" Journal of Experimental Psychology 4 4 4 5 2 - 4 5 4 Attneave F, 1971 "Multistability in perception" Scientific American 225 6 1 - 7 1 Blake R, 1977 "Threshold conditions for binocular rivalry" Journal of Experimental Psychology: Human Perception and Performance 3 251-257 Blake R, Camisa J, 1978 "Is binocular vision always monocular?" Science 200 1497 - 1499 Blake R, Camisa J, 1979 "On the inhibitory nature of binocular rivalry suppression" Journal of Experimental Psychology: Human Perception and Performance 5 3 1 5 - 3 2 3 Blake R, Fox R, Mclntyre C, 1971 "Stochastic properties of stabilized-image binocular rivalry alternations" Journal of Experimental Psychology 8 8 3 2 7 - 3 3 2 Blake R, Overton R, 1979 "The site of binocular rivalry suppression" Perception 8 143 - 152 Blake R, Overton R, Lema-Stern S, 1981 "Interocular transfer of visual aftereffects" Journal of Experimental Psychology: Human Performance and Perception 7 367 - 3 81 Blakemore C, Iversen S, Zangwill O, 1972 "Brain functions" Annual Review of Psychology 23 413-450 Bolanowski S L, 1987 "Contourless stimuli produce binocular brightness summation" Vision Research 27 1943- 1951 Borsellino A, De Marco A, Allazetta A, Rinesi S, Bartolini B, 1972 "Reversal time distribution in the perception of visual ambiguous stimuli" Kybernetik 10 139-144 Breese B, 1899 "On inhibition" Psychological Review 3 1 - 6 5 Cogan A, 1982 "Monocular sensitivity during binocular viewing" Vision Research 22 1-16 Cogan A, 1987 "Human binocular interaction: Towards a neural model" Vision Research 27 2125-2139 Fahle M, 1982 "Binocular rivalry: suppression depends on orientation and spatial frequency" Vision Research 22 787 - 800 Fox R, Check R, 1972 "Independence between binocular rivalry suppression duration and magnitude of suppression" Journal of Experimental Psychology 93 283 - 289 Fox R, Herrmann J, 1967 "Stochastic properties of binocular rivalry alternations" Perception & Psychophysics 2 432-436 Fox R, Rasche F, 1969 "Binocular rivalry and reciprocal inhibition" Perception & Psychophysics 5 215-217 Fox R, Todd S, Bettinger L, 1975 "Optokinetic nystagmus as an objective indicator of binocular rivalry" Vision Research 15 8 4 9 - 8 5 3 Helmholtz H von, 1909/1962 Physiological Optics volume 3 (New York: Dover, 1962); English translation by J P C Southall for the Optical Society of America (1924) from the 3rd German edition of Handbuch derphysiologischen Optik (Hamburg: Voss, 1909) Julesz B, Tyler C , 1976 "Neurontropy, an entropy-like measure of neural correlation in binocular fusion and rivalry" Biological Cybernetics 23 25 - 32 Kaufmann L, 1963 "On the spread of suppression and binocular rivalry" Vision Research 3 401-415 Lack L, 1978 Selective Attention and the Control of Binocular Rivalry (The Hague: Mouton) Lehky S, 1983 "A model of binocular brightness and binaural loudness with general applications to nonlinear summation of sensory inputs" Biological Cybernetics 49 89 - 97 Levelt W, 1965 On Binocular Rivalry {Soesterberg: Institute of Perception)

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