Modeling predictive tracking of eye movement control system with a simple neural network

MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

Copyright ~) ] 999 lFAC ] 4tb Triennial \Vortd Congress,

Beijing~

14th World Congress ofIFAC

L-4c-03-1

P.R. China

l\-tODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTROL SYSTEiVI "VITI-I A SI~IPLE NEURAL NET\VORK L.A. AbeJ" Y. Chcn 2, and P .. A. NaJlari

2

}School of 011hoptics La Trobe University Bundoora, Vie. 3083, AUSTRALl4

?Departlnent of Electrical Engineering Purdue University at lndianapolis lndianapolis, lA' 46202, U.S.A. e-mail: [email protected]

Abstract: The rapid adaptation seen in hun1an ocular tracking of repetitive stin1uli is both functionally important and difficult to model. A n10dified back propagation network was trained to predict future eye velocity using error signals [fOrTI a human subject. It accurately tracked a sinusoid at the training frequency and sho\ved reasonably good ability to track at other frequencies. Eventual incorporation of such an element into existing lnode]s of transient pursuit could produce a more broadly useful tracking system for active vision applications. C~opyright © J 999lFAC KEYWORDS; Prediction, neural networks, tracking, eye rnOVClllent control

I.TNTRODLTCTION Problems of sensory processing and motor control which continue to present considerable challenges to researchers have in l"nany cases been solved efficiently and robustly by organiSI11S ranging froln flies to hunlans (Nakayanlu, 1985; Reichardt, 1996~ Vaina et aI., 1990~ \Vurtz ct aI., ] 990; ChurchJand and Sejnowski, 1992). Complex perceptual functions and motor bchaviors are often executed effortlessly. One process readily carried au t by humans (and other prinlates) is the ability to Inaintain visual fixation on a rnoving object. While we do this unthinkingly, it. requires a C0I11plcx interaction aJnong the neuromuscular rncchanislns that control 1110venlent of the head and eyes. Prcci:.ic control is necessary because the primate retina is highly heterogcneous--a snlaH (about 1 0), cCIltral~ high-resolution fovea is surrounded by regions \vith far poorer spatial resolution but higher sensitivity to low light levels and mOlion. The peripheral retina is thus well~sulled la detection of ncw~ potentially i01portant targets~ to which the eyes must be direclcd~ If such targets are moving, then accurate tracking is essential if accurate

exaolinalion of lhenl is to be carried out. This system gives foveate aninlaIs high visual acuity \vilhout incurring the Inassive computational penalty that vvould ar)se if the entire visual field were to be simu1Lancously saTnpled with the same resolution as is possible in the fovea. This tradeoff between reduced visual processing demands and increased visuomotor requirements has only recently been applied in robotic active vision systen1S (Baloch and Waxman~ 1992; Bro\vn, ] 990). The mechanism by which fixation of lTIoving targets is achieved includes t\\'O relatively independent physiologicaI subsystems (Leigh and zec, 1991; Stark et al., 1962). One, the smooth pursuit system, responds primarily to stimulus velocity and operates in a continuous nlodc. rrhe other. the fast eye nlovenlent or saccadic systen1, rapidly moves the eye in discrete steps. The saccadic system thus serves independently to acquire novel stimuli or to redirect gaze to\vards a point of interest. It also functions synergistically with the pUl-suit systenl in COITccting for the accU111ulated posilion errors which occur when pursuit perfnnnancc is inade-quale; i.e., when the gain

5731

Copyright 1999 IFAC

ISBN: 0 08 043248 4

MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

gaze towards a point of interest. It also functions synergistically with the pursuit system in correcting for the accumulated position errors which occur ""hen pursuit perfonnance is inadequate; i.e.~ when the gain (eye velocity/target velocity) is less than 1. O.

Because the spatial extent of the high-resolution ponion of the visual field is only about 1°, both reduced gain and increased phase tag markedly degrade visual performance during tracking. Quantitative studies of saccadic and smooth pursuit function have repeatedly shown that accurate, virtually zero phase lag tracking of a range of repetitive stimuli is possible for both systems. Recently, suggestions have been made about Lhe possible neural substrate for this predictive capahility (Heinen, 1993). Such perfonnance is impossible for any physically realizable causal system, making its simulation difficult In spite of this, numerous models have been developed over the years of the saccadic system (AbeI et at, 1978; Young and Stark, 1963a; Scudder, 1988), the pursuit system (Robinson et aI., 1985; Krauzlis and Lisbergar, 1989; Deno et aI., 1989~ van den Berg, 1988; Bames and Assehnan, 1991 and combinations of the tvJo (Young and Stark, 1963b, Young, 1971). Robotic implementations of these functions have also been developed (Bro\vu, 1990a; 1990b, 1990c). Pursuit models have generally focused upon the tracking of brief, tTansiently presented stimuli such as ramps, explicitly excluding consideration 0 f continuous, predictable stimuli (Robinson et aI., 1985~ Krauzlis and Lisbergar t 1989; Deno et al., 1989), although predictive tracking models have been developed with varying degrees ofphysiologic.al justification (Bames and Assehnan, 1991; Yasui and Young, 1984; Bahill and Harvey, 1986). This more recent emphasis on transient models has facilitated their development while significantly reducing their applicability.

A number of attempts have been made to include predictive components in pursuit models. These have included look-up tables (Bahill and McDonald, 1983), frequency estimators (Barnes and Asselman, 1991), sequential input adaptive mechanisms (Greene and Ward, 1979) and arbitrary elements labeled t'predictoTs" and placed into transient pursuit models \\thich were otherwise more straightforward in both engineering and biologicaJ terms. Pavel has reviewed these efforts in some detail. The present study reports on initial efforts to develop a predictor model using a simple neural net\Vork trained on data derived from measurements of normal human sinusoidal tracking performance. No a priori constraints were placed upon its function. The longterm goal is to integrate a successful predictor into a comprehensive model which can realistically emulate both transient and predictive tracking and which will be applicable both to investigations of the

14th World Congress of IFAC

functioning of the biologicaJ systenl and to use in active vision systems. \Vhy use a neural network to model the predictive pursuit element? Estimation of the future position of a moving object is a time series prediction problem. In the case of linear trajectories~ adaptive filters have proven to be effective tools to address this problenl. Since the targets used in these experiments were nonlinear in nature) the need for non-linear, adaptive devices arose. AJso~ the many different constraints in the prediction system were not clearly enough defined for a definite mathematical model to be developed. Two of the most important properties of most neural networks are non-linearity and adaptive ability. The non-linearity is distributed throughout such networks, have the inherent capability to adapt their synaptic weights to changes in the surrounding environment. Hence, a net\vork trained to operate in one environment can be retrained to deal \vith minor changes in the environment if necessary. 2. METHODS

Horizontal SlllOOth pursuit eye movement data \vere collected from six normal human subjects, age range 2 I~36 years, using an infrared eye tracker vlhiIe the subject was asked to followed a laser spot 11loving sinusoidally at frequencies of 0.5, 0.75 and 1.0 Hz behveen ±12.5° horizontally. Data \\I'ere digitized at 1000 Hz, differentiated and digitally low-pass filtered with a Blackman filter at 25 Hz. Saccadcs were detected and removed from the data using an automatic removal technique based on a nlethod adopted from Sautcr et al. (1991) and replaced using euhie spline interpolation, F or each frequency, the signal used as the input to the nenvork \vas that which corresponded to the error signal which would be presented to the brain during a tracking task; that is, the difference ben.veen target velocity and eye velocity. This is known as retinal slip--the velocity at which the inlage of the target drifts across the retina during tracking. Given that one of our goals was to attempt to model predictive tracking as carried out by normal human subjects, hvo factors governed the selection of the retinal error signal as the net\\l'ork input instead of the target velocity signal. First, retinal error is the signal feeding the closed loop smooth pursuit control system and hence is one of the signals used by the oculomotor system to keep the gaze on a moving target. Second, at a given frequency, the use of target velocity as the input would result in the same input sequence being presented for different desired output sequences. This would mean that during training, no new infoffilation would be presented to the network each time and the output generated by the nehvork after training "vould correspond to the desired sequence of the last training set used, hence 5732

Copyright 1999 IFAC

ISBN: 0 08 043248 4

MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

14th World Congress ofIFAC

where il.W is the weight change matrix; J is the Jacobian matrix of derivatives of each error to each weight; J is the identity matrix; e the error vector; and ex the search parameter. The value of ex.

producing trivial results. The re tinal error on the other hand presents new infonnatioIl each time to the network hence exposing :it to a wider range of characteristics. If we ,,"'ere developing a predictor unconstrained by human performance, then, clearly,

determines whether learning progresses according to

target motion itself could have been used as the input

Newton's method or steepest descent. When a is

to the network.

small, the relation approximates Newton method. As

The

neural

network

was

a

three-layer

back

propagation network, implemented using the MA TLAB Neural Ne1vlork Toolbox package running on a Zeo5 Pentium-90M Hz system. Since the model \\'as constrained to behave as a one step ahead predictor, only one output node was required. Since the input to the network was temporal in nature, the number of inputs selected depended on the desired duration of the input sample in each run. Different values ranging between 10-50 were experimented \vith and it was observed that a large number of inputs (35-50) resulted in highly redundant data and too few inputs required the network to train for a long time. A value of 25 showed good network performance at 0.5 and 1.0 Hz, while 35 input units were needed for best performance at 0.25 I-Iz. Selection of the number of hidden nodes is important to the network design as too few would result in the network not training at all or training at a very slow rate and too many would lead to the network Qvertraining and subsequently being unable to correctly respond to new data. A value of 10 was selected for the networks being trained at 1 Hz and 0.75 Hz after different trials using values between 5 and 30 were run. A hidden layer of 5 or 10 neurons resulted in the network not training to criterion even after 1000 iterations at 0.5 Hz, while 20 neurons achieved a nOIDlalized sum squared error (SSE) of 0.02 in 783 iterations. The network received as input 25 samples of the retinal slip signal at a time and was trained to produce the next corresponding eye velocity signal as output. The inputJ output characteristics of the hidden layer neurons are defmed by a non-linear squashing

function. The squashing function selected for our application was the tangential sigmoid function. For this time series prediction problem; the output should resemble the input as closely as possible, hence requiring the output neuron to be linear. Ordinary back propagation is based on simple gradient descenL This is usually a slow process, although adding a momentum tenn can speed it up by making changes proportional to the running average of the gradient. But this does not always provide a substantial increase in learning speed. In thIs work, the Levenberg-Marquardt method was used for updating the network weights (Hagan et al., 1995). The update rule fOT the weights in a neural nenvork is given by the relation ~W=::(JTJ+aI)-1 JT e

(1)

a gets large, the J T J term becomes negligible and learning progresses according to a -1 J T e , \vhich is steepest descent. Since Ne\\'ton 'g method is faster and more accurate near an error minimum~ initialIy Cl is chosen to be large enough for the algoritlun to begin as a steepest descent method and is gradually decreased so as to activate the Ne\vton method as soon as possible Whenever a step is taken and the error increases, et. is increased until this is no longer

the case. However, if a becomes too large, no learning takes place as a -1 J T e approaches zero~ This occurs when an error minimum has been reached and learning stops. 3. RE·SULTS Network training involves the repeated presentation of all the training data sets to the netw'ork~ Vectors from the training set are presented to the network one after the other. If the network output is correct, no changes are made; else, the Vtleights and biases are updated using the learning rule. An entire pass through all of the input vectors is termed as an epoch.

When such an entire pass of the training set has occurred without

error,

training

is

complete.

Usually, obtaining a zero error is difficult so a minimum error threshold is set and if the error crosses below this threshold, training is stopped. This minimum error threshold is selected depending on the complexity of the problem. Another criterion for stopping training would be to set a maximum number of epochs. In this project, both stopping criteria \vere used and training was stopped when either of the criteria ,vas reached. Training was done using three data sets for each frequency. After the network was trained, it was tested with its training data set and with a test set at the same frequency. Then cross frequency testing was done to test for generalization across frequencies. The training data were taken from three subjects and the test data from the other three. Hence this was a more stringent test for the network as it had to generalize over the perfonnance of different subjects and not just different trials on the same subject. The comparison metric chosen was the normalized

sum squared, dermed

±[desired{t) - netoutput(t»)' a error

(2)

=: t==l

n 5733

Copyright 1999 IFAC

ISBN: 0 08 043248 4

14th World Congress of IFAC

MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

where •n' ,vas the number of points in the signal. This

satisfactorily

described

the

379 and 354 iterations respectively.

netw'ork

performance. The network parameters selected during training are shown in Table 1 and the net\~'ork performance during training and testing is shown in Table 2. Figures 1 and 2 sho\v the testing results across frequencies for nenvorks trained at 0.5 and 1.0 11z, respectively,

The result of cross frequency testing also proved to be reasonably good, with relatively smooth outputs, although the error was not very low ('Table 2). This inlplied appreciable generalizing ability across both frequencies and subjects. To see whether cross frequency performance would be better if the network were trained with a mixture of frequencies t an input was llsed which contained a sequence of all three frequencies. Upon training, it was observed that the nen.vork tended to learn the pattern in \vhich the different frequencies ",rere arranged in the input and hence when it was tested with a single frequency, the error followed this pattern, in the sense that it w·as less for regions in the input ~'here it expected the same test frequency and higher in the other regions. Hence this method of training was not adopted.

Table 1. Network trainin g parameters Input frequency (Hz)

0.5 0.75 1.0

# input

nodes 35

25 25

# of hidden nodes

Stopping criterion (SSE)

10 10

]5.0 10.0 10.0

]0

Table 2. Network performance during training and testing Training frequency (Hz) Normalized SSE trai ning data

0.5

0.75

1.0

0.01918

0,005907

0.005355

Normalized SSE

0.07331

O.154R

0.1919

0.162)

0.02781

0.05821

0.]819

0.08744

0-01396

0.5 Hz res t data Nonnalizcd SSE 0.75 Hz test data 1\orrnahzed SSE 1.0 Hz test data

4. DISCUSSION

Training using the Levenberg-Marquardt method of optimization proceeded very quickly, reaching the stopping criterion usually before 500 epochs. An interesting phenomenon noticed during training \vas that the higher frequency signals trained much more qUickly and to a lower SSE than the lower frequency signals. This initially seems paradoxical, given that human pursuit perfonnancc deteriorates with increasing frequency) but the reason for this becomes obvious when the input sequences are examined. As the frequency increased, the retinal error became larger and more periodic. The retinal error for the 1 Hz signal almost resembled the desired output and hence required little training to achieve it. On the other hand, the retinal error for 0.5 flz was much smaller and noisier, requiring more training to reach criterion. Although this network \vas trained for tw'lce as many epochs as the other nehvorks, the minimum SSE it achieved was 34.52 dUring training, which gave a normalized SSE of 0.01918. This error ~ras obtained by also increasing the number of input nodes to 35 from 25 originally used. With 25 nodes, the minimum SSE that was obtained was 56.38. The network trained much better for the 0.75 Hz signal and the 1 lIz signal, achieving SSEs of 10.63 and 9.639 respectively. These values \',I'ere obtained in

The nenvorks described above are clearly still far from being ready for incorporation into a comprehensive tracking model suitable for either neurophysiological research or engineering applications. lbey were trained not in rea] time but off-line and in their present fonn are not easily interfaced with other models. However, the

performance

observed

suggests

that

additional

development may prove worth~rhile. These small nenvorks were readily trained to generate a reasonably accurate eye velocity signal when presented with only a relatively brief sample of past

tracking error data. Interestingly, they v./ere able to do so not only at the frequency for which they had been trained but also at nearby frequencies. This \-vas better seen for networks trained at 1.0 Hz than at 0.5 Hz. This may be due to the fact that networks trained at the higher frequency were presented with t\vice the proportion of the input waveform at a time, Vw'hich may have improved their ability to generalize their responses to inputs of the same waveform but different frequencies. The generalization observed suggests that even as simple a nen\'ork as the design used here is capable of capturing certain characteristics of the sinusoidal \vavefonn, independent of the specific frequency. This may be analogous to the adaptive controller described by Bahill and McDonald (1983) and could represent a way in which certain familiar trajectories such as sinusoids are gradually learned by the brain during development. In contrast, the behavior of the linear predictor using the LMS algorithm (Widrow and Winter, 1988) may represent the rapid increase in pursuit gain seen in tracking any relatively repetitive stimulus trajectory which is present for a cycle or more. The development of a comprehensive tracking model suitable for practical application may require both types of mechanism. 5. CONCLUSIONS 5734

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MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

This type of predictor model could find future applications in the field of active robot vision. If the target is predictable, this type of system would significantly reduce the response lag. The robotic tracking models described by Brown (1990a, 1990b, 1990c) used variations of a Smith predictor to compensate for tracking lags. Variations on Kalman filters were used to anticipate future target position. Pe·rfonnance on sinusoidal targets could be improved by digital filtering to reduce the high-frequency noise seen in the cross-frequency responses. Variations on these networks should be able to adapt to a wide range of stimuli. Pre-training a nern:ork on commonly encountered inputs \\'ould be the model equivaJent of the performance improvement obtained with practice in human subjects. An ensemble of these pre-trained networks could be operated in parallel and that giving the best perfonnance could be the one selected for use on a given task, in the same \vay that Bro\Nn (1990a) describes selecting the model w·hich best fits the data.

ACKNOWLEDGEMENTS This research was supported by NSF Grant BCS9216598 and in part by an Unrestricted Grant from Research to Prevent Blindness to the Indiana University Department ofOphthahnology.

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Bro\Vll, C. (1990c), "Prediction and cooperation in gaze control," Biological Cybernetics) \f01. 63, pp. 61-70. Churchland, P.S., and T.J. Sejno\vski (1992)~ The COfnputational Brain, Cambridge, Massachusetts, MIT Press, 1992, . Deno, D.C., E.L. KeIler, W~F. Crandall (1989)~ "Dynamical neural network organization of the visual pursuit system,t' IEEE Transactions on Biornedical Engineering~ Vol. 36, pp. 85-92. Greene, D.E. and F.E. \Vard (1979), "l-ruman eye tracking as a sequential input adaptive process, Biological Cybernetics, Vot 33 pp. 1-7. Hagan, M.T., H.B. Demuth, and M. Beale (1995)) Neural Jv"ehvork Design~ PWS Publishing Company, Boston, MA. I-Ieinen) S.l. (1993), "Characteristics of predictive smooth-pursuit neurons in the dorsomedial frontal cortex,r' Investigative Ophthalmology and \!isual Science (Supplement), \lol. 34, p. 1500. Krauzlis, R.J. S.G. Lisberger (1989), llA control systems model of smooth pursuit eye movements v-rith realistic emergent properties~H Neural Computation, Vot 1, pp. 116-122. Leigh) R.J. and D.S. Zce (1991)J The 1Veurology of' E.~ve Movements, Philadelphia, F. A. Davis. Nakayama, K. (1985), "Biological image motion processing: A review, n Vision Research, Vol. 25, pp. 625-660. Pavel, M., "Predictive control of eye nl0vement," in Eye Movements and Their Role in Visual and Cognitive Processes, Kowler, E., ed., Amsterdam, Elsevier Science Publishers BV, pp. 71-114. ReichaTdt, W. (1986), "Processing of optical information by the visual system of the fly, Vision Research, Vol. 26, pp. 113-126. Robjnson, D.A., J.L. Gordon, J.L. and S.E. Gordon (1985) llA model of the smooth pursuit eye movement system,H Biological Cybernetics, Vol. 55, pp. 43-57. Sauter, D., B.J. Martin, N. Di Renzo, C. Vomscheid (1991), tlAnalysis of eye tracking movements using innovations generated by a Kalman filter, " Medical and Biological Engineering & Computing, Va!' 29, pp. 63-69. Scudder~ C.A. (1988), t'A new local feedback model of the saccadic burst generator," Journal of Neuroph}'siology, \'01. 59, pp. 1455-1475. Stark; L., G. Vossius, and L.R. Young (1962) 'tpredictive control of eye tracking movements, tI iRE Transactions on Human Factors in Electronics, Vol. HFE-3;o pp. 52-57. Vaina, L.M., M. Lemay, D.e. Bienfang, A.Y. Choi t and K. Nakayama (1990) "Intact f'biological motion and "structure from motion" perception in a patient \vith impaired motion mechanisms: A case study~q VisuallVeuroscience, Vol. 5, pp. 353369. pp

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t

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MODELING PREDICTIVE TRACKING OF EYE MOVEMENT CONTR...

van den Berg, A,V4 (1988), "Human smooth pursuit during transient perturbations of predictable and unpredictable target movement," Experimental Brain Research~ Val. 72, PP4 95-108. Widrow~ B~ and R. Winter (1988), uNeural nets for adaptive filtering and adaptive pattern recognition,'f Computer, Val. 21, Pp4 25-39. Wurtz, R.H., H. Komatsu, D.S.G. Yamasaki, and M.R. Diirsteler (1990), uCortical visual motion processing for oculomotor control,lf in Vision and the Brain, Cohen, H., Bodis- Wollner, I., eds., New York, Raven Press, Ltd.) pp. 211-231. Yasui S. amd L.R. Young (1984}, "On the predictive control of foveal eye tracking and slo\v phases of 1

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optokinetic and vestibular nystagmus, n Journal of Physiology (London), Vo!. 347, pp. 17-33. Young, L.R. and L. Stark (1963a), "A discrete model for eye tracking movements, 0 IEEE Transactions on Military Electronics, Vot 7, pp. 113-115~ 1963. Young, L.R., L. Stark (1963b), "Variable feedback experiments testing a salnpled data nlodel for eye tracking movements, n IEEE Transactions on Human Factors in Electronics, Vo!. HFE-4) pp. 38-51. Young, L.R. (1971), "Pursuit eye tracking movements,U in Control of Eye Movements, Bachy-Rita, P., Collins, C.C., Hyde, I.E., eds., New York, Academic Press, pp. 429-443,~

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Fig. I. Testing results at a) 0.5 Hz) b) 0.75 Hz and c) 1.0 Hz for network trained at 0.5 Hz.

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Fig. 2. Testing results at a) 0.5 Hz, b) 0.75 Hz and c) 1.0 Hz for network trained at 0.5 Hz.

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