1 Introduction

Optokinetic nystagmus (OKN) is an involuntary motion of the eye that occurs as a person views a drifting stimulus. It is characterised by a slow tracking (the slow phase) and a subsequent resetting motion in the opposite direction (the quick phase) that allows the eye to fixate and track a different stimulus feature. The overall visual appearance of OKN, typically elicited by drifting vertical bars, is a repeated “beating” of the eye, that appears as sawtooth eye movements in the horizontal displacement signal (see Fig. 1).

OKN is an established means to detecting deficits along the visual pathway [5, 24, 25]. The literature suggests [1, 9, 11, 17, 21] the presence/absence of OKN (in response to carefully designed stimulus) can be used to detect clinically significant deficits in visual acuity, the (self-reported) ability of the eye to see fine detail. Visual acuity can be difficult to obtain in non-verbal patients, such as young children [2] and the involuntary nature of OKN presents a potential method for rapidly and accurately assessing VA in these patients.

Fig. 1.
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An example of the horizontal displacement signal (coordinates normalised to the eye camera image) showing OKN. Also indicated on the figure is the direction of the stimulus (i.e., in this case, L = leftward, R = rightward, synchronised to eye data.

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The automated detection of the slow/quick phases of the optokinetic and related vestibulo-ocular reflexes have been studied by a number of authors. Velocity threshold was used to determine the saccadic portion of the signal [13, 18]. We found threshold of the velocity signal to be effective in an off-line situation in which a consumer grade camera was used to record video of the eye performing OKN in adult participants [28] as well as children [23]. Alternate approaches include a recursive digital filter that responds to the changes of phase of the signal obtained using electronystagmography (ENG) [13], and an system identification approach utilising ARX model for identifying the relationship between fast phase and slow phase velocity [22]. Recently, Ranjabaran et al. demonstrated a fully objective approach based on K-means clustering to provide an initial classification of data as belonging to fast/slow phase or non-slow phase followed by a system identification approach using ENG [20].

The major focus of this paper is to provide proof-of-concept for a simple approach to OKN detection; highly suited for real-time application. Our method takes as input the horizontal eye displacement obtained from a head-mounted eye tracking system. The method generates time points corresponding to the onset/peak and end of triangular “sawtooth” features characteristic of OKN from the incoming signal. The resulting feature vectors are filtered using heuristic rules to determine whether they are legitimate candidates for OKN. From this process, we find that the repetitive nature of OKN appears to be a discriminative factor for the presence/absence of OKN. Our overall finding is a high true positive rate and low false detection rate using this as a discriminating criteria.

The paper is organized as follows: Sect. 2 provides a general definition of OKN and an explanation of the background of our research. In Sect. 3, the experimental methods are described as used in the data collection stage of the research. Section 4 gives experimental results and evaluation. Section 5 provides a discussion of challenges for the detection of OKN along with some results. Section 6 concludes.

2 Background

We denote the input signal vector by \(x(t) = (d(t), v(t), \gamma (t))\); the concatenation of the (horizontal) displacement of the eye d(t), the velocity v(t) and auxiliary information, \(\gamma (t)\) (consisting of the direction of the stimulus and data quality). Our aim is to determine the start \(x_s\), peak \(x_p\) and end points \(x_e\) of triangular features from x(t), and to test the resulting feature vector \((x_s, x_p, x_e)\) using reasonable decision criteria, to be described, to eliminate unlikely sawtooth candidates.

Consider a sample of d(t) containing OKN as shown in Fig. 2. The onset of a sawtooth is given by the point \(x_s = (t_{s}, d_{s})\), the point where a rising displacement in the eye signal is first detected, the peak of the sawtooth by \(x_p = (t_{p}, d_{p})\) which occurs as the eye transitions to the quick resetting eye motion, and the end of the sawtooth by \(x_e = (t_{e}, d_{e})\) where the descending edge now transitions to rising or stationary. These points yield the (average) slow/quick phase velocities, \(v_{SP}\) and \(v_{QP}\):

$$\begin{aligned} v_{SP} = \frac{\triangle d_{SP}}{\triangle t_{SP}} = \frac{d_{p} - d_{s}}{t_{p} - t_{s}} \end{aligned}$$
(1)
$$\begin{aligned} v_{QP} = \frac{\triangle d_{QP}}{\triangle t_{QP}} = \frac{d_{e} - d_{p}}{t_{e} - t_{p}} \end{aligned}$$
(2)

where \(\triangle t_{SP}\) and \(\triangle t_{QP}\) are the slow/quick phase durations, and \(\triangle d_{SP}\) and \(\triangle d_{QP}\) are slow/quick phase amplitudes. Figure 2 illustrates basic consistency constraints summarised by Table 1(a). The durations (\(\triangle t_{SP/QP}\)) should be positive and non-zero: the quick phase duration must be shorter than the slow phase duration. The slow/quick phase velocities (\(v_{SP/QP}\) must be non-zero and of opposite sign. The magnitude of the quick phase velocity should not exceed that of the slow phase. Furthermore, additional empirically based thresholds were applied as summarised by Table 1(b). This thresholding was used to eliminate potential OKN candidates based on lower and upper estimates for quick/slow phase amplitude/duration and speed.

Fig. 2.
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Components of the OKN displacement signal

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Table 1. Constraints applied to the detected sawtooth features
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Fig. 3.
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State description of the algorithm.

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State-Machine Description of Algorithm

The optokinetic response is generated physiologically by independent slow phase and quick phase systems [30]. This behaviour naturally suggests a state-machine solution to detection; which is also highly suited for real-time implementation. Our algorithm is now explained. In broad terms, the input data stream x(t) drives our machine through three states (either slow phase detection, quick phase detection or finalise as shown in Fig. 3).

The purpose of the slow phase detection state is to find a rising edge of sufficient duration; if this is found then the start point of the rising edge is registered as the beginning of a sawtooth \((t_s, d_s)\) and the machine transitions to the extend edge state. Whilst in the extension phase, the machine now looks for a falling edge to indicate the end of the slow phase, whereupon the end of SP/start of QP \((t_p, d_p)\) will be registered. Any failure (for example, due to lost data caused by blinking) will discard the candidate and cause a reset to the find rising edge state (and also increment a chain group counter to be explained presently). In any event, given a successful detection for the start of a QP, the machine will transition to the QP phase. The machine now looks for a non-decreasing edge indicating the end of the QP \((t_e, d_e)\).

Once the end is found, and given the points of the sawtooth, the machine transitions to the finalize state: the purpose of which is to retain OKN like sawtooth features and discard candidates unlikely to be due to OKN. We do this by applying the criteria described in Table 1.

We measured also contiguous groupings of sawtooth features, using a chain group counter. This counter value was carried across to each new sawtooth candidate. In the case of a failure (i.e., reset event) the group counter advanced thereby indicating a new group. This labelled each repeated sawtooth as belonging to a particular group, and the number of features belonging to a group gave the chain length as shown by variable CL in Fig. 2. In this example, the chain length is \(CL = 2\) the number of complete sawtooth features detected.

Our aim in this work was to see whether there were readily discernible patterns in the measured parameters that would allow us to determine whether stimulus was present or absent. We were particularly interested in whether slow phase properties (velocity and duration) or chain-length could be of value in differentiating between OKN present or absent cases.

3 Experimental Methods

The study was approved by the Auckland University ethics committee and complied with all Helsinki declarations. All participants gave full, written informed consent.

Fig. 4.
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Left: Experimental setup. Right: Used head-mounted eye tracking system [27].

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Fig. 5.
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The stimulus array shown to participants. The array was shown drifting leftward/rightward or stationary.

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Healthy participants (n = 6 adult volunteers) were recruited for this study. OKN was elicited for each participant using an array of drifting disks (see Fig. 5) presented on a 24” LCD display (AOC G2460PG with Ultra Low Motion Blur). The arrays comprised of disks with a central disk diameter chosen to ensure that the stimulus was easily seen (0.7 logMAR, 5 min of arc). The central intensity of the disks was 35 cd/m\(^2\), the peripheral intensity of the disks was 9 cd/m\(^2\) and the background intensity of the screen was 13 cd/m\(^2\). The arrays were shown over intervals of 5 s, during which time it was shown either stationary (0 deg/sec) or drifting horizontally (±5 deg/sec) in a random left/right direction. Each state (left, right, stationary) was shown to the participant 5 times.

The experimental setup is shown in Fig. 4. Participants were asked to stare at the centre of the screen with one eye covered (the protocol was repeated for each eye). The viewing distance was 1.5 m. The eye displacement was recorded using a 120 fps, head mounted eye-tracker (Pupil-Labs, Berlin, Germany). The raw horizontal displacement was smoothed using a Savitsky-Golay (SG) filter. The SG filter preserves high frequency content, and is conveniently specified in the time-domain by polynomial order N and frame-length M [19]. Moreover, the velocity v(t) is readily computed from these filter coefficients. In this work, the order was \(M = 2\), the region frame-length was chosen as \(f = 13\).

The algorithm was run with \((d(t), v(t), \gamma (t))\) data (across all participants and for each eye). The auxiliary function used in this work was \(\gamma (t) = ( \gamma _1(t), \gamma _2(t) )\) comprising the known state of the stimulus (\(\gamma _1(t) \in \{ L, R, X, F \}\)), and data quality measure (\(0 \le \gamma _2(t) \le 1\)) from the eye-tracker device. The latter measure was used to determine whether the data was of sufficient quality to be useful (maximum quality was 1 and minimum quality was 0). The former quantity passed the a-priori direction of the stimulus to the algorithm. Here, the potential values for \(\gamma _1(t)\) were \(L = \) “leftward”, \(R = \) “rightward”, \(X = \) “stationary”, or \(F = \) “fixation”) (see Fig. 5).

The slow phase velocity \(v_{SP}\), duration (\(\triangle t_{SP}\)) and the chain length (CL) were extracted and categorized as depending on whether they were obtained whilst the stimulus was moving (i.e., trials labelled “L” or “R”) or whilst the stimulus was stationary (i.e., trials labelled “X”). The fixation trials labelled “F” were ignored. For trials in which the stimulus array was stationary, the algorithm was run twice. This avoided choosing a particular direction for these trials; and allowed an unbiased estimate of the false positive (FP) detection rate of the method.

The apparent direction of travel of the stimulus as perceived by the observer was recorded, for comparison purposes, by asking the participant to press keys to indicate the direction of travel as they watched the stimulus on-screen. This was used to confirm that the stimulus was perceived as expected by the observer. The eye tracking, experiment management and key-press collection where performed on a second computer running a custom web-server application (node.js) with an JavaScript/HTML5 interface. The display of the stimulus, ran on the primary display by accessing the server using the chrome web-browser. Figure 4 shows the experimental setup used.

4 Results

The stimulus was seen by all observers (n = 6) for all trials (n = 11 eyes) as indicated by correct key-presses measured during the trial. Data for one eye was excluded because stimulus direction information \(\gamma _1(t)\) was lost. The detection algorithm completed successfully for all other test runs/participants. The output from the system is given by Fig. 6. The figure shows unshaded areas corresponding to intervals of time not identified as containing OKN, compared with shaded green areas where OKN was detected. The labels under the graph indicate the direction of travel as a function of time \(\gamma _1(t)\), the numbered intervals above the graph show the chain length computed for the data (chain lengths of 1 are not indicated). Visual inspection (by the authors, who are experienced in identifying OKN) suggested the algorithm was effective in identifying regions containing OKN.

Fig. 6.
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The result of an example of horizontal displacement signal.

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Fig. 7.
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Eye displacement signal for the first sample.

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A total of \(n = 661\) sawtooth features were detected for the moving stimulus category. A total of \(n = 41\) sawtooth features were detected in the the stationary category. The FP rate at the level of features detected was \(5.8\%\) of all sawtooth detections. Figure 7a shows the distribution of results obtained for the slow phase speed \(|v_{SP}|\). The mean slow phase velocity (mean ± 2SD) were 0.024 ± 0.014 and 0.017 ± 0.016 (s\(^{-1}\)) for the moving (\(n = 661\)) and stationary categories (\(n = 41\)) respectively. Figure 7b shows the distribution results obtained for the slow phase duration \(\varDelta t_{SP}\). The SP duration was 0.48 ± 0.52 s and 0.33 ± 0.50 s for the moving and stationary categories. The CL (chain length) is shown in Fig. 7c. In this instance the mean and standard deviations were 3.10 ± 4.44 and 1.03 ± 0.30 for moving (\(n = 215\) chains) and stationary categories (\(n = 40\) chains). A two-sample t-test rejected the null hypothesis (no difference between moving and still distributions) at \(5\%\) significance level for the three parameters.

Figure 8 summarizes all three features (SP velocity, SP duration and chain length CL) plotted on a single graph. The \(n=41\) false sawtooth detections appear as orange hued circles, compared to true detections (\(n = 664\)) shown in blue. Visual inspection of the data (e.g., Fig. 8) indicated that these false detections, were shifted toward lower durations and speeds. Most visually significant was the observation that FP detections were clustered along the \(CL = 1\) and \(CL=2\) planes; indicating that CL could be a discriminating factor for OKN present/absent. The performance of CL as an indicator of OKN present/absent is shown in Table 2. This table shows TP as a proportion of the total number of moving trials (\(n = 110\)) and FP as a proportion of total stationary trials (\(n = 55\)) shown to the observer. This table shows the reduction in FP rate for increasing CL as well as a drop in TP rate. The table suggests that a threshold of \(CL = 2\) was the best balance between TP and FP for trial-by-trial detection of OKN. As a consequence of this result, the effects of SP duration and speed were not considered further, but would be the subject of future work.

Fig. 8.
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Illustration of the distribution of three features from two views

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Table 2. Per trial TP and FP rates as a function of the CL parameter.
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5 Discussion

There is a clinical need for automated approaches able to identify the presence or absence of optokinetic nystagmus, particularly suited to real-time application. In this work we developed a method suitable for real-time detection of optokinetic nystagmus based on a simple state-machine approach. The algorithm was developed and run on a small cohort of adult participants, who watched drifting or stationary patterns whilst having their eye movements recorded.

Sawtooth patterns were detected readily in moving trials (\(n = 664\) detections) but also during some stationary trials (\(n = 41\) detections) (a per feature FP detection rate of \(5.8\%\)). The effects of false detections were eliminated by considering the per trial criteria that OKN should be repetitive. For example, we found that a criteria of \(CL >= 2\) would identify trials with moving stimulus (\(TP rate was 94\%\)) whilst eliminating false detections (\(FP rate was 2\%\)). We suggest that chain-length may be a key factor in assessing the presence or absence of OKN.

Having said that, it is intended that the performance be evaluated more carefully in the future. We found that the mean slow-phase speed and durations for moving and stationary conditions were different, but we did not analyse this finding further. In this work, we presented data for the calibration set only, and we did not perform a robust validation analysis. We need to perform a full ROC analysis of the method which will the subject of further work. It is emphasised that the aim here was to present the basic concept, which was the use of a state-machine approach to determine and analyse OKN.

In this work we utilised a web-browser to display our stimulus. This was facilitated by the jsPsych package (www.jsPsych.org), a web browser based API for psychophysical trials. The jsPsych package utilises a plug-in architecture that allows the user to perform pre-programmed tasks (e.g., show a movie, play audio, record a reaction) or custom tasks that execute in a sequence defined by the experimenter. We wrote a custom plugin was written that facilitated the display of the disk stimulus for the purpose of web browser display.

The web-browser display was controlled from a second computer (the controller) that managed the experiment. Crucially the system synchronised the start and end of each trial of the experiment with the pupil labs eye tracker. In this work the server code was written using node.js and the interface to the server was written JavaScript/HTML5 thereby maintaining a non-platform specific implementation with the possibility of distributing more widely in future work. Furthermore, we developed a batch extraction of pupil location which can extract the location of the pupil for many participants simultaneously. This model can extract the (x, y) of pupil based on 2-D frame on the video stream. In the future, we are going to have an autonomous pupil detection based on cloud computing platform.

There are a number of limitations of the present study. It would be desirable to increase the number of participants tested which would allow a more detailed examination of the behaviour of participants during eye testing and to allow further generalization (if possible) of the threshold we have used already. As mentioned, we require to perform a more in-depth sensitivity-specificity analysis. We looked at a limited set of parameters in this work (essentially chain-length and slow phase duration/speeds), and a more in-depth analysis would be required to indicate optimal features for quantification of OKN. Our aim is to provide these methods for clinical use, and therefore future studies will quantify performance on target groups such as children. Future work will now look to determine whether the present protocols and processing approaches can be improved, and work is under-way to examine whether machine learning approaches will benefit the technique we have developed.

6 Conclusion

We have presented a method for detecting optokinetic nystagmus designed for real-time applications. We have obtained encouraging results for a cohort of adult participants (n = 11 eyes). Further research is warranted, and we will continue to improve upon and further validate the methods presented here. In a forthcoming publication, we will use machine learning model to detect OKN through signal processing and pattern recognition techniques.