The output from eye-tracking devices varies with individual differences in the shape or size of the eyes, such as the corneal bulge and the relationship between the eye features (pupil and corneal reflections) and the foveal region on the retina. Ethnicity, viewing angle, head pose, colour, texture, light conditions, position of the iris within the eye socket and the state of the eye (open or closed) all influence the appearance of the eye ( 4 ) and, therefore, the quality of eye-tracking data ( 6 ). In particular, the individual shapes of participant eye balls, and the varying positions of cameras and illumination require all eye-trackers to be calibrated.

Calibration refers to a procedure to gather data so that the coordinates of the pupil and one or more corneal reflections in the coordinate system of the eye-video can be converted to x- and y-coordinates that represent the participant’s point of regard in the stimulus space. The procedure usually consists of asking the participant to look at a number of pre-defined points at known angular positions while storing samples of the measured quantity ( 7-9 ). There is no consensus on exactly when to collect these samples, but Nyström, Andersson ( 3 ) showed that participants know better than the operator or the system when they are looking at a target.

The transformation from eye-position to point of regard can be either model-based (geometric) or interpolation-based ( 4 ). With model-based gaze estimation, a model of the eye is built from the observable eye features (pupil, corneal reflection, etc.) to compute the gaze direction. In this case, calibration is not used to determine the actual gaze position but rather to record the e ye features from different angles. See Hansen and Ji ( 4 ) for a comprehensive overview of possible transformations.

Interpolation might involve, for example, a linear regression between the known data set and the corresponding raw data, using a least squares estimation to minimize the distances between the observed points and the actual points ( 5 ). Other examples of 2-dimensional interpolation schemes can be found in McConkie ( 10 ) as well as Kliegl and Olson ( 8 ) while a cascaded polynomial curve fit method is described in Sheena and Borah ( 11 ).

Theoretically, the transformation should remove any systematic error, but the limited number of calibration points that are normally used limits the accuracy that can be achieved. Typical calibration schemes require 5 or 9 pre-defined points, and rarely use more than 20 points ( 12 ).

Huang, Kwok ( 13 ) presented an auto-calibrating system that identifies and collects gaze data unobtrusively during user interaction events since there is a likely correlation between gaze and cursor and caret locations. The procedure presented by Huang, Kwok ( 13 ) recalibrates continuously and becomes more and more accurate with additional use. They reported an average error of 2.56° which is not good but has the advantage that there is no need for an explicit calibration phase.

Swirski and Dodgson ( 14 ) describe a procedure that fits a pupil motion model to a set of eye images. Information from multiple frames is combined to build a 3D eye model that is based on assumptions on how the motion of the pupil is constrained. No calibration is needed and since the procedure is based on pupil ellipse geometry alone, it is not necessary to illuminate the eyes to create a corneal reflex. At best, a mean error of 1.68° was reported.

In summary, while auto-calibration might solve the problem of calibrating for participants who struggle to maintain concentration, it is not good enough for studies where high accuracy is needed.

Smooth-pursuit eye movements are continuous, slow rotations of the eyes ( 20 ) that are used to stabilise the image of a moving object of interest on the fovea, thus maintaining high acuity ( 21, 22 ). Conscious attention is needed to maintain accurate smooth pursuit ( 23, 24 ).

Smooth pursuit gain is expressed as the ratio of smooth eye movement velocity to the velocity of a foveal target ( 25 ). If the gain is less than 1, gaze will fall behind the target to create a retinal slip that will have to be reduced by one or more "catch-up" saccades ( 26 ). According to Meyer, Lasker ( 27 ), normal subjects can follow a target with a gain of 90% up to a target velocity of 100 deg/s.

Smooth pursuit gain increases with age, especially for the first 3 months of an infant’s life ( 28, 29 ). Accardo, Pensiero ( 30 ) found that velocity gain of children aged 712 is slightly lower than that of adults.

Smooth pursuit can also be affected by attention ( 31, 32 ). More specifically, performance with smooth pursuit tasks can be dramatically improved when subjects are asked to analyse some or other changing characteristic of the target, such as reading a changing letter or number on the target ( 33 ) or pressing a button ( 34 ).

Smooth pursuit performance is also affected by stimulus background ( 35-37 ), target position ( 38 ), target velocity ( 27, 39 ), target visibility ( 40, 41 ), target direction ( 42 ) and predictability of target direction ( 43 ).

Smooth pursuit impairment and dysfunction can be linked to mental illnesses such as schizophrenia ( 33,44,45,46 ), autism ( 47 ), physical anhedonia and perceptual aberrations ( 48-50 ), Alzheimer’s disease ( 51 ) and attentiondeficit hyperactivity disorder (ADHD) ( 52 ).

The concept of calibrating while a participant follows a moving target has been exploited with success in the past. Pfeuffer, Vidal ( 53 ) explains a procedure where gaze data for calibration is only sampled when the participant is attending to the target as indicated by high correlation between eye and target movement. They showed that pursuit calibration is tolerant to interruption and can be used to calibrate without participants being aware of the procedure.

Pfeuffer, Vidal ( 53 ) used a Tobii TX300 eye tracker to test their calibration procedure and collected gaze data at 60 Hz. At a target speed of 5.8°/s, it took 20 seconds to complete the target trajectory and an accuracy of just less than 0.6° were achieved. The results were compared with the 5-point calibration routine of Tobii which took 19 seconds to complete and delivered an accuracy of ≈0.7°.

Celebi, Kim ( 54 ) follows the approach of Pfeuffer, Vidal ( 53 ) but argues that an Archimedean spiral would provide better spatial coverage of the stimulus plane with little redundancy. At a linear velocity of 6.4°/s, the calibration procedure took 27 seconds during which 1600 data points were collected. Upon testing 10 healthy adults on an Eyelink 1000 eye tracker running at at 500 Hz, their approach delivered an average accuracy of 0.84° compared to 1.39° with a standard 9-point calibration procedure (which took 23 seconds to complete).

Celebi, Kim ( 54 ) stated explicitly that the goal of their smooth pursuit approach towards calibration is to improve the calibration for toddlers and children with or without developmental disabilities although they did not test the approach with such participants.

Gredebäck, Johnson ( 55 ) describes a calibration routine that makes use of a moving object to lure infants’ eyes to 2 or 5 calibration targets, but they reported accuracy according to the manufacturer’s specifications of 0.5° - a value which has been computed with a conventional calibration routine under ideal circumstances and with cooperating adult participants.

Participants who struggle to maintain concentration o n tedious tasks can be cognitively stimulated by indicating or counting the number of transitions of the target from one stimulus to another ( 33 ). In this study, participants were requested to follow a grey disk of 1.5° diameter on a white background (Figure 1) that contained a coloured dot (0.2°) in the centre. The dot changed colour in cycles of blue (2 seconds) and red (500 ms) and the participants were then asked to say the word "Red" aloud every time that the disk changed to red.

The target is initially displayed statically in the top left corner and the participant can be prepared as to the direction and nature of the motion that could be expected. The experimenter can initiate movement with a button as soon as the participant is ready. Three alternative trajectories were tested with the target moving along an even horizontal path (Figure 1a) , a wavy horizontal path (Figure 1b) and vertical Figure 1c.

Depending on the speed of movement, the interval between windows and the trajectory, a large number of targets can be extracted from the continuous gaze data. In the procedure of Pfeuffer, Vidal ( 53 ), gaze data is collected whenever a participant attends to the moving target. In our approach, gaze samples (or more specifically, pupil-glint vectors for each eye) are captured for very short windows (100 ms) at intervals of 500 ms. When data is not available at a specific interval, the point is ignored. This means that, at a framerate of 200 Hz, 20 samples were recorded within a 100 ms window. At a velocity of 6.65°/s (gaze distance 700 mm, 300 px/s on a 19.5", 1600×900 screen), the samples would span 0.665° in the direction of movement.

The radius of curvature was set so that the horizontal and vertical trajectories would cover 6 and 9 distinct Y and X coordinates respectively (cf Figure 1). This resulted in 76 targets (in 38 s) being captured for both the even and wavy horizontal movements and 66 targets (in 33 s) for the vertical movement.

Since the eyes move smoothly to follow the target, it can be expected that a convex hull around the sample points would be elongated along the direction of movement. The samples within every window were sorted according to the x and y dimensions of the pupil-glint vectors and only the intersection of the centre 80% of samples around the median in each dimension are retained.

In contrast with a standard 5-point or 9-point calibration procedure where all points are needed for the regression, the multitude of points that are available with this procedure allows the removal of points where participants blinked or where their attention was distracted. All windows for which the dispersion (Max(maxX-minX, (maxYminY)) of contained samples are above 5°, are also removed. For each of the remaining windows of gaze data samples, the average location and the average pupil-glint vector are calculated.

From here on, the procedure as explained in Blignaut ( 2 ) is followed. The gaze data windows represent calibration points at known locations and are used to determine a gaze mapping polynomial set per participant. Regression coefficients are recalculated in real-time – based on a subset of calibration points in the region of the current gaze. Real-time localized corrections are done that are based on calibration targets in the same region. See Blignaut ( 2 ) for a detailed discussion of the procedure.

For this study, an eye tracker with two infrared illuminators, 480 mm apart, and the UI-1550LE camera from IDS Imaging (https://en.ids-imaging.com) was assembled. All recordings were made at a framerate of 200 Hz.

Every frame that is captured by the eye camera was analysed and the centres of the pupils and the corneal reflections (glints) were identified. A regression-based approach was followed to map the pupil-glint vector to a point of regard in display coordinates. The regression coefficients are determined through a calibration process.

Seventeen healthy and cooperating adult participants were recruited through convenience sampling and presented with four calibration routines, namely a moving target along an even horizontal path, a moving target along a wavy horizontal path and a target moving vertically (cf Figure 1). The 45-dots routine as proposed in a previous study ( 2 ) was also presented for comparison purposes. The procedure was executed only once for every participant.

After every routine, a 7×4 grid of dots was displayed to determine the accuracy of the procedure. As for the 45 dots, the 28 dots appeared in random order to prevent participants from pre-empting the position of the next dot and prematurely look away. The regression coefficients as determined in the preceding calibration routine was used to map the gaze data to screen coordinates. The accuracy for a specific participant was calculated as the average offset between the known locations and the reported gaze coordinates across the 28 dots. The performance of a calibration routine is expressed as the average accuracy over all participants.

Figure 2 shows the calibration points that were recorded for a specific participant while the target was moving along an even horizontal path. The mapped gaze coordinates of the sample data are enclosed by convex hulls – green for the left eye and red for the right eye.

In the example presented in Figure 2, five of the calibration windows did not contain enough sample data – probably due to blinks. Table 1 shows that for routines that involve a moving target, on average between 2 and 4 calibration windows are lost in this way. Since there are more than enough other points to be used in the subsequent regression and because the lost points are seldom at successive locations, this does not pose a problem.

Initially, the set of calibration points was also used as validation targets and the offsets between the calibration points and the mapped gaze coordinates were calculated. All points with offsets larger than 1.0° were then removed from the set of calibration targets and the regression procedure was repeated. The remaining calibration points are shown in blue in Figure 2, while black dots indicate points that were excluded for real-time interpolation. Table 1 also shows the final number of points that was used to determine the polynomial coefficients through regression.

Figure 3 shows the validation points for a calibration that was done for a moving target along an even horizon-tal path. The average of all samples within a window is shown for the left and right eyes. A + indicates the average position between the left and right eyes.

The example in Figure 3 was specifically selected to illustrate the occurrence of outliers. These outliers may occur if the participant loses concentration or is distracted by external stimuli. Sometimes (some of) the samples are captured during a blink, in which case the samples for the left and right eyes appear to be disconnected. Validation points were excluded from the calculation of average offset if the offset was larger than 3° or if the mapped gaze coordinates for the two eyes were more than 3° apart. Table 2 shows the average number of validation points that was included for each of the calibration routines. These thresholds were set large enough not to exclude valid data but small enough to ensure that unwanted gaze behaviour is excluded.

Table 2 also shows the average error across the 28 validation points and 17 participants per calibration routine. The important column that needs to be interpreted to compare the four calibration routines is boldfaced. Figure 4 provides a visualisation of the same results. The vertical bars denote the 95% confidence intervals of the means. Table 2

Average number of validation points that was included and the average error (over participants and validation targets) for each of the calibration routines. (SD: Standard deviation, SEM: Standard error of the mean)

A repeated measures analysis of variance (each participant calibrated with four different routines) showed that the calibration routine has a significant (α = .001) effect on the magnitude of the error (F(3,48) = 9.74, p < .000). Table 3 shows the results of Tukey’s test for the honestly significant difference between pairs of means. The differences between the means for the 45-dots and vertical movement as well as the difference between 45-dots and horizontal movement along a wavy path were significant (α = .01). Although the accuracy for the moving target along an even horizontal path was worse than that of the 45-dots routine, it was not significantly so (α = .05).

It can, therefore, be concluded that a moving target along an even horizontal path has the potential to be used as alternative calibration routine. This will be tested in the next section with a sample of difficult-to-calibrate participants. Table 3

p-Values for the significance of the difference in error between pairs of means

The same self-assembled eye tracker was used as in the previous section.

A school for learners with special education needs were visited and all learners from Grade 1 to Grade 3 (ages 6 – 11) for which permission of the parents were obtained, were tested. The school accommodates learners who are cerebrally palsied, physically and/or learning disabled. The school has specially qualified remedial teachers as well as a multi-disciplinary support structure that includes psychologists, social workers, occupational therapists, speech therapists, physiotherapists as well as a professional nurse. The school follows the normal mainstream syllabi but there are no more than 10 learners in a class to enable teachers to provide specialised and individual attention.

Several lessons were learned in the process of capturing data. Initially, learners were requested to follow the moving target without any further instruction. It soon became evident that they struggle to maintain focus on the target for the duration of the trajectory. The target was then programmed to change colour in cycles of blue (2 seconds) and red (500 ms) and learners were instructed to call out the word "Red" whenever the target changes to red. For the procedures where dots were involved, every dot appeared in a different colour and learners were instructed to call out the colour for the dot every time.

Although the system allows moderate head movements, many learners had excessive sideways and back and forth head movements – some of which were involuntary. A chinrest was then used to maintain head position, but it caused instability of the eyes every time that the learners vocalised their response on a colour change of the target. Finally, the learners were instructed to push their foreheads against a barrier that was set such that a fixed gaze distance of 700 mm was maintained.

It was also realised that the sets of 45 dots for calibration and 28 dots for validation was too exhausting and therefore these were limited to 23 calibration targets (in rows of 5, 4, 5, 4, 5 targets each) and 15 validations targets in a grid of 5×3.

Eventually, 24 participants were tested with the final configuration of target movement, headrest and calibration sets. The number of learners per grade and condition is shown in Table 4. Note that some learners had more than one condition. Table 4

Number of learners per grade and condition (ADD: Attention deficit disorder; ADHD: Attention deficit hyperactivity disorder; ASP: Asperger syndrome; DSL: Dyslexia; EPSY: Epilepsy; LD: Learning disability)

The learners were presented with a moving target along an even horizontal path (SP) (cf Figure 1) and the 23-dots routine. After every routine, the 5×3 grid of dots was displayed to determine the accuracy of the procedure. As was the case for the validation of accuracy with healthy adults, the dots appeared in random order to prevent learners from pre-empting the position of the next dot and prematurely look away. The performance of both the 23-dot and SP calibration routines was expressed as the average accuracy over all participants as determined through the 15 dots validation routine.

As for the validation of accuracy with healthy adults, validation points were excluded from the calculation of average offset if the offset was larger than 3° or if the mapped gaze coordinates for the two eyes were more than 3° apart. Table 5 shows the average number of validation points that were included for each one of the calibration routines. A repeated measures analysis of variance for the effect of calibration routine (23-dots vs SP) on the number of valid points showed that the SP routine leads to more reliable data as there are significantly less points that have to be discarded (F(1,47) = 47.7, p < .001).

Table 5 also shows the average error across the 15 validation points and 24 participants per calibration routine. A repeated measures analysis of variance for the effect of calibration routine (23-dots vs SP) on the accuracy of tracking showed that the SP routine is significantly better than a dots-based routine (F(1,47) = 12.57, p < .000) for difficult-to-calibrate participants. Table 5

Average number of validation points that was included and the average error (over participants and validation targets) for each of the calibration routines. (SD: Standard deviation, SEM: Standard error of the mean)