Driving is an everyday task involving a complex interaction between visual and cognitive processes. As such, an increase in the cognitive and/or visual demands can lead to a mental overload which can be detrimental for driving safety. Compiling evidence suggest that eye and head movements are relevant indicators of visuo-cognitive demands and attention allocation. This study aims to investigate the effects of visual degradation on eye-head coordination as well as visual scanning behavior during a highly demanding task in a driving simulator. A total of 21 emmetropic participants (21 to 34 years old) performed dual-task driving in which they were asked to maintain a constant speed on a highway while completing a visual search and detection task on a navigation device. Participants did the experiment with optimal vision and with contact lenses that introduced a visual perturbation (myopic defocus). The results indicate modifications of eye-head coordination and the dynamics of visual scanning in response to the visual perturbation induced. More specifically, the head was more involved in horizontal gaze shifts when the visual needs were not met. Furthermore, the evaluation of visual scanning dynamics, based on time-based entropy which measures the complexity and randomness of scanpaths, revealed that eye and gaze movements became less explorative and more stereotyped when vision was not optimal. These results provide evidence for a reorganization of both eye and head movements in response to increasing visual-cognitive demands during a driving task. Altogether, these findings suggest that eye and head movements can provide relevant information about visuo-cognitive demands associated with complex tasks. Ultimately, eye-head coordination and visual scanning dynamics may be good candidates to estimate drivers’ workload and better characterize risky driving behavior.
Citation: Mikula L, Mejía-Romero S, Chaumillon R, Patoine A, Lugo E, Bernardin D, et al. (2020) Eye-head coordination and dynamic visual scanning as indicators of visuo-cognitive demands in driving simulator. PLoS ONE 15(12): e0240201. https://doi.org/10.1371/journal.pone.0240201
Editor: Feng Chen, Tongii University, CHINA
Received: September 19, 2020; Accepted: December 16, 2020; Published: December 31, 2020
Copyright: © 2020 Mikula et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Relevant files are available from the Open Science Framework repository (https://osf.io/da9yp/).
Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada, NSERC – Essilor Industrial Research Chair (IRCPJ 305729-13), Research and development cooperatif NSERC – Essilor Grant (CRDPJ 533187 - 2018), Prompt (https://www.nserc-crsng.gc.ca/index_eng.asp & https://www.essilor.ca). The funders provided support in the form of salary for author DB but had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Authors LM and AP received support from student awards from the Road Safety Research Network (Réseau de Recherche en Sécurité Routière) of Québec (https://rrsr.ca/en).
Competing interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: author DB is an adjunct professor of the NSERC/Essilor Chair, RDC NSERC-Essilor project at Université de Montréal and is employed by Essilor Canada as research project manager. This does not alter our adherence to PLOS ONE policies on sharing data and materials.
Vision is one of the most important sensory input used when driving , and as such intact visual processing and functions are a prerequisite for driver’s license application. The most widespread vision assessment comprises measurements of visual acuity and the extent of visual field. However, not all drivers are subject to the same regulations since legal visual requirements for driving can vary between, and sometimes within, countries. For instance, the minimum visual acuity imposed in the United States ranges between 20/40 and 20/100 depending on the jurisdiction , whereas Canadian vision standards are set to 20/50 except for the provinces of New Brunswick and Nova Scotia which require a minimum of 20/40, in accordance with the recommendation of the International Council of Ophthalmology [3,4].
Although focus has been primarily directed to the vision standards for driving, to date studies have shown relatively weak or inconsistent relationships between stationary visual acuity by itself and motor vehicle collision involvement [1,5–10]. Besides, the likelihood of road accidents is not increased in drivers with visual acuity less than 20/40 compared to those with better vision [8,11]. Given the highly visual complexity of driving, it is not surprising that visual acuity alone does not reflect all the capacities necessary to safely operate a motor vehicle.
In contrast, visual attention and cognitive functions appear to be better predictors of driver safety behavior. The Useful Field of View (UFOV) test for example, has been designed to evaluate visual speed processing and divided as well as selective attention. Previous research has revealed that the impaired performance on the UFOV observed in older adults is indeed related to greater crash risk [5,10,12–14] and poorer driving performance [15–17]. Similarly, it has been reported that diminished cognitive functions are associated with unsafe driving [18–20]. And more recently, perceptual-cognitive abilities measured using 3-Dimensional Multiple Object Tracking (3D-MOT) have been shown to predict the performance of older adults in driving simulator [21,22].
Therefore, driving is a cognitively demanding task that requires not only proper visual but also cognitive functions. As a result of the limited human brain capacity, the increased mental workload associated with multitasking results in impaired behavioral performance [23–25]. Distracted driving refers to any concurrent activity that can withdraw attention from the primary task of driving and includes but is not limited to eating, texting, interacting with passengers or using entertainment and navigation systems . Indeed, about 21% of fatalities and 27% of serious injuries that happened in 2016 involved some form of distracted driving according to Transport Canada’s National Collision Database. The use of in-vehicle devices has been shown to increase drivers’ cognitive resources, resulting in a reduced ability to control their car [27–29]. Performing concurrent tasks while driving is thus a major concern for road safety as it is likely to disrupt visual attention allocation [30–32].
The coupling between eye movements and attention has been well-documented, showing that attention is deployed to the location of a future saccade [33–35]. As a consequence of greater mental workload, the attentional resources available to visually explore the environment are drastically reduced. In the context of driving, it results in spatial gaze concentration as well as more frequent and longer fixations away from the road, which can affect the detection of potential hazards [36–39]. In addition to classical eye movement metrics, including fixation rate and duration, entropy has been derived from information theory  to provide a quantitative analysis of gaze behavior in naturalistic environments such as flight simulation [41–44], surgery [45–47] and driving [48–51]. The entropy captures visual scanning complexity and, by extension, the spatial distribution of visual attention using two measures. The stationary entropy characterizes the overall gaze dispersion across the visual scene whereas the transition entropy reflects the randomness (or the predictability) in the scanning pattern [52–54].
Previous research has shown decreased gaze entropy in pilots during high-complexity flights [42,44] and when performing a subsidiary task while driving . Thus, increasing cognitive demands seem to be associated with lower entropy, which indicates less exploration and a more predictable pattern of visual scanning . In contrast, more traditional eye metrics such as saccade amplitude and fixation duration were not found to be as sensitive to the modulation of mental workload in these situations. Furthermore, pilots’ electroencephalographic (EEG) recordings revealed that the reduction of gaze entropy induced by flight complexity is accompanied by enhanced frontal theta oscillations . Interestingly, EEG frontal theta power is known to be a neurophysiological index of cognitive and attentional demands [55–58]. These results suggest that entropy measures reflect changes of the ocular behavior in response to the task workload. However, it should be noted that the calculation of transition entropy in the aforementioned studies relies on the spatial discretisation of the visual space and is therefore highly dependent on the visual content of the scene. This can be problematic in the case of dynamically changing stimuli that can modify fixation probabilities and thus entropy measures. An alternative method that has been put forward this limitation is to investigate eye movements over multiple temporal segments, instead of spatial areas of interest . The benefit of this time-based entropy measure is that it is less sensitive to shifts of the visual scene in more naturalistic settings, where head and body movements occur.
When driving, as opposed to less naturalistic environments, head movements are likely to be involved . Indeed, gaze shifts greater than 15° usually rely on a combination of both eye and head movements [61–64]. Moreover, it has been shown that the processing of visual stimuli is enhanced when presented in the straight-ahead direction, independently of gaze direction [65,66]. These results suggest that there is a relationship between visuospatial attention and head movements, as was described for eye movements. Using a driving simulator, different eye-head coordination dynamics have been recorded following exogenous (i.e., stimulus-driven) and endogenous (i.e., goal-oriented) attention shifts . Furthermore, progressive lens wearers have been shown to modify their eye-head coordination in real-world driving  or when presented with driving-related scenes , providing evidence that eye-head movements are modulated by the quality of visual inputs. Altogether, these findings show that coordinated movements of the eyes and head are related to visuo-cognitive processing .
As stated above, driving is a complex activity and if the associated visuo-cognitive needs are not met, driver’s safety can be compromised. The present study aims to investigate the effects of increasing visual and cognitive demands on eye-head coordination as well as visual scanning behavior in a driving simulator scenario. The driving task load was manipulated by introducing a concurrent visual search and detection task while visual demands were challenged by an experimental visual degradation induced by contact lens wear. The spatial distributions of eye-head movements were analyzed as well as the coordination between the eyes and the head. For this study, in contrast to traditional entropy measures which describe the spatial distribution of movements, entropy was computed based on temporal dynamics. Consequently, time-based entropy metrics were implemented for the gaze, but also the eyes and the head signals in order to better describe the changes in scanning behavior as a result of greater visuo-cognitive demands.
Materials and methods
Twenty-one participants (15 males, 6 females) aged between 21 and 34 years old (mean ± SD = 24.8 ± 3.7) were recruited for this study. They all had a valid driver’s license for at least 5 years and they had normal vision or corrected with contact lenses (i.e., far visual acuity of 4/10 or better in ETDRS chart, stereoscopic acuity of minimum 50 seconds of arc in Randot test and a visual field of at least 100 continuous degrees along the horizontal meridian and at least 10 continuous degrees above and 20 continuous degrees below fixation). All participants had myopia and hyperopia lower than 3.00 diopters (D), maximum astigmatism of 0.75 D and anisometropia lower than 1.00 D. Participants did not suffer from any visual, vestibular, neurological, musculoskeletal or cardiovascular impairment. In addition, scores on the UFOV test showed that all individuals were classified in the low or very-low risk groups for probability of driving difficulties. All participants provided informed written consent and received a compensation of 15$ after the completion of the experiment. This study and all the experimental procedures were approved by the ethics committee of Université de Montréal (Comité d’éthique de la recherche clinique CERC; certificate N°18-090-CERES-D).
The Virage VS500M car driving simulator (Virage Simulation Inc.®, Montréal, Canada) was used for the driving tasks. The cockpit consisted of real car parts including a seat, a force feedback steering wheel, accelerator and brake pedals, a dashboard and automatic transmission and controls. The visualization system included a PC 5-channel image generator as well as three 50-inch high-resolution (1280 x 720 pixels) overhead projection screens providing 180° front views. In addition, two smaller lateral screens were positioned in the back to replicate blind spot and mirror visualization. Rearview and side mirrors were projected on the central screen at their approximate locations in a real car. The driving cabin of the simulator was mounted on a three-axis platform with electric actuators that recreated the haptic feedback of acceleration, braking, engine-induced vibrations and road texture. A stereo sound system provided realistic engine and external road sounds, and Doppler effects were used to generate naturalistic sounds of surrounding traffic. All auditory information was adjusted to the driving speed. The navigation device consisted of an 8-inch LCD monitor (1024 x 768 pixels) which was located on the car center console, at the level of the air vents and approximately 70 cm away from participants’ head.
Head movements were recorded using an OptiTrack motion capture system and the Motive software (NaturalPoint Inc., Oregon, USA) at a sampling rate of 120 Hz. Participants wore a helmet with 4 retro-reflective markers located above the head. The 3D positions of the markers were recorded by a camera placed on top of the simulator's center screen, in order to track yaw, pitch and roll rotations of the head while participants were driving. Eye movements were recorded using SMI Eye Tracking Glasses 2 Wireless (SensoMotoric Instruments, Teltow, Germany) which is a mobile eye-tracking system providing native, binocular tracking with a sampling rate of 120 Hz. The infrared light emitted by the glasses allowed two cameras located in the lower frame to track the corneal reflections and determine the center of the pupils. Eye rotations were recorded in yaw and pitch after a standard 3-point calibration.
Both eye and head recordings were synchronized in time. In order to estimate the gaze-in-space rotation, eye-in-head orientation recorded by the eye-tracker was combined with head-in-space position measured by the motion capture system. These coordinate system transformations required additional calibration procedures. First, the position of the eye rotation center relative to the head and the wearable eye-tracker was computed based on pictures taken at different angles . Then, participants were instructed to move their eyes, but not their head, to fixate a set of 18 points displayed on the central screen of the driving simulator. This particular procedure ensures an accurate estimation of gaze position in 3D world coordinates and allows the computation of intersections with the driving simulator screen and the navigation device on the center console.
In the driving scenario, participants were on a highway and the task consisted of maintaining their speed at 90 km/h, as accurately as possible. They were instructed to drive normally, as they would in real life and respect road signs, speed limits and other road users. While driving, participants were asked to perform a visual search task on a navigation device located in periphery, on the center console. One trial of the visual search task proceeded as follows. The navigation device turned on and displayed a picture of direction road signs with multiple information (Fig 1A) for 6 seconds and then the device was turned off. Participants had to verbally report the number associated with the city “Montréal” which appeared on each road signs among other directions. They were not given any cue to the onset of a given trial; however, no time limit was imposed and they were allowed to respond during and after the stimuli presentation. A total of 7 visual search trials were randomly distributed in time throughout the driving scenario, which lasted approximately 6 minutes and 30 seconds (Fig 1B). In total, 14 different pictures could be presented to participants so that they did not see the same road sign twice.
A. Example of a direction road sign presented on the navigation device during the visual search task. Participants were asked to give the number associated with the city “Montréal” (here 76). B. Temporal sequence of the driving scenario. Driving speed, head rotation and eye rotation as a function of time. Grey shaded areas depict the 7 visual search trials. Yaw rotations are represented in red and pitch rotations in blue.
Each participant performed the experiment in two conditions: with normal or corrected-to-normal vision (Optimal vision) and with reduced visual acuity (Degraded vision). The order of both experimental conditions was counterbalanced across participants to control for practice effects. For the degraded vision condition, participants were divided into two different groups. In the “lower degradation” group, the contact lenses power was chosen so that participants’ visual acuity would approach 4/10 at 3 m distance whereas for the “higher degradation” group, the targeted visual acuity was still 4/10 but at a distance of 1m20. Eleven out of the 21 participants (8 males, 3 females; age = 24.2 ± 3.5 years old) were in the lower perturbation group and the remaining 10 participants (7 males, 3 females; age = 25.5 ± 3.9 years old) were in the higher perturbation group. Disposable soft contact lenses (CooperVision Inc.®) were used to reduce participants’ visual acuity. The power of contact lenses was defined by calculating the difference between the target threshold visual acuity and the visual acuity without correction of the participant.
Head rotations were recorded in the world coordinate system whereas eye rotations were measured in the head coordinate frame. In addition, gaze (eye-in-space) rotations were computed afterwards by using the head-in-space and the eye-in-head recorded signals. For the purpose of this study, yaw and pitch rotations were analyzed. Negative yaw angles indicate left and positive yaw angles indicate right. On the other hand, negative pitch angles correspond to downward rotations whereas positive pitch rotations describe upward rotations in the corresponding coordinate system.
Eye-head coordination was investigated by considering the linear regression of head versus eye rotations. If the eyes move without any head rotation, the slope would equal 0. In contrast, the bigger the slope, the more involved the head is in coordinated eye-head movements. In both visual conditions, linear regressions slopes were computed for each individual and then averaged across participants within the same degradation group. In order to exclude potential outliers and data artefacts from the regression analysis, data with low-density distribution (less than 20 occurrences per 1x1 degree bin) were removed. Eye-head coordination was analyzed only during the visual search trials, separately for yaw and pitch rotations.
In contrast to eye-head coordination, entropy was evaluated throughout the whole driving scenario, and not only during the visual search task. The X and Y positions of eye, head and gaze were first combined to compute the Euclidean distance of each effector’s movement (). In order to evaluate time-based entropy, the eye, head and gaze data were divided into time bins of 120 ms, which approximates the minimum fixation duration. Time-based transition entropy was then calculated by using the conditional entropy equation  as follows: Where pi is the probability of transitioning between the simulator central screen and the navigation device in time bin i and p(i,j) the probability to find the same transition pattern in time bins i and j. By analogy to traditional transition entropy, where pi represents the probability that one fixation is in the area of interest i and p(i,j) the probability to transition from area i to j. The entropy calculated was then normalized by the maximum entropy so that it ranged between 0 and 1. As supported by previous research, higher entropy depicts a more complex and less predictable pattern of visual scanning. On the other hand, lower entropy suggests a more structured and less random pattern of scanning behavior [52–54]. All data processing and computations were performed using a custom-written Matlab® toolbox (The MathWorks, Natick, MA, USA).
In order to compare the distributions of eye, head and gaze rotations between optimal and degraded vision, two-sample Kolmogorov-Smirnov tests were used, where the null hypothesis assumes that the two samples come from the same continuous distribution. Two-way mixed ANOVAs were conducted to explore the effect of the visual condition (within-subjects factor–optimal and degraded vision) and the severity of the visual perturbation (between-subjects factor–lower and higher degradation groups). Non-normal data were corrected for distribution skew using the Box-Cox transformation . Tukey’s HSD post-hoc tests were used to further explore significant main effects and interactions. Statistical threshold was set to 0.05.
First of all, we made sure that participants were completing the visual search task on the navigation device. This was confirmed by the overall success rate which was 84.4 ± 3.4% (mean ± SEM; optimal vision, lower degradation group: 92.2 ± 3.0%; degraded vision, lower degradation group: 71.4 ± 7.5%; optimal vision, higher degradation group: 85.7 ± 8.5%; degraded vision, higher degradation group: 88.6 ± 5.9%).
The density distributions of head, eye and gaze rotations during the visual search task are depicted in Fig 2. In optimal vision (Fig 2A), most of the eye, gaze and head rotations in yaw and pitch were centered around the origin (yellow areas). These observations indicate that both the head and the gaze were primarily oriented towards the middle of the central driving simulator screen (i.e., the road ahead). In addition, it shows that the eyes were mostly in the primary position–in other words, the visual axis is parallel to the sagittal plane of the head. Furthermore, the distributions of eye, head and gaze rotations appear to stretch out to the bottom right quadrant (blue green areas) which roughly corresponds to the position of the car center console. This demonstrates that participants were actually involved in the visual search task displayed on the navigation device located in periphery. Interestingly, the distributions of rotations seemed to be modified by the visual degradation induced by the contact lenses (Fig 2B). These differences are better captured through the kernel density estimates depicted in Fig 3. Two-sample Kolmogorov-Smirnov tests revealed that the distributions of rotations between the optimal and degraded vision conditions were significantly different for the eye and the gaze in pitch, and for the head in yaw (all p < 0.01). Similar to the optimal vision condition; head, eye and gaze rotations in degraded vision were mostly aligned with the origin. This shows that, irrespective of the visual perturbation, participants tend to keep their head and eyes directed towards the road straight ahead while driving and performing the concurrent visual search task in periphery. However, as a result of the visual degradation, rotations around 0 were reduced and more rotations were observed around -12° in pitch for the eyes (Fig 3A), +20° in yaw for the head (Fig 3B) and -15° in pitch for the gaze (Fig 3C). These findings suggest that, in presence of the visual degradation, participants are more likely to direct their eyes and head towards the navigation device located on the car center console.
In optimal vision (A) and degraded vision (B) during the visual search task. Pitch rotations are plotted as a function of yaw rotations for the eye (left column), the head (middle column) and the gaze (right column). The color scale depicts the number of data points from all participants (n = 21) for a given combination of yaw-pitch angles.
Kernel density estimates of eye (A), head (B) and gaze (C) yaw and pitch rotations depicted in Fig 2, in the optimal and degraded vision conditions. **p < 0.01, ***p < 0.001.
The coordination between eye and head rotations was first analyzed in the yaw axis (Fig 4). In the optimal vision condition, the average slope of the linear regression between head yaw and eye yaw was -0.47 ± 0.43 for the lower degradation group and -0.22 ± 0.29 for the higher degradation group. In the degraded vision condition, the slopes were -0.50 ± 0.32 and -0.66 ± 0.43 for the least and most impaired group, respectively. A two-way ANOVA revealed a significant main effect of the visual perturbation showing that the average linear regression slope was steeper in the degraded vision condition compared to the optimal vision condition (F(1,38) = 5.07, p = 0.030, η2 = 0.11). However, there was no significant main effect of the degradation group (F(1,38) = 0.25, p = 0.617) and no significant interaction (F(1,38) = 2.98, p = 0.092). The eye-head coordination in the pitch axis is illustrated in Fig 5. When vision was optimal, the average slopes were very close to 0 for both degradation groups (lower degradation group: -0.01 ± 0.09 and higher degradation group: 0.00 ± 0.08). In the degraded vision condition, the slope for the lower degradation group was -0.11 ± 0.21 and -0.07 ± 0.24 for the higher degradation group. The two-way ANOVA conducted showed neither significant main effects of the visual degradation (F(1,38) = 2.73, p = 0.107) and degradation severity (F(1,38) = 1.00, p = 0.323), nor a significant interaction (F(1,38) = 0.28, p = 0.598). These findings suggest that the eye-head coordination in yaw, but not in pitch, is modified in response to the visual degradation introduced. More specifically, when vision is not optimal, more head movements are recruited to perform the visual search task while driving. However, eye-head coordination does not seem to reveal differences between the two degradation groups.
In optimal (right column) and degraded vision (right column) for the lower degradation group (top row) and the higher degradation group (top row) during the visual search task. Head rotations are represented as a function of eye rotations (grey data points). Average slopes of the linear regression (red lines) are reported in each plot. Ellipses represent the joint probability distributions and colored lines correspond to iso-probability contours.
In optimal (right column) and degraded vision (right column) for the lower degradation group (top row) and the higher degradation group (top row) during the visual search task. Head rotations are represented as a function of eye rotations (grey data points). Average slopes of the linear regression (red lines) are reported in each plot. Ellipses represent the joint probability distributions and colored lines correspond to iso-probability contours.
In order to further explore the scanning behavior of participants, the time-based entropy was computed across the entire driving scenario and the resulting measures are presented in Table 1. Transition entropies for the eye, the head and the gaze are depicted in Fig 6. For the eye signal, the two-way ANOVA revealed a main effect of the visual condition (F(1,38) = 14.94, p < 0.001, η2 = 0.25) showing that eye entropy was significantly reduced in the presence of the visual perturbation, compared to the optimal vision condition. In addition, there was a main effect of the degradation severity; the higher degradation group showed reduced eye entropy than the lower degradation group (F(1,38) = 4.53, p = 0.040, η2 = 0.08). One could assume that this effect may be driven by one participant in the lower degradation group having greater eye entropy in degraded vision (Fig 6, top left subplot). However, performing the ANOVA without this participant led to similar results (significant main effect of degradation severity: F(1,38) = 4.35, p = 0.044, η2 = 0.06). In contrast, no significant interaction was reported between visual condition and experimental group (F(1,38) = 1.76, p = 0.192). Analyses on the head entropy showed no significant main effects of the visual condition (F(1,38) = 3.35, p = 0.075) or the severity of the degradation (F(1,38) = 1.27, p = 0.267) and no significant interaction (F(1,38) = 0.06, p = 0.816). As for the gaze, the ANOVA revealed a significant main effect of the visual condition (F(1,38) = 6.69, p = 0.014, η2 = 0.15) where entropy was decreased when vision was degraded. However, no main effect of degradation severity (F(1,38) = 0.10, p = 0.757) and no significant interaction (F(1,38) = 0.08, p = 0.778) were found. These results show that the scanning dynamics of both the eyes and the gaze are similarly affected by the visual perturbation induced.
The histograms represent the average entropy across participants. The error bars represent the SEM and the light grey circles depict the entropy for each individual. Boxes on the right side of each subplot depict the mean entropy for both degradation groups (optimal and degraded vision conditions combined). *p < 0.05, ***p < 0.001.
This study was designed to explore the effects of increasing visual and cognitive demands on eye-head movements and visual scanning pattern while driving. Participants in a driving simulator were asked to maintain constant speed and perform a concurrent visual search and detection task on a navigation device located in the periphery. A visual perturbation was experimentally induced by the wear of contact lenses. The distributions of eye and gaze movements in the pitch axis, and head movements in the yaw axis were found to be affected by the introduction of the visual degradation. Namely, rotations were modified in such a way that participants directed their eyes and head more towards the navigation device on the car center console, where the visual search task was displayed. Nevertheless, in both the optimal and the degraded vision conditions, the head and the gaze were mostly directed on the road ahead as shown by the maxima of density estimates which were centered around 0°. These observations resemble the findings reporting more gaze concentration towards the road center area as the driving speed or the task difficulty increases [38,74,75]. Furthermore, eye-in-head rotations revealed that the eyes remained somewhat aligned with the front head direction. This is consistent with previous studies that have shown that eye fixations are strongly biased towards the head orientation and that eye-head misalignments can result in impaired visual processing [70,76]. Taken together, these findings suggest that although our participants were performing a visual search in the periphery, their focus remained largely centered on the road in front of the car. One possible explanation could be that participants were able to complete the subsidiary task on the navigation device faster than the maximum 7-second window allowed and, then shifted their eyes and head back to the road for the main driving task. Alternatively, they could have switched multiple times between the road and the navigation device before giving their answer. The examination of reaction times to the visual search task, which we did not measure in the present study, would have been helpful to confirm or refute this hypothesis.
The analysis of eye-head coordination showed that, participants exhibited head movements of greater amplitude in the horizontal plane (i.e., yaw angle), when wearing the contact lenses compared to when vision was optimal. Considering more specifically the degraded vision condition however, no significant difference was observed between the lower and higher degradation groups. Moreover, the eye-head coordination in the pitch axis was not significantly modified when vision was impaired by contact lens wear. These results highlight the specific reorganization of horizontal eye-head movements in response to the visual degradation, while performing a subsidiary visual search task. Our results are in accordance with the observation that participants tend to make more head movements towards the visual stimuli of interest when task difficulty increases . Nevertheless, the slope of the linear regression of head versus eye rotations never exceeded -1. This implies that overall, the eyes contribute more than the head to gaze shifts, as previously described for the discrimination of visual targets in the periphery . Interestingly, the change in eye-head strategy highlighted in the present study echoes earlier work that has reported more and larger vertical head movements in participants adapting to progressive addition lenses [69,79]. This is attributed to the gradual change in power from the top to the bottom of progressive lenses, necessary to provide clear vision at all distances. In our study, however, horizontal movements were more likely to be involved as the secondary visual search task was displayed on the car center console. That would explain why our visual perturbation specifically affected the eye-head coordination across the horizontal, and not the vertical, plane.
The present study sought to investigate drivers’ scanning behavior by means of the entropy. We adopted a new approach which takes into consideration the temporal rather than the standard spatial features of eye and head movements, which are typically used for the calculation of entropy. Our modified entropy measures revealed that the scanning pattern of the head was not strongly affected by the visual perturbation induced by the contact lenses. This difference may be due to slower head movements compared to the eyes, thus requiring the use of longer time windows for the calculation of time-based head entropy. However, for the sake of this study we decided to use the same time window of 120 ms for the eyes, the gaze and the head in order to compare entropy measures between all three effectors. On the other hand, both eye and gaze entropies were found to be significantly decreased when vision was impaired, compared to when it was optimal. The entropy of the eye, but not the gaze, was lower in the most compared to the least impaired group. This result suggests that the eyes’ scanning pattern might be more sensitive to various levels of blur and could be a more reliable marker of visuo-cognitive demands. Reduced eye and gaze entropies while wearing contact lenses demonstrate that increasing visual demands altered drivers’ visual scanning pattern, which became less explorative and more stereotyped. These results are similar to those reporting a reduction in gaze transition entropy when portions of visual stimuli are blurred . Unfortunately, the authors did not discuss this result and it remains unclear why and how a visual perturbation can influence scanning patterns. Two non-mutually exclusive explanations can be advanced. The first is that transition entropy is dependent on the visual scene complexity, as suggested by Shiferaw and colleagues . In that case, the loss of high spatial frequency content due to the blur induced by the contact lenses would result in reduced visual complexity and thus, in lower transition entropy. The second is that non-optimal vision substantially increases the overall cognitive task load. There again, a reduction in transition entropy is expected as it has been shown to decrease during high-complexity flights, complex pattern recognition tasks or dual-task driving [41,42,44,48,81]. Transition entropy is considered to be an indicator of visual scanning efficiency and to reflect the top-down modulation of gaze control . As a consequence, the reduction in transition entropy related to task difficulty or distraction is likely to demonstrate impaired allocation of resources for gaze control, due to overall greater cognitive demands.
Ultimately, our present findings demonstrate that the calculation of entropy based on temporal characteristics of the scanpath provides some advantages over the more traditional entropy measures considering spatial distribution. Indeed, transition entropy as commonly used to characterize scanning patterns quantifies the transition of fixations between different areas of interest that divide the visual scene [52,53,82]. However, under normal viewing conditions, eye movements are for the most part stimulus-driven and attracted to salient elements of the environment [83–85]. This thus suggests that transition entropy, assessed using regions of interest, might be highly dependent upon the visual scene composition and how the visual space is been discretized . Under those circumstances, it makes it difficult to compare transition entropies between paradigms in which visual stimuli are more dynamic and change over time, such as in driving simulator. Furthermore, it has been acknowledged that fixation durations are also relevant to describe scanning patterns and can vary as a function of task difficulty [86,87]. Hence, the use of time-based entropies would allow to minimize the confounding effects of various visuospatial task demands . Our modified measures of entropy have been shown to vary in the same way as traditional transition entropy does in aviation and driving [41,42,48], therefore providing evidence that this particular method constitutes a valid approach to quantify visual scanning behavior in complex environments. In addition, transition entropy so far has been derived from gaze shifts which combine eye and head signals and to our knowledge, this is the first study to examine the entropy related to eyes and head, separately. These findings suggest that transition entropy can be applied to eye and head recordings as well and, this would allow a better understanding of the relationship between eye and head scanning behaviors and strategies. Although further research is needed to strengthen the present findings, this is of particular interest for studies using more naturalistic or real-world settings in which the head is not restrained.
In this study, we introduced a blur in emmetropic participants in order to challenge their visual system and increase the visuo-cognitive demands of the task. For this purpose, they wore contact lenses with a positive addition which impose myopic defocus, thus resulting in a reduction of visual acuity. The plus lens caused the image to focus in front of, instead of on, the retina. As a result, a change in accommodative demand occurred leading to a mismatch between the vergence and the accommodative responses, referred to as vergence-accommodation conflict. Furthermore, myopic defocus imposed during development is known to trigger structural changes in eye growth to compensate for the lens-induced refractive errors, as reported in a number of animal species [88–91]. These observations corroborate the effect of defocus on visual demands. In addition, the vergence-accommodation conflict has been shown to interfere with cognitive executive functions . It is speculated that the neural correlates between cognitive control and the vergence-accommodation coupling partially overlap at the level of the frontal and parietal lobes. Consequently, both processes compete for visual attention resources when disrupting the balance between vergence and accommodation. Similarly, visual blur has been related to impaired cognitive functioning  and the recognition of blurry objects requires larger field of view as well as longer viewing times . These findings support the need to consider the impact of visual degradation on the interaction between vision and cognition, especially as the simple measure of visual acuity appears to be dependent on the effect of both retinal blur and covert attention . This underscores the importance of the quality of vision during highly demanding cognitive tasks, such as driving for example.
Finally, it has been reported that the visual system shows weaker vergence and accommodation responses to blur compared to disparity cues [96,97]. This suggests that the modulation of the vergence response, such as prism-induced disparity for example, would have a greater impact and would potentially allow to reveal distinct effects as a function of the magnitude of the visual perturbation. Moreover, young adults may have sufficient accommodative reserve to partially compensate for the vergence-accommodation mismatch [96,98,99]. It is thus possible that our participants were able to somewhat compensate, even for the blur induced by the stronger addition. That would explain why, in most cases, we did not observe significant differences between the lower and the higher visual degradation groups, and hence found a very limited effect of the severity of visual degradation. That said, it would be interesting to test older adults in order to investigate whether the decline of the accommodative ability exacerbate the effect of the visual degradation on their eye-head coordination and visual scanning behavior while driving.
To conclude, this study has provided evidence that when performing a highly demanding driving task, drivers adapt their eye-head coordination in order to meet the increasing visual demands related to vision degradation. By contrast, the overall spatial distribution of eye and head movements appears to be rather insensitive to perturbations of the visual input. Lastly, time-based transition entropy measures have revealed that the scanning behavior of the eyes and the gaze is modified by the visual perturbation induced. This modification in transition entropy suggests a decline in visual scanning efficiency in response to increased visuo-cognitive demands, which can be potentially detrimental for drivers’ safety on the road. These findings demonstrate that quantitative measures of visual scanning provide relevant information about the visuo-cognitive demands and possibly the mental workload involved in performing complex tasks such as driving. If so, time-based entropy could be used in upcoming research to help better identify distraction in fields where traditional entropy measures are currently being used, such as driving, aviation or surgery. Ultimately, dynamic visual scanning assessed through time-based entropy might be able to discriminate between safe and unsafe behaviors during these complex and demanding tasks.
- 1. Owsley C, McGwin G. Vision and driving. Vision Res. 2010 Nov 23;50(23):2348–61. pmid:20580907
- 2. Casson EJ, Racette L. Vision standards for driving in Canada and the United States. A review for the Canadian Ophthalmological Society. Can J Ophthalmol J Can Ophtalmol. 2000 Jun;35(4):192–203. pmid:10900516
- 3. International Council of Ophthalmology. Vision Requirements for Driving Safety. In Sao Paulo, Brazil; 2006.
- 4. Yazdan-Ashoori P, ten Hove M. Vision and driving: Canada. J Neuro-Ophthalmol Off J North Am Neuro-Ophthalmol Soc. 2010 Jun;30(2):177–85. pmid:20523185
- 5. Cross JM, McGwin G, Rubin GS, Ball K, West SK, Roenker DL, et al. Visual and medical risk factors for motor vehicle collision involvement among older drivers. Br J Ophthalmol. 2009 Mar;93(3):400–4. pmid:19019937
- 6. Decina LE, Staplin L. Retrospective evaluation of alternative vision screening criteria for older and younger drivers. Accid Anal Prev. 1993 Jun 1;25(3):267–75. pmid:8323661
- 7. Desapriya E, Harjee R, Brubacher J, Chan H, Hewapathirane DS, Subzwari S, et al. Vision screening of older drivers for preventing road traffic injuries and fatalities. Cochrane Database Syst Rev. 2014 Feb 21;(2):CD006252. pmid:24563119
- 8. Gresset JA, Meyer FM. Risk of accidents among elderly car drivers with visual acuity equal to 6/12 or 6/15 and lack of binocular vision. Ophthalmic Physiol Opt J Br Coll Ophthalmic Opt Optom. 1994 Jan;14(1):33–7. pmid:8152818
- 9. Owsley C, McGwin G, Ball K. Vision impairment, eye disease, and injurious motor vehicle crashes in the elderly. Ophthalmic Epidemiol. 1998 Jun;5(2):101–13. pmid:9672910
- 10. Rubin GS, Ng ESW, Bandeen-Roche K, Keyl PM, Freeman EE, West SK. A prospective, population-based study of the role of visual impairment in motor vehicle crashes among older drivers: the SEE study. Invest Ophthalmol Vis Sci. 2007 Apr;48(4):1483–91. pmid:17389475
- 11. Keeffe JE, Jin CF, Weih LM, McCarty CA, Taylor HR. Vision impairment and older drivers: who’s driving? Br J Ophthalmol. 2002 Oct;86(10):1118–21. pmid:12234890
- 12. Ball K, Owsley C, Sloane ME, Roenker DL, Bruni JR. Visual attention problems as a predictor of vehicle crashes in older drivers. Invest Ophthalmol Vis Sci. 1993 Oct;34(11):3110–23. pmid:8407219
- 13. Ball K, Roenker DL, Wadley VG, Edwards JD, Roth DL, McGwin G, et al. Can high-risk older drivers be identified through performance-based measures in a Department of Motor Vehicles setting? J Am Geriatr Soc. 2006 Jan;54(1):77–84. pmid:16420201
- 14. Owsley C, Ball K, Sloane ME, Roenker DL, Bruni JR. Visual/cognitive correlates of vehicle accidents in older drivers. Psychol Aging. 1991 Sep;6(3):403–15. pmid:1930757
- 15. Clay OJ, Wadley VG, Edwards JD, Roth DL, Roenker DL, Ball K. Cumulative meta-analysis of the relationship between useful field of view and driving performance in older adults: current and future implications. Optom Vis Sci Off Publ Am Acad Optom. 2005 Aug;82(8):724–31. pmid:16127338
- 16. Myers RS, Ball KK, Kalina TD, Roth DL, Goode KT. Relation of useful field of view and other screening tests to on-road driving performance. Percept Mot Skills. 2000 Aug;91(1):279–90. pmid:11011899
- 17. Wood JM, Chaparro A, Lacherez P, Hickson L. Useful field of view predicts driving in the presence of distracters. Optom Vis Sci Off Publ Am Acad Optom. 2012 Apr;89(4):373–81. pmid:22366710
- 18. Emerson JL, Johnson AM, Dawson JD, Uc EY, Anderson SW, Rizzo M. Predictors of driving outcomes in advancing age. Psychol Aging. 2012 Sep;27(3):550–9. pmid:22182364
- 19. Hollis AM, Duncanson H, Kapust LR, Xi PM, O’Connor MG. Validity of the mini-mental state examination and the montreal cognitive assessment in the prediction of driving test outcome. J Am Geriatr Soc. 2015 May;63(5):988–92. pmid:25940275
- 20. Lee JA, Choi H, Kim D-A, Lee B-S, Lee JJ, Bae JH, et al. Relationship Between Cognitive Perceptual Abilities and Accident and Penalty Histories Among Elderly Korean Drivers. Ann Rehabil Med. 2016 Dec;40(6):1092–9. pmid:28119840
- 21. Michaels J, Chaumillon R, Nguyen-Tri D, Watanabe D, Hirsch P, Bellavance F, et al. Driving simulator scenarios and measures to faithfully evaluate risky driving behavior: A comparative study of different driver age groups. PloS One. 2017;12(10):e0185909. pmid:29016693
- 22. Woods-Fry H, Deut S, Collin CA, Gagnon S, Faubert J, Bédard M, et al. Three-Dimensional Multiple Object Tracking Speed Thresholds are Associated with Measures of Simulated Driving Performance in Older Drivers: Proc Hum Factors Ergon Soc Annu Meet [Internet]. 2017 Sep 28 [cited 2020 Mar 21]; Available from: pmid:28492869
- 23. Pashler H. Dual-task interference in simple tasks: data and theory. Psychol Bull. 1994 Sep;116(2):220–44. pmid:7972591
- 24. Salvucci DD, Taatgen NA. Threaded cognition: an integrated theory of concurrent multitasking. Psychol Rev. 2008 Jan;115(1):101–30. pmid:18211187
- 25. Strayer DL, Cooper JM, Goethe RM, McCarty MM, Getty DJ, Biondi F. Assessing the visual and cognitive demands of in-vehicle information systems. Cogn Res Princ Implic. 2019 Jun 21;4(1):18. pmid:31227955
- 26. Canadian Council of Motor Transport Administrators. Distracted Driving White Paper. 2018 Jun.
- 27. Blaschke C, Breyer F, Färber B, Freyer J, Limbacher R. Driver distraction based lane-keeping assistance. Transp Res Part F Traffic Psychol Behav. 2009 Jul 1;12(4):288–99.
- 28. Dewing WL, Johnson SM, Stackhouse SP. The interaction of non-driving tasks with driving. Minnesota, Department of Transportation; 1995. pmid:8548542
- 29. Lansdown TC, Brook-Carter N, Kersloot T. Distraction from multiple in-vehicle secondary tasks: vehicle performance and mental workload implications. Ergonomics. 2004 Jan 15;47(1):91–104. pmid:14660220
- 30. Lee Y-C, Lee JD, Ng Boyle L. The Interaction of Cognitive Load and Attention-Directing Cues in Driving. Hum Factors. 2009 Jun 1;51(3):271–80. pmid:19750791
- 31. Mackenzie AK, Harris JM. A link between attentional function, effective eye movements, and driving ability. J Exp Psychol Hum Percept Perform. 2017;43(2):381–94. pmid:27893270
- 32. Strayer DL, Drews FA, Johnston WA. Cell phone-induced failures of visual attention during simulated driving. J Exp Psychol Appl. 2003;9(1):23–32. pmid:12710835
- 33. Corbetta M, Akbudak E, Conturo TE, Snyder AZ, Ollinger JM, Drury HA, et al. A common network of functional areas for attention and eye movements. Neuron. 1998 Oct;21(4):761–73. pmid:9808463
- 34. Deubel H, Schneider WX. Saccade target selection and object recognition: evidence for a common attentional mechanism. Vision Res. 1996 Jun;36(12):1827–37. pmid:8759451
- 35. Rizzolatti G, Riggio L, Dascola I, Umiltá C. Reorienting attention across the horizontal and vertical meridians: evidence in favor of a premotor theory of attention. Neuropsychologia. 1987;25(1A):31–40. pmid:3574648
- 36. Mackenzie AK, Harris JM. Eye movements and hazard perception in active and passive driving. Vis Cogn. 2015 Jul 3;23(6):736–57. pmid:26681913
- 37. Recarte MA, Nunes LM. Mental workload while driving: Effects on visual search, discrimination, and decision making. J Exp Psychol Appl. 2003;9(2):119–37. pmid:12877271
- 38. Victor TW, Harbluk JL, Engström JA. Sensitivity of eye-movement measures to in-vehicle task difficulty. Transp Res Part F Traffic Psychol Behav. 2005 Mar 1;8(2):167–90.
- 39. Wang Y, Reimer B, Dobres J, Mehler B. The sensitivity of different methodologies for characterizing drivers’ gaze concentration under increased cognitive demand. Transp Res Part F Traffic Psychol Behav. 2014 Sep 1;26:227–37.
- 40. Shannon CE. A mathematical theory of communication. Bell Syst Tech J. 1948 Jul;27(3):379–423.
- 41. Diaz-Piedra C, Rieiro H, Cherino A, Fuentes LJ, Catena A, Di Stasi LL. The effects of flight complexity on gaze entropy: An experimental study with fighter pilots. Appl Ergon. 2019 May 1;77(1):92–9. pmid:30832783
- 42. Harris RL, Tole JR, Ephrath AR, Stephens AT. How a New Instrument Affects Pilots’ Mental Workload: Proc Hum Factors Soc Annu Meet. 1982;26:1010–3.
- 43. Harris RL, Glover BJ, Spady AA. Analytical Techniques of Pilot Scanning Behavior and Their Application [Internet]. NASA Langley Research Center, Hampton, VA, US; 1986 [cited 2020 Mar 27]. Report No.: NASA TP-2525. Available from: https://ntrs.nasa.gov/search.jsp?R=19860018448.
- 44. Tole JR, Stephens AT, Vivaudou M, Harris RL, Ephrath AR. Entropy, instrument scan and pilot workload. In IEEE, New York, NY, USA; 1982 [cited 2020 Mar 27]. Available from: https://ntrs.nasa.gov/search.jsp?R=19830011205.
- 45. Di Stasi LL, Diaz-Piedra C, Rieiro H, Sánchez Carrión JM, Martin Berrido M, Olivares G, et al. Gaze entropy reflects surgical task load. Surg Endosc. 2016;30(11):5034–43. pmid:26983440
- 46. Di Stasi LL, Díaz-Piedra C, Ruiz-Rabelo JF, Rieiro H, Sanchez Carrion JM, Catena A. Quantifying the cognitive cost of laparo-endoscopic single-site surgeries: Gaze-based indices. Appl Ergon. 2017 Nov 1;65:168–74. pmid:28802436
- 47. Diaz-Piedra C, Sanchez-Carrion JM, Rieiro H, Stasi LLD. Gaze-based Technology as a Tool for Surgical Skills Assessment and Training in Urology. Urology. 2017 Sep 1;107:26–30. pmid:28666793
- 48. Schieber F, Gilland J. Visual Entropy Metric Reveals Differences in Drivers’ Eye Gaze Complexity across Variations in Age and Subsidiary Task Load: Proc Hum Factors Ergon Soc Annu Meet [Internet]. 2008 Sep 1 [cited 2020 Jan 14]; Available from: https://journals.sagepub.com/doi/10.1177/154193120805202311.
- 49. Shiferaw BA, Downey LA, Westlake J, Stevens B, Rajaratnam SMW, Berlowitz DJ, et al. Stationary gaze entropy predicts lane departure events in sleep-deprived drivers. Sci Rep. 2018 Feb 2;8(1):1–10. pmid:29311619
- 50. Shiferaw BA, Crewther DP, Downey LA. Gaze entropy measures detect alcohol-induced driver impairment. Drug Alcohol Depend. 2019 Nov 1;204:107519. pmid:31479863
- 51. Wang Y, Bao S, Du W, Ye Z, Sayer JR. Examining drivers’ eye glance patterns during distracted driving: Insights from scanning randomness and glance transition matrix. J Safety Res. 2017 Dec 1;63:149–55. pmid:29203013
- 52. Krejtz K, Duchowski A, Szmidt T, Krejtz I, González Perilli F, Pires A, et al. Gaze Transition Entropy. ACM Trans Appl Percept TAP. 2015 Dec 10;13(1):4:1–4:20.
- 53. Krejtz K, Szmidt T, Duchowski AT, Krejtz I. Entropy-based statistical analysis of eye movement transitions. In: Proceedings of the Symposium on Eye Tracking Research and Applications [Internet]. Safety Harbor, Florida: Association for Computing Machinery; 2014 [cited 2020 Mar 28]. p. 159–166. (ETRA ‘14). Available from: https://doi.org/10.1145/2578153.2578176.
- 54. Shiferaw BA, Downey LA, Crewther DP. A review of gaze entropy as a measure of visual scanning efficiency. Neurosci Biobehav Rev. 2019;96:353–66. pmid:30621861
- 55. Borghini G, Astolfi L, Vecchiato G, Mattia D, Babiloni F. Measuring neurophysiological signals in aircraft pilots and car drivers for the assessment of mental workload, fatigue and drowsiness. Neurosci Biobehav Rev. 2014 Jul;44:58–75. pmid:23116991
- 56. Di Stasi LL, Diaz‐Piedra C, Suárez J, McCamy MB, Martinez‐Conde S, Roca‐Dorda J, et al. Task complexity modulates pilot electroencephalographic activity during real flights. Psychophysiology. 2015;52(7):951–6. pmid:25728307
- 57. Lin C-T, Chen S-A, Chiu T-T, Lin H-Z, Ko L-W. Spatial and temporal EEG dynamics of dual-task driving performance. J NeuroEngineering Rehabil. 2011 Feb 18;8:11. pmid:21332977
- 58. Wang Y-K, Jung T-P, Lin C-T. Theta and Alpha Oscillations in Attentional Interaction during Distracted Driving. Front Behav Neurosci. 2018;12:3. pmid:29479310
- 59. Grindinger T, Duchowski AT, Sawyer M. Group-wise similarity and classification of aggregate scanpaths. In: Proceedings of the 2010 Symposium on Eye-Tracking Research & Applications [Internet]. Austin, Texas: Association for Computing Machinery; 2010 [cited 2020 May 10]. p. 101–104. (ETRA ‘10). Available from: https://doi.org/10.1145/1743666.1743691.
- 60. Land MF. Predictable eye-head coordination during driving. Nature. 1992 Sep 24;359(6393):318–20. pmid:1406934
- 61. Bartz AE. Eye and head movements in peripheral vision: nature of compensatory eye movements. Science. 1966 Jun 17;152(3729):1644–5. pmid:5936888
- 62. Fuller JH. Head movement propensity. Exp Brain Res. 1992;92(1):152–64. pmid:1486950
- 63. Pelz J, Hayhoe M, Loeber R. The coordination of eye, head, and hand movements in a natural task. Exp Brain Res. 2001 Aug;139(3):266–77. pmid:11545465
- 64. Stahl JS. Amplitude of human head movements associated with horizontal saccades. Exp Brain Res. 1999 May;126(1):41–54. pmid:10333006
- 65. Cicchini GM, Valsecchi M, De’Sperati C. Head movements modulate visual responsiveness in the absence of gaze shifts. Neuroreport. 2008 May 28;19(8):831–4. pmid:18463496
- 66. Durand J-B, Camors D, Trotter Y, Celebrini S. Privileged visual processing of the straight-ahead direction in humans. J Vis. 2012 Jun 26;12(6). pmid:22739269
- 67. Doshi A, Trivedi MM. Head and eye gaze dynamics during visual attention shifts in complex environments. J Vis. 2012 Feb 9;12(2). pmid:22323822
- 68. Rifai K, Wahl S. Specific eye-head coordination enhances vision in progressive lens wearers. J Vis. 2016 01;16(11):5. pmid:27604068
- 69. Chu BS, Wood JM, Collins MJ. Influence of presbyopic corrections on driving-related eye and head movements. Optom Vis Sci Off Publ Am Acad Optom. 2009 Nov;86(11):E1267–1275. pmid:19786931
- 70. Fang Y, Nakashima R, Matsumiya K, Kuriki I, Shioiri S. Eye-head coordination for visual cognitive processing. PloS One. 2015;10(3):e0121035. pmid:25799510
- 71. Nauche M, Chauveau J-P, Baranton K, Evain S. Method of measuring at least one geometric/physiognomic parameter for fitting the frame of vision-correction spectacles to the face of a wearer. International Patent WO2008129168A1, 2008.
- 72. Ciuperca G, Girardin V. On the estimation of the entropy rate of finite Markov chains. In 2005.
- 73. Box GEP, Cox DR. An Analysis of Transformations. J R Stat Soc Ser B Methodol. 1964;26(2):211–52.
- 74. Engström J, Johansson E, Östlund J. Effects of visual and cognitive load in real and simulated motorway driving. Transp Res Part F Traffic Psychol Behav. 2005 Mar 1;8(2):97–120.
- 75. van Leeuwen PM, Happee R, de Winter JCF. Changes of Driving Performance and Gaze Behavior of Novice drivers During a 30-min Simulator-based Training. Procedia Manuf. 2015 Jan 1;3:3325–32.
- 76. Nakashima R, Shioiri S. Why do we move our head to look at an object in our peripheral region? Lateral viewing interferes with attentive search. PloS One. 2014;9(3):e92284. pmid:24647634
- 77. Dunham DN. Cognitive difficulty of a peripherally presented visual task affects head movements during gaze displacement. Int J Psychophysiol Off J Int Organ Psychophysiol. 1997 Dec;27(3):171–82. pmid:9451577
- 78. Schwab S, Würmle O, Altorfer A. Analysis of eye and head coordination in a visual peripheral recognition task. J Eye Mov Res [Internet]. 2012 Dec 15 [cited 2020 Apr 26];5(2). Available from: https://bop.unibe.ch/index.php/JEMR/article/view/2330.
- 79. Hutchings N, Irving EL, Jung N, Dowling LM, Wells KA, Lillakas L. Eye and head movement alterations in naïve progressive addition lens wearers. Ophthalmic Physiol Opt J Br Coll Ophthalmic Opt Optom. 2007 Mar;27(2):142–53. pmid:17324203
- 80. Ryu D, Mann DL, Abernethy B, Poolton JM. Gaze-contingent training enhances perceptual skill acquisition. J Vis. 2016;16(2). pmid:26824639
- 81. Raptis GE, Fidas CA, Avouris NM. On Implicit Elicitation of Cognitive Strategies using Gaze Transition Entropies in Pattern Recognition Tasks. In: Proceedings of the 2017 CHI Conference Extended Abstracts on Human Factors in Computing Systems [Internet]. Denver, Colorado, USA: Association for Computing Machinery; 2017 [cited 2020 Apr 1]. p. 1993–2000. (CHI EA ‘17). Available from: https://doi.org/10.1145/3027063.3053106.
- 82. Ellis SR, Stark L. Statistical dependency in visual scanning. Hum Factors. 1986 Aug;28(4):421–38. pmid:3793110
- 83. Antes JR. The time course of picture viewing. J Exp Psychol. 1974;103(1):62–70. pmid:4424680
- 84. Mackworth NH, Morandi AJ. The gaze selects informative details within pictures. Percept Psychophys. 1967 Nov 1;2(11):547–52.
- 85. Parkhurst D, Law K, Niebur E. Modeling the role of salience in the allocation of overt visual attention. Vision Res. 2002 Jan 1;42(1):107–23. pmid:11804636
- 86. Henderson JM, Graham PL. Eye movements during scene viewing: evidence for mixed control of fixation durations. Psychon Bull Rev. 2008 Jun;15(3):566–73. pmid:18567256
- 87. Rayner K. Eye movements in reading and information processing: 20 years of research. Psychol Bull. 1998 Nov;124(3):372–422. pmid:9849112
- 88. Schaeffel F, Glasser A, Howland HC. Accommodation, refractive error and eye growth in chickens. Vision Res. 1988;28(5):639–57. pmid:3195068
- 89. Howlett MHC, McFadden SA. Spectacle lens compensation in the pigmented guinea pig. Vision Res. 2009 Jan;49(2):219–27. pmid:18992765
- 90. Smith EL, Hung LF. The role of optical defocus in regulating refractive development in infant monkeys. Vision Res. 1999 Apr;39(8):1415–35. pmid:10343811
- 91. Metlapally S, McBrien NA. The effect of positive lens defocus on ocular growth and emmetropization in the tree shrew. J Vis. 2008 Mar 1;8(3):1–1. pmid:18484807
- 92. Daniel F, Kapoula Z. Induced vergence-accommodation conflict reduces cognitive performance in the Stroop test. Sci Rep. 2019 04;9(1):1247. pmid:30718625
- 93. Bertone A, Bettinelli L, Faubert J. The impact of blurred vision on cognitive assessment. J Clin Exp Neuropsychol. 2007 Jul;29(5):467–76. pmid:17564912
- 94. Kwon M, Liu R, Chien L. Compensation for Blur Requires Increase in Field of View and Viewing Time. PLoS ONE [Internet]. 2016 Sep 13 [cited 2020 Nov 6];11(9). Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5021298/. pmid:27622710
- 95. Lestrange-Anginieur ED, Leung TW, Kee CS. On the joint effect of spatial attention and defocus blur on acuity: attentional limit to the resolving power of the eye. bioRxiv. 2020 Aug 26;2020.08.25.266700.
- 96. Bharadwaj SR, Candy TR. Accommodative and vergence responses to conflicting blur and disparity stimuli during development. J Vis. 2009 Oct 5;9(11):4.1–18. pmid:20053067
- 97. Horwood AM, Riddell PM. The use of cues to convergence and accommodation in naïve, uninstructed participants. Vision Res. 2008 Jul;48(15):1613–24. pmid:18538815
- 98. Fincham EF, Walton J. The reciprocal actions of accommodation and convergence. J Physiol. 1957 Aug 6;137(3):488–508. pmid:13463783
- 99. Morgan MW. Accommodation and vergence. Optom Vis Sci. 1968 Jul;45(7):417–454. pmid:4875838