Non-Linearity of Visual Sensitivity and Pursuit Velocity during Smooth Pursuit Eye Movements

Xu-Fang Chen, Tao Deng, and Hong-Mei Yan

Non-Linearity of Visual Sensitivity and Pursuit Velocity during Smooth Pursuit Eye Movements

Xu-Fang Chen, Tao Deng, and Hong-Mei Yan

——During pursuit eye movements, whether the relationships among the visual sensitivity, pursuit velocity, and target velocity are linear or non-linear is an old issue. In this study, we reexamined their relationships with seven speeds by a simple character discrimination task using an infrared eye tracker. Our results found that the pursuit velocity and accuracy were non-linearly related with the target velocity. Besides, the perceptual sensitivity was not linearly related with the pursuit velocity either. A significant difference existed between lower (less than 20 deg/s) and higher speeds (greater than 20 deg/s). In addition, we found there was no position bias of visual sensitivity between ahead of and behind the pursuit target, but there was a significant perceptual dissymmetry between horizontal and vertical directions at lower pursuit speeds.

Index Terms——Perceptual sensitivity, pursuit accuracy, smooth pursuit, velocity.

1. Introduction

When an object we determine to see moves through our visual field, we track the moving object with pursuit eye movements. The principal objective is to maintain smooth eye velocity close to object velocity, thus minimizing retinal image motion and maximizing its visibility[1]. Of course, ocular pursuit movements allow moving objects to be tracked with a combination of smooth movements andfast saccadic eye movements. Saccadic eye movement serve to realign the image if it falls outside the fovea, the area of highest acuity[2]. Usually, the faster target moves, the more saccades occur.

Therefore, the relationship between smooth pursuit velocity and the target velocity is an old issue. Early research made by Rashbass concluded that the pursuit velocity of eyes was linearly related to the target velocity for target velocities less than 10 deg/s[3]. Puckettet al.repeated Rashbass’ experiment and found that the pursuit velocity was not linearly related to the target velocity[4]. Their results were disagreement although the velocity they chose was very low. Now, all researchers agree that, on the average, the smooth pursuit velocity is lower than the target velocity. However, a question remains unsolved that the pursuit velocity is generally linearly or not linearly related with the target velocity.

Visual sensitivity of pursuit eye movements is a hot point concerned by neuroscientists. Eye movements produce movements of retinal image of the stationary background, so it is generally believed that the improved visibility of the moving object is obtained at the cost of reduced visibility of stationary background[5]. Most researches supported the fact that the visual sensitivity and the ability of object recognition deteriorate during pursuit eye movements[6],[7]. However, Haarmeieret al.found no loss of acuity for pursuit velocities up to 14 deg/s in healthy subjects[8]. What’s more, some visual features, such as color and high spatial frequency components, were observed to be enhanced during smooth pursuit eye movements[9],[10].

The relationship between visual sensitivity and the velocity of pursuit eye movements is another old issue. A very early study made by Murphy in 1978 found that dynamic visual acuity decreases with increases in the angular velocity of the target[5]. The velocity of the targets he chose was comparatively low, ranged from 49 arc/s to 420 arc/s, and only two subjects were recorded in his research. Since then, seldom studies repeated the experiment. However, the question remains unanswered concerning visual sensitivity linearly or not linearly decreasing with the velocity of pursuit eye movements. As we know that pursuit eye movements are essentially a feedback process, is the neural mechanism at low pursuit velocities the same with that of high speeds? It is still unclear till now.

With regard to spatial sensitivity, some studies have suggested that while visual attention is allocated to the pursuit of a target, visual performance in the periphery may be impeded[11],[12]. Donkelaaret al.[13]reported that the allocation of attention could be altered by the pursuit velocity and biased to a position in front of the pursuit target, namely, the visual sensitivity ahead of the pursuit target is better than that of behind it. However, a study by Lovejoyet al.[14]suggested that there was no position bias and visual performance decreased sharply and symmetrically with the increasing eccentricity. It appears to be contradictions in these results.

This paper reexamines the relationships among the visual sensitivity, smooth pursuit velocity, and target velocity from a large range of speed by a very simple experiment design. The aim is to address the following three questions: 1) Is the pursuit velocity linearly or not linearly related with the target velocity? 2) Is visual sensitivity linearly or not linearly decreasing with the velocity of pursuit eye movements? Namely, is the neural mechanism at low pursuit velocities the same with that of high speeds? 3) How is the spatial perceptual sensitivity of pursuit eye movements? Is there a position bias of visual sensitivity between ahead of and behind the pursuit target? Is there a perceptual bias between horizontal and vertical directions?

2. Experimental Paradigm

2.1 Subjects

Seven right-handed subjects (4 male and 3 female) aged between 21 and 24 years with normal visual acuity participated in the experiments. All were undergraduates or postgraduate students at the University of Electronic Science and Technology of China. All subjects provided written informed consent and the research was approved by the Ethics and Human Participants in Research Committee, University of Electronic Sciences and Technology of China. The subjects were given an initial training period of an hour before the experiments, in order to practice pursuit eye movements and coordinate their motor responses well enough to be able to perform the task. Each subject accomplished 2 sessions×10 blocks×40 trials for each pursuit speed, in total 5600 trials for seven conditions.

2.2 Experiment Setup and Visual Stimuli

The subjects were seated in a dark room specially designed for carrying out psychophysical experiments. Ambient luminance was 5 cd/m2. The visual stimuli were generated by a Psychophysics Toolbox[15],[16]based on MATLAB and presented on a 21" color monitor (DELL Trinitron) at a frame frequency of 100 Hz with a spatial resolution of 1280×1024 pixels. The viewing distance was 55 cm and stimuli appeared on a grey background which was adjusted to the mean luminance of 22 cd/m2.

Two concentric circles presented on a gray background were used as fixation or pursuit targets. The inner circle was white and the external one was black. Their diameters were 0.15 degree and 0.6 degree, respectively. In fixation trials, the fixation target was located at the center of the screen; in pursuit trials, the pursuit target was randomly presented 10 degree left or right of the screen center.

The discrimination stimuli contained L and T, extended about 0.4 degree in diameter, and rotated randomly with 8 possible angles (45 degree, 90 degree, 135 degree, 180 degree, 225 degree, 270 degree, 315 degree, and 360 degree), which flashed 10 ms in both fixation and pursuit conditions. The discrimination stimulus was presented at locations that were 6 degree above, below, left or right of the center point of the screen.

Eye movements were recorded with an infrared eye tracker (Eyelink2000, SR Research Ltd.). Head movements were restricted by a forehead and chin rest. The pupil of the left eye was tracked at a sample rate of 1000 Hz. Calibration and validation of 3×3 dots was carried out before each block.

2.3 Experimental Procedure

The experiment consisted of two tasks comprising fixation and smooth pursuit. The pursuit task was carried out at six velocities (V=5 deg/s, 10 deg/s, 15 deg/s, 20 deg/s, 25 deg/s, 30 deg/s) and the fixation task was considered as speed of 0 deg/s. Fig. 1 (a) shows the procedure used for the pursuit tasks. During the pursuit experiments, the pursuit target was presented for 1000 ms at either the left or the right side of the screen, after which it started to move horizontally towards the opposite direction. When the target moved to the center of the screen, the discrimination stimulus L or T flashed for 10 ms at one of four designed locations. Then, the pursuit target continued to move for 500 ms until the end of the trial. Subjects were required to track the pursuit target as accurately as possible and to discriminate the letter stimulus, then report the results by pressing keys. In fixation trials (Fig. 1 (b)), a fixation target was presented at the center of the display screen and subjects were instructed to maintain fixation on this point during the trial. After 1000 ms, the letter stimulus was randomly presented for 10 ms at one of the four predetermined locations and the subjects were asked to discriminate the letter and press the appropriate key to record their answers.

Fig. 1. Experimental protocol. Schematic trial sequence in both (a) pursuit and (b) fixation trials.

2.4 Data Analysis

Eye movements were recorded during the trials. All data were collected by the computer and analyzed offline using MATLAB. Trials were discarded if a) a blink occurred during the trial; b) the distance between the pursuit target and the position of the eye was larger than 3 degree.

3. Results

3.1 Measurement of Pursuit Velocity and Accuracy at Different Speeds of Target

Eye movements data shown in Fig. 2 are those obtained from all subjects. Fig. 2 (a) shows that the mean velocity of horizontal eye movements vary as a function of time when tracking at seven speeds (0 deg/s, 5 deg/s, 10 deg/s, 15 deg/s, 20 deg/s, 25 deg/s and 30 deg/s). Grey horizontal lines indicate corresponding target velocities. The asterisk indicates the presentation time of the discrimination stimulus. At the initiation of pursuit eye movements, subjects have to speed up their eye movements to catch up with the pursuit target, which is reflected in the rising phase of the velocity curves. The higher velocity of the pursuit target is, the faster the accelerated speed is needed for the subject’s eyes to catch up the moving target. Then, a peak is reached and the curve declines to a relative stable speed, until the end of the pursuit. Generally, subjects could trace the target relatively well at the lower speeds (5 deg/s, 10 deg/s, 15 deg/s, and 20 deg/s). However, when the speed is greater than 20 deg/s, it becomese difficult for them to smoothly keep up with the tracking target. Fig. 2 (b) shows tracking accuracy evaluated from the frequency distribution of actual eye positions relative to the target position while performing a discrimination task during pursuit eye movements. Zero eccentricity at the abscissa represents the real location of the pursuit and/or fixation target. The degree of deviation between the peak position and the real position of the target (eccentricity 0, indicated by the vertical line) represents the accuracy of pursuit eye movements. The negative values indicate that the actual positions of the eyes always lag behind the target position and deviation increased with an increasing speed of eye movements. In the steady fixation condition (velocity=0 deg/s), the actual eye position (peak of the dark line) coincided well with target position (zero position at the abscissa), with a half-width of the distribution curve of 0.66 degree. During pursuit conditions, the eye positions always lag behind the pursuit target, represented by the increasing deviation between the peak value and the zero position, the lag for 5 deg/s, 10 deg/s, 15 deg/s, 20 deg/s, 25 deg/s, 30 deg/s are 0.16 degree, 0.24 degree, 0.25 degree, 0.44 degree, 0.50 degree, and 0.69 degree, respectively (see Fig. 2 (c)). When the target speed was fast (25 deg/s and 30 deg/s), the lag became out of the range of 0.5 degree. The decrease in pursuit accuracy with the increasing speed is also reflected in the half-width of the frequency distribution curves, which could be an indicator of pursuit instability. The greater the half-width is, the more unstable pursuit becomes. The half-width of the frequency distribution curves for 5, 10 deg/s, 15 deg/s, 20 deg/s, 25 deg/s, and 30 deg/s are 0.82, 0.69 degree, 0.82 degree, 0.84 degree, 1.09 degree, and 1.53 degree, respectively (see Fig. 2 (d)). From Fig. 2 (d), the half-width goes beyond 1 degree when target speed is greater than 20 deg/s. Bearing in mind that gain and acceleration are also good indicators of pursuit accuracy and stability, Fig. 2 (e) and 2 (f) show tracking gain (the ratio of eye velocity to target velocity) and acceleration while performing a discrimination task during pursuit eye movements at six velocities. As a whole, there are no significant differences in gain and acceleration for different velocities (P＞0.05). However, the average acceleration shifts away from 0 deg/s (-9.58 at 25 deg/s and 7.67 at 30 deg/s) and with larger deviation at the higher speed conditions, which indicated instability of pursuit at higher target speeds. From Fig. 2, it seems the pursuit velocity and accuracy is not linearly related with the target velocity. A comparative variance exists between lower speeds (less than 20 deg/s) and higher ones (greater than 20 deg/s).

Fig. 2. Relationships between smooth pursuit eye movements and the seven target velocities: (a) mean velocity responses of horizontal eye movements of a subject when tracking at seven velocities, (b) frequency distribution of the actual eye positions measured at seven different velocities of eye movements, (c) the variation in lag between peak real eye position and the target position at seven velocities of eye movements, (d) half-width of the frequency distribution curves at seven velocities, (e) average pursuit gains at six pursuit speeds when a discrimination target was presented, and (f) average pursuit accelerations at six pursuit speeds when a discrimination target was presented. Error bars indicate SEM.

3.2 Measurement of Perceptual Sensitivity at Different Speeds of Eye Movements

Fig. 3 shows the average discrimination performances of the target letter for the seven subjects while tested at different pursuit speeds. The abscissa indicates the specific position of the stimuli occurred above, below, ahead or behind the pursuit target. For the fixation condition, ahead and behind means that the stimuli are presented to the left and right of the fixation target. Discrimination accuracy is the highest in the fixation condition (0 deg/s) and is reduced gradually with an increasing pursuit speed. This result is in agreement with previous reports in that performance in the fixation condition was better than in pursuit conditions[6],[7],[13],[17]. What’s more, pairedttest shows that a significant drop in recognition performance occurred at higher speeds (25 deg/s and 30 deg/s) (P＜0.05) (except for the “down” condition,P=0.071). From Fig. 3, the perceptual sensitivity is not linearly related with the pursuit velocity. A significant difference exists between lower speeds (less than 20 deg/s) and higher ones (greater than 20 deg/s).

Fig. 3. Average performance of seven subjects in seven pursuit velocities when the stimulus was presented above, below, ahead or behind the pursuit target. Error bars indicate SEM. *P＜0.05.

3.3 Spatial Perceptual Sensitivity at Different Speeds of Eye Movements

The results shown in Fig. 4 (a) reveal that there is no significant difference in the speed-dependent variation in perceptual performance, regardless of which discrimination object is presented ahead of or behind the pursuit target (Repeated measures ANOVA,F(1, 6)=6.000,P=0.267). These results are in agreement with those obtained by Lovejoyet al.[14], but are not in accord with those obtained by Van Donkelaaret al.[13], who reported that perceptual performance for the position in front of the pursuit target was better than that for behind.

It could be argued that as the eyes lag the pursuit target under most conditions, and the position behind has smaller retinal eccentricity than the position in front. It could be suggested that attention is actually leading the pursuit target, but this beneficial effect for the front position is counteracted by its larger retinal eccentricity. We compared the perceptual performance when the eye lagged behind and advanced in front of the pursuit target and found that there was no significant difference in perceptual performance using repeated measures ANOVA (F(1, 6)=0.042,P=0.845), as shown in Fig. 4 (b). Our results showed that the front bias was certainly not significant not only at lower but also higher speed of pursuit.

Fig. 4. Comparison of perceptual performances: (a) average performance of all subjects for seven velocities when a stimulus was presented ahead or behind the pursuit target and (b) average perceptual performance when the eye lagged behind and advanced ahead of the pursuit target. Error bars indicate SEM.

However, a significant difference is observed for recognition performance when comparing the accuracy to the stimuli presented at the horizontal (ahead and behind) and the vertical (up and below) positions for lower speeds by a pairedt-test (P＜0.05), as shown in Fig. 5. The sensitivity of perception iss higher for the horizontal dimension than for the vertical dimension, with the exception of higher speeds (25 deg/s and 30 deg/s). Similar horizontal-vertical dissymmetry of perception are observed under steady fixation conditions[18].

Fig. 5. Average performance of subjects for seven velocities when the stimulus was presented at vertical and horizontal positions. Error bars indicate SEM. *P＜0.05.

4. Discussion

We carefully reexamined the relationships among the visual sensitivity, smooth pursuit velocity, and target velocity from low to high speed. Our results showed that firstly, the pursuit velocity and accuracy was not linearly related with the target velocity. A comparative variance existed between lower speeds (less than 20 deg/s) and higher ones (greater than 20 deg/s). Our results were in consistence with Meyer’s study about the pursuit gain. Hefound that the gain was normally in the range 0.9-1.0 for target velocities ＜20 deg/s, but declined at higher velocity[19]. His results also implied that gain changed non-linearly with low and high speeds. Secondly, the perceptual sensitivity was not linearly related with the pursuit velocity. A significant difference of perceptual performance existed between lower speeds (less than 20 deg/s) and higher ones (greater than 20 deg/s), showing non-linear velocity dependence. These results seemed to imply that our brain possibly adopted different mechanisms to deal with low and high speed pursuit. Ocular pursuit is thought to be an example of a negative feedback control system, and some models based on control theory have been used successfully to describe the dynamic characteristics of pursuit. Simple models, in which the feedback relationship between eye velocity and target velocity was described as linear, have proved to fail to explain many behaviors[2]. We can confer that feedback information from the high level is incapable of processing in time when pursuit speed was very fast, which leaded to the rapid decrease of perceptual performance at high speeds.

Finally, there was no position bias of visual sensitivity between ahead of and behind the pursuit target although the real positions of the eye lagged behind the pursuit target at all pursuit velocities. However, there was a perceptual dissymmetry between horizontal and vertical directions at lower pursuit speeds (less than 20 deg/s).

Previous research has suggested that smooth pursuit was supported by catch-up saccades to compensate for retinal image slip when target velocity exceeded 30 deg/s[3],[20]. Our results revealed that subjects could pursue a target well when the velocity was less than 20 deg/s (including 20 deg/s). With increasing velocity, however, they had to execute catch-up saccades, in order to keep pace with the target, more or less. Therefore, a large amount of the trials were discarded at velocities of 25 deg/s and 30 deg/s, in our experiment, due to movements outside of the pursuit window. Therefore, we concluded that the eyes have difficulty in pursuing a target smoothly at high speed and velocities below 20 deg/s are recommended for studying pursuit eye movements. Our experiments provided a detailed reference point for those intending to carry out behavioral studies on smooth pursuit eye movements.

5. Conclusions

The relationship among the visual sensitivity, pursuit velocity, and target velocity is an important and basic question in visual cognition. Our experiments showed that pursuit velocity and accuracy were non-linearly related with the target velocity, and the perceptual sensitivity was not linearly related with pursuit velocity either. A significant difference existed between lower (less than 20 deg/s) and higher speeds (greater than 20 deg/s), showing non-linear velocity dependence. These results seemed to imply that our brain possibly adopted different mechanisms to deal with low and high speed pursuit. In addition, our results showed that there was no obvious position bias of visual sensitivity between ahead of and behind pursuit target, but a significant perceptual dissymmetry was observed between horizontal and vertical directions at lower pursuit speeds.

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Xu-Fang Chen was born in Guizhou, China in 1987. She received the M.S. degree from University of Electronic Science and Technology of China (UESTC), Chengdu in 2012. Her research interests include visual cognition and eye movements.

Tao Deng was born in Chongqing, China in 1989. He is pursing his Ph.D. degree at UESTC now. His research interests include visual cognition and digital image process.

Hong-Mei Yan was born in Chongqing, China in 1974. She got her Ph.D. degree from Chongqing University in 2003. She is now a professor with UESTC. Her research interests include visual cognition and eye movements.

Manuscript received November 13, 2013; revised February 17, 2014. This work was supported by the National Natural Science Foundation of China under Grant No. 60972108, 91120013, 61375115, 31300912; 973 Project under Grant No. 2013CB329401; Key Technology Research & Development Programs of Sichuan Province under Grant No. 2011GZ0073; the Fundamental Research Funds for the Central Universities under Grant No. ZYGX2013J098, ZYGX2011X017.

X.-F. Chen and T. Deng are with the Key Laboratory for NeuroInformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, China (e-mail: xfchentoefl@163.com; dt20052008@163.com).

H.-M. Yan is with the Key Laboratory for NeuroInformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, China (Corresponding author e-mail: hmyan@uestc.edu.cn).

Color versions of one or more of the figures in this paper are available online at http://www.journal.uestc.edu.cn.

Digital Object Identifier: 10.3969/j.issn.1674-862X.2014.04.010