Trajectory prediction of saccadic eye movements using a compressed exponential model.

Gaze-contingent display paradigms play an important role in vision research. The time delay due to data transmission from eye tracker to monitor may lead to a misalignment between the gaze direction and image manipulation during eye movements, and therefore compromise the contingency. We present a method to reduce this misalignment by using a compressed exponential function to model the trajectories of saccadic eye movements. Our algorithm was evaluated using experimental data from 1,212 saccades ranging from 3° to 30°, which were collected with an EyeLink 1000 and a Dual-Purkinje Image (DPI) eye tracker. The model fits eye displacement with a high agreement (R² > 0.96). When assuming a 10-millisecond time delay, prediction of 2D saccade trajectories using our model could reduce the misalignment by 30% to 60% with the EyeLink tracker and 20% to 40% with the DPI tracker for saccades larger than 8°. Because a certain number of samples are required for model fitting, the prediction did not offer improvement for most small saccades and the early stages of large saccades. Evaluation was also performed for a simulated 100-Hz gaze-contingent display using the prerecorded saccade data. With prediction, the percentage of misalignment larger than 2° dropped from 45% to 20% for EyeLink and 42% to 26% for DPI data. These results suggest that the saccade-prediction algorithm may help create more accurate gaze-contingent displays.

[1]  Martina Poletti,et al.  Stability of the Visual World during Eye Drift , 2010, The Journal of Neuroscience.

[2]  J. H. Bertera.  The effect of simulated scotomas on visual search in normal subjects. , 1988, Investigative ophthalmology & visual science.

[3]  Piotr Winkielman,et al.  Autism and the extraction of emotion from briefly presented facial expressions: stumbling at the first step of empathy. , 2008, Emotion.

[4]  Daniel R Saunders,et al.  Direct measurement of the system latency of gaze-contingent displays , 2013, Behavior Research Methods.

[5]  J. Reynolds,et al.  Temporal Resolution for the Perception of Features and Conjunctions , 2007, The Journal of Neuroscience.

[6]  Lester C. Loschky,et al.  Investigating spatial vision and dynamic attentional selection using a gaze-contingent multiresolutional display. , 2002, Journal of experimental psychology. Applied.

[7]  Wieske van Zoest,et al.  Stimulus-salience and the time-course of saccade trajectory deviations. , 2012, Journal of vision.

[8]  Jeffrey S. Perry,et al.  Visual search: the role of peripheral information measured using gaze-contingent displays. , 2006, Journal of vision.

[9]  Bernice E. Rogowitz,et al.  Human Vision and Electronic Imaging II , 1997 .

[10]  Robert S. Allison,et al.  Using Saccadic Suppression to Hide Graphic Updates , 2004, EGVE.

[11]  Robert S. Anderssen,et al.  The Kohlrausch function: properties and applications , 2004 .

[12]  Peter E Pidcoe,et al.  Oculomotor tracking strategy in normal subjects with and without simulated scotoma. , 2006, Investigative ophthalmology & visual science.

[13]  Nobuyasu Ito,et al.  A simple model for skewed species-lifetime distributions , 2010 .

[14]  Eric Castet,et al.  Gaze-contingent simulation of retinopathy: Some potential pitfalls and remedies , 2011, Vision Research.

[15]  Jean-Baptiste Bernard,et al.  Page mode reading with simulated scotomas: A modest effect of interline spacing on reading speed , 2007, Vision Research.

[16]  Werner Marx,et al.  The history of the stretched exponential function , 2007 .

[17]  R VanRullen,et al.  Is it a Bird? Is it a Plane? Ultra-Rapid Visual Categorisation of Natural and Artifactual Objects , 2001, Perception.

[18]  D. Robinson.  The mechanics of human saccadic eye movement , 1964, The Journal of physiology.

[19]  Wilson S. Geisler,et al.  Gaze-contingent real-time simulation of arbitrary visual fields , 2002, IS&T/SPIE Electronic Imaging.

[20]  Wei Zhou,et al.  An updated Time-Optimal 3rd-Order Linear Saccadic Eye Plant Model , 2009, Int. J. Neural Syst..

[21]  J. Henderson,et al.  Initial scene representations facilitate eye movement guidance in visual search. , 2007, Journal of experimental psychology. Human perception and performance.

[22]  M. A. Frens,et al.  Recording eye movements with video-oculography and scleral search coils: a direct comparison of two methods , 2002, Journal of Neuroscience Methods.

[23]  Eli Peli,et al.  Intrasaccadic Perception , 2001, The Journal of Neuroscience.

[24]  F. Campbell,et al.  Saccadic omission: Why we do not see a grey-out during a saccadic eye movement , 1978, Vision Research.

[25]  Suiping Wang,et al.  Semantic and plausibility effects on preview benefit during eye fixations in Chinese reading , 2012, Reading and writing.

[26]  Eric Castet,et al.  Page mode reading with simulated scotomas: Oculo-motor patterns , 2008, Vision Research.

[27]  Oleg V. Komogortsev,et al.  Eye movement prediction by oculomotor plant Kalman filter with brainstem control , 2009 .

[28]  G. Westheimer.  Mechanism of saccadic eye movements. , 1954, A.M.A. archives of ophthalmology.

[29]  S. Reder.  On-line monitoring of eye-position signals in contingent and noncontingent paradigms , 1973 .

[30]  Michael Dorr,et al.  A gaze-contingent display to study contrast sensitivity under natural viewing conditions , 2011, Electronic Imaging.

[31]  John D. Enderle,et al.  The Linear Homeomorphic Saccadic Eye Movement Model - A Modification , 1984, IEEE Transactions on Biomedical Engineering.

[32]  L. Stark,et al.  Dynamic overshoot in saccadic eye movements is caused by neurological control signal reversals , 1975, Experimental Neurology.

[33]  Jochen Triesch,et al.  Saccade contingent updating in virtual reality , 2002, ETRA.

[34]  A. J. Van Opstal,et al.  Three-dimensional analysis of strongly curved saccades elicited by double-step stimuli , 2004, Experimental Brain Research.

[35]  Lester C. Loschky,et al.  Perception onset time during fixations in free viewing , 2002, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

[36]  A. Safran,et al.  Development of a viewing strategy during adaptation to an artificial central scotoma , 2004, Vision Research.

[37]  D. Sornette,et al.  Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales , 1998, cond-mat/9801293.

[38]  Christopher B. Currie,et al.  Visual stability across saccades while viewing complex pictures. , 1995, Journal of experimental psychology. Human perception and performance.

[39]  R B Daroff,et al.  Corrective movements following refixation saccades: type and control system analysis. , 1972, Vision research.

[40]  A. Terry Bahill,et al.  Linear Homeomorphic Model for Human Movement , 1980, IEEE Transactions on Biomedical Engineering.

[41]  J. V. Van Gisbergen,et al.  Skewness of saccadic velocity profiles: a unifying parameter for normal and slow saccades. , 1987, Vision research.

[42]  Graham Williams,et al.  Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function , 1970 .

[43]  Guillaume S. Masson,et al.  Motion perception during saccadic eye movements , 2000, Nature Neuroscience.

[44]  Andrew T. Duchowski,et al.  Gaze-Contingent Displays: A Review , 2004, Cyberpsychology Behav. Soc. Netw..