Daniel Jansson

Visual stimulus design in parameter estimation of the human smooth pursuit system from eye-tracking data

The dynamical properties of the human smooth pursuit system (SPS) are studied. Linear black-box and nonlinear Wiener models of the SPS are identified from eye-tracking data in view of their potential applications in diagnosing and staging various clinical conditions. A novel approach to visual stimuli design is suggested and evaluated. Accurate estimation of the linear dynamics requires sufficient input frequency excitation, while the identification of the nonlinear part is dependent upon the signal amplitude distribution. Both aspects of input design are taken into account. Visual stimuli generated using the presented method are shown to yield favorable identification results compared to existing stimuli design techniques in terms of reduced variance of parameter estimates and smaller spread of the parameter clouds pertaining to different individuals. The nonlinear Wiener models of the SPS appear to outperform the linear ones provided the visual stimuli are properly designed.

Dynamic smooth pursuit gain estimation from eye tracking data

The smooth pursuit gain (SPG) is defined as the ratio of the angular velocity of the eye to that of the moving target. Being evaluated at a certain frequency of harmonic visual stimuli, it has been widely used in medicine as a measure of oculomotor system performance. In this study, the smooth pursuit system (SPS) is modeled as a dynamical system whose output signal is the angular velocity of the eye and the input is the angular velocity of a moving stimulus. Then, by means of system identification, the entire dynamics of SPS can be estimated, provided the visual stimuli are properly designed. This technique is referred to as the dynamic SPG (DSPG). Systems appearing equivalent in terms of SPG, can therefore be distinguished between using DSPG. Modern eye tracking techniques register gaze direction over time, but do not measure gaze velocity. Hence, to estimate the SPG/DSPG, differentiation must be applied to the output of the eye tracker. Four approaches to differentiation of eye-tracking data are evaluated in this paper with respect to the estimation of DSPG, out of which the method based on Laguerre functions stands out as the most reliable technique for this particular application.

Mathematical modeling and grey-box identification of the human smooth pursuit mechanism

A mathematical model of the human eye smooth pursuit mechanism was constructed by combining a fourth order nonlinear biomechanical model of the eye plant with a dynamic gain controller model. The biomechanical model was derived based on knowledge of the anatomical properties and characteristics of the extraocular motor system. The controller model structure was chosen empirically to agree with experimental data. With the parameters of the eye plant obtained from the literature, the controller parameters were estimated through grey-box identification. Randomly generated and smoothly moving visual stimuli projected on a computer monitor were used as input data while the output data were the resulting eye movements of test subjects tracking the stimuli. The model was evaluated in terms of accuracy in reproducing eye movements registered over time periods longer than 10 seconds, frequency characteristics and angular velocity step responses. It was found to perform better than earlier models for the extended time data sets used in this study.

Stochastic Anomaly Detection in Eye-Tracking Data for Quantification of Motor Symptoms in Parkinson’s Disease

Two methods for distinguishing between healthy controls and patients diagnosed with Parkinsons disease by means of recorded smooth pursuit eye movements are presented and evaluated. Both methods are based on the principles of stochastic anomaly detection and make use of orthogonal series approximation for probability distribution estimation. The first method relies on the identification of a Wiener model of the smooth pursuit system and attempts to find statistically significant differences between the estimated parameters in healthy controls and patients with Parkinsons disease. The second method applies the same statistical method to distinguish between the gaze trajectories of healthy and Parkinson subjects tracking visual stimuli. Both methods show promising results, where healthy controls and patients with Parkinsons disease are effectively separated in terms of the considered metric. The results are preliminary because of the small number of participating test subjects, but they are indicative of the potential of the presented methods as diagnosing or staging tools for Parkinsons disease.

System identification of wiener systems via volterra-laguerre models: Application to human smooth pursuit analysis

This paper presents novel means for estimating the polynomial static nonlinearity coefficients of a Wiener system in absence of a priori information about the linear block. To capture the system structure, the identification is performed with respect to a Volterra series model, whose kernels are parameterized in terms of Laguerre functions. A property of the resulting Volterra-Laguerre model is exploited to allow for straightforward identification of the coefficients of the output polynomial. The proposed method is shown to provide accurate estimates of the polynomial coefficients even for noisy data. Finally, the method is applied to eye-tracking data obtained to characterize the human smooth pursuit system. The resulting models are evaluated in terms of prediction accuracy and shown to outperform models of previous research.

Volterra modeling of the Smooth Pursuit System with application to motor symptoms characterization in Parkinson's disease

A new way of modeling the Smooth Pursuit System (SPS) in humans by means of Volterra series expansion is suggested and utilized together with Gaussian Mixture Models (GMMs) to successfully distinguish between healthy controls and Parkinson patients based on their eye movements. To obtain parsimonious Volterra models, orthonormal function expansion of the Volterra kernels in Laguerre functions with the coefficients estimated by SParse Iterative Covariance-based Estimation (SPICE) is used. A combination of these two techniques is shown to greatly reduce the number of model parameters without significant performance loss. In fact, the resulting models outperform the Wiener models of previous research despite the significantly lower number of model parameters. Furthermore, the results of this study indicate that the nonlinearity of the system is likely to be dynamical in nature, rather than static which was previously presumed. The difference between the SPS in healthy controls and Parkinson patients is shown to lie largely in the higher order dynamics of the system. Finally, without the model reduction provided by SPICE, the GMM estimation fails, rendering the model unable to separate healthy controls from Parkinson patients.

Parametric and Nonparametric Analysis of Eye-Tracking Data by Anomaly Detection

An approach to smooth pursuit eye movements analysis by means of stochastic anomaly detection is presented and applied to the problem of distinguishing between patients diagnosed with Parkinsons disease and normal controls. Both parametric Wiener model-based techniques and nonparametric modeling utilizing a description of the involved probability density functions in orthonormal bases are considered. The necessity of proper visual stimuli design for the accuracy of mathematical modeling is highlighted and a formal method for producing such stimuli is suggested. The efficacy of the approach is demonstrated on experimental data collected by means of a commercial video-based eye tracker.

Parametric and non-parametric stochastic anomaly detection in analysis of eye-tracking data

Two methods for distinguishing between healthy subjects and patients diagnosed with Parkinsons disease by means of recorded smooth pursuit eye movements are presented and evaluated. Both methods are based on the principles of stochastic anomaly detection and make use of orthogonal series approximation for probability distribution estimation. The first method relies on the identification of a Wiener-type model of the smooth pursuit system and attempts to find statistically significant differences between the estimated parameters due to Parkinsonism. For accurate estimation of the model parameters, visual stimuli designed to excite the essential nonlinear dynamics of the oculomotor system are used and a method of generating the stimuli is presented. The second method applies the same statistical method to distinguish between the gaze trajectories of healthy and Parkinson subjects attempting to track the visual stimuli. Both methods show promising results, where healthy individuals and patients diagnosed with Parkinsons disease are effectively separated in terms of the considered metric. The results are preliminary because of the small number of participating test subjects, but they are indicative of the potential of the presented methods as diagnosing or staging tools for Parkinsons disease.

Capturing age-related alternations in the human smooth pursuit mechanism by Volterra models

A method for quantifying the effects of aging in the human smooth pursuit system is proposed. The dynamical properties of the oculomotor system are characterized by means of a truncated Volterra model that has previously been utilized for distinguishing between patients diagnosed with Parkinsons disease and healthy controls. The orthonormal basis of Laguerre functions is employed for the parameterization of the Volterra model kernels. The Volterra-Laguerre model coefficients are estimated from gaze direction data collected by means of eye tracking from healthy adults of different age responding to specially designed visual stimuli. The experimental results suggest that aging primarily impacts the linear term of the Volterra model through gain and frequency bandwidth reduction. Parameter variability increases with age, both in the linear and quadratic term of the Volterra model. The mean values of the nonlinear term coefficients appear though to be essentially independent of age within the studied population.