Microsaccade characterization using the continuous wavelet transform and principal component analysis

During visual fixation on a target, humans perform miniature (or fixational) eye movements consisting of three components, i.e., tremor, drift, and microsaccades. Microsaccades are high velocity components with small amplitudes within fixational eye movements. However, microsaccade shapes and statistical properties vary between individual observers. Here we show that microsaccades can be formally represented with two significant shapes which we identfied using the mathematical definition of singularities for the detection of the former in real data with the continuous wavelet transform. For character-ization and model selection, we carried out a principal component analysis, which identified a step shape with an overshoot as first and a bump which regulates the overshoot as second component. We conclude that microsaccades are singular events with an overshoot component which can be detected by the continuous wavelet transform

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems

Bayesian estimation of the scaling parameter of fixational eye movements

In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably

Horizontal FEM trajectory with detected microsaccades and illustration of the sequence of microsaccade directions.

<p>(a) Trajectory of a 20 FEM trial with (<i>upper panel</i>) detected microsaccades and (<i>lower panel</i>) directions of microsaccades. (b) Sequence of microsaccade directions represented as discrete time series of binary states. For the analysis of microsaccade direction sequences, we neglect the temporal proximity existent in the sequence of microsaccades.</p

Markov order estimation for sequences of simulated different order Markov chains.

<p>Using a parameterization as zeroth-order Markov chain as null hypothesis, we compared in the Bayes factor the evidences against first-, second-, and third-order parameterization of Markov chain. We simulated sequences of: (a) uncorrelated random processes, (b) first-order Markov chain, and (c) second-order Markov chains, each of two symbols. In (a) we obtained support for zeroth-order parameterization, in (b) evidence against the null for all orders but highest with a first-order parameterization and (c) accordingly for a second-order parameterization. This validated the estimator to be correct.</p

Each box represents the transition matrix for each participants.

<p>Participants are ordered as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0043388#pone-0043388-g004" target="_blank">Figure 4</a>. The values are color-coded to facilitate reading. Only the transition matrix for a first order Markov chain is reported.</p

Illustration of microsaccade shape properties reported microsaccade sequence patterns.

<p>(a) illustrates a typical microsaccade shape occurring during fixational eye movements with the designated microsaccade properties. (b) shows microsaccade sequence patterns, composed of one, two or three subsequent microsaccadic events, so-called <i>saccadic intrusions</i> (SI). From left: single saccadic pulse (SSP), double saccadic pulse (DSP), square-wave jerks (SWJ), biphasic square wave intrusion (BSWI). All patterns have been hand-picked from the horizontal trajectories of fixational eye movements. The separating time intervals are not representative for all participants.</p