Abstract:
Eye movement refers to the voluntary or involuntary movement of the eyes. Eye
trajectories explain human search behavior. It has been revealed that variations of
these trajectories reflect the dynamics of the oculomotor system. Eye movement
trajectories under free exploration contain a lot of noise with saccades and fixations.
As a result eye movement trajectories cannot be treated as any other trajectory. It has
been a challenge to analyze gaze during free exploration, preserving spatial and
temporal characteristics of eye movements. Therefore, most of the experiments are
carried in laboratories under restrictions. Here we address the problem of analyzing
the binocular eye movement trajectory under free exploration, to understand the
underlying patterns in the movement. First eye movement trajectory is mapped onto
the unit sphere as a set of time indexed points. The obtained eye movement
trajectories on the sphere are not simple curves and with repeated movements.
Therefore, the whole trajectory was segmented using the speed at each time instance
in order to obtain simple trajectories. For each segment, we have estimated a
smoothed curve given by a set of time-indexed points on the sphere so that the
estimated curve would approximate the data points best at given time instants while
being regular as possible. These smoothed curves as cubic splines can be used to
analyze patterns in the whole trajectory. Furthermore, the estimated curves as a set
of time indexed points were used in interpolation and clustering. Distances between
different curves are calculated using the geodesic distance on the unit sphere. Using
the distance matrix of the segmented smoothed curves and the software called
cystoscope, curves are grouped to obtain four different clusters. Each cluster from
the binocular eye movement was analyzed for both left and right eye movement to
obtain curves overlapped where both eyes move together in the same direction. These
overlapped curves can be analyzed further to compare eye movement patterns in
different individuals.
