  This study proposes a novel self-calibration method for eye tracking in a
virtual reality (VR) headset. The proposed method is based on the assumptions
that the user's viewpoint can freely move and that the points of regard (PoRs)
from different viewpoints are distributed within a small area on an object
surface during visual fixation. In the method, fixations are first detected
from the time-series data of uncalibrated gaze directions using an extension of
the I-VDT (velocity and dispersion threshold identification) algorithm to a
three-dimensional (3D) scene. Then, the calibration parameters are optimized by
minimizing the sum of a dispersion metrics of the PoRs. The proposed method can
potentially identify the optimal calibration parameters representing the
user-dependent offset from the optical axis to the visual axis without explicit
user calibration, image processing, or marker-substitute objects. For the gaze
data of 18 participants walking in two VR environments with many occlusions,
the proposed method achieved an accuracy of 2.1$^\circ$, which was
significantly lower than the average offset. Our method is the first
self-calibration method with an average error lower than 3$^\circ$ in 3D
environments. Further, the accuracy of the proposed method can be improved by
up to 1.2$^\circ$ by refining the fixation detection or optimization algorithm.
