  A method to identify a quantum vortex in a three-dimensional Gross-Pitaevskii
simulation has been developed. A quantum vortex was identified by the use of
eigenvalues and eigenvectors of the Hessian of the mass density, together with
a condition to distinguish a point to constitute a swirling vortex from other
confusing data points. This method has been verified to identify vortex axes in
a Gross-Pitaevskii simulation appropriately, being useful to elucidate various
statistics associated with turbulent quantum vortices. This method provides us
with a unified approach to studying vortex statistics in the turbulence of both
classic and quantum fluids. Our study reveals that the maximum radius of a
swirling region of a quantum vortex can be as large as sixty times the healing
length. The characterization of the vortex core radius relative to the healing
length is reported for the first time in this paper. Furthermore, the
geometrical natures of vortex axes such as the probability density function of
the curvature are characterized by the healing length.
