  We have carried out a search for filamentary structures in the Taurus
molecular cloud using $\rm^{13}CO$ line emission data from the FCRAO survey of
$\rm \sim100 \, deg^2$. We have used the topological analysis tool, DisPerSe,
and post-processed its results to include a more strict definition of filaments
that requires an aspect ratio of at least 3:1 and cross section intensity
profiles peaked on the spine of the filament. In the velocity-integrated
intensity map only 10 of the hundreds of filamentary structures identified by
DisPerSe comply with our criteria. Unlike Herschel analyses, which find a
characteristic width for filaments of $\rm \sim0.1 \, pc$, we find a much
broader distribution of profile widths in our structures, with a peak at 0.4
pc. Furthermore, even if the identified filaments are cylindrical objects,
their complicated velocity structure and velocity dispersions imply that they
are probably gravitationally unbound. Analysis of velocity channel maps reveals
the existence of hundreds of `velocity-coherent' filaments. The distribution of
their widths is peaked at lower values (0.2 pc) while the fluctuation of their
peak intensities is indicative of stochastic origin. These filaments are
suppressed in the integrated intensity map due to the blending of diffuse
emission from different velocities. Conversely, integration over velocities can
cause filamentary structures to appear. Such apparent filaments can also be
traced, using the same methodology, in simple simulated maps consisting of
randomly placed cores. They have profile shapes similar to observed filaments
and contain most of the simulated cores.
