  We present observations of a new group of structures in the diffuse Galactic
ISM: slender, linear HI features we dub "fibers" that extend for many degrees
at high Galactic latitude. To characterize and measure the extent and strength
of these fibers, we present the Rolling Hough Transform (RHT), a new machine
vision method for parameterizing the coherent linearity of structures in the
image plane. With this powerful new tool we show the fibers are oriented along
the interstellar magnetic field as probed by starlight polarization. We find
that these low column density (N(HI) ~ 5 x 10^18 cm^-2) fiber features are most
likely a component of the local cavity wall, about 100 pc away. The HI data we
use to demonstrate this alignment at high latitude are from the Galactic
Arecibo L-Band Feed Array HI (GALFA-HI) Survey and the Parkes Galactic All Sky
Survey (GASS). We find better alignment in the higher resolution GALFA-HI data,
where the fibers are more visually evident. This trend continues in our
investigation of magnetically aligned linear features in the Riegel-Crutcher HI
cold cloud, detected in the Southern Galactic Plane Survey (SGPS). We propose
an application of the RHT for estimating the field strength in such a cloud,
based on the Chandrasekhar-Fermi method. We conclude that data-driven,
quantitative studies of ISM morphology can be very powerful predictors of
underlying physical quantities.
