  Filamentary structures in neutral hydrogen (H I) emission are well-aligned
with the interstellar magnetic field, so H I emission morphology can be used to
construct templates that strongly correlate with measurements of polarized
thermal dust emission. We explore how the quantification of filament morphology
affects this correlation. We introduce a new implementation of the Rolling
Hough Transform (RHT) using spherical harmonic convolutions, which enables
efficient quantification of filamentary structure on the sphere. We use this
spherical RHT algorithm along with a Hessian-based method to construct H
I-based polarization templates. We discuss improvements to each algorithm
relative to similar implementations in the literature and compare their
outputs. By exploring the parameter space of filament morphologies with the
spherical RHT, we find that the most informative H I structures for modeling
the magnetic field structure are the thinnest resolved filaments. For this
reason, we find a $\sim10\%$ enhancement in the $B$-mode correlation with dust
polarization with higher-resolution H I observations. We demonstrate that
certain interstellar morphologies can produce parity-violating signatures,
i.e., nonzero $TB$ and $EB$, even under the assumption that filaments are
locally aligned with the magnetic field. Finally, we demonstrate that $B$ modes
from interstellar dust filaments are mostly affected by the topology of the
filaments with respect to one another and their relative polarized intensities,
whereas $E$ modes are mostly sensitive to the shapes of individual filaments.
