  Both simulations and observations of the interstellar medium show that the
study of the relative orientations between filamentary structures and the
magnetic field can bring new insight into the role played by magnetic fields in
the formation and evolution of filaments and in the process of star formation.
We provide a first application of FilDReaMS, the new method to detect and
analyze filaments. Our goal is to investigate the relative orientations between
the detected filaments and the magnetic field. We apply FilDReaMS to a sample
of four Herschel fields (G210, G300, G82, G202) characterized by different
Galactic environments and evolutionary stages. First, we examine the networks
formed by filaments of different bar widths as well as their hierarchical
organization. Second, we compare the filament orientations to the magnetic
field orientation inferred from Planck polarization data and, for the first
time, we study the statistics of the relative orientation angle as functions of
both spatial scale and ${\rm H_2}$ column density. We find preferential
relative orientations in the four Herschel fields: small filaments with low
column densities are slightly more parallel than perpendicular to the magnetic
field, while large filaments (higher column densities) are oriented nearly
perpendicular (or, in the case of G202, nearly parallel). In the two nearby
fields (G210 and G300), we observe a transition from mostly parallel to mostly
perpendicular at an $N_{\rm H_2} \simeq 1.1$ and $1.4\times10^{21}\,$cm$^{-2}$,
respectively, consistent with the results of previous studies. Our results
confirm the existence of a coupling between magnetic fields at cloud scales and
filaments at smaller scale. They also illustrate the potential of combining
Herschel and Planck observations, and they call for further statistical
analyses with our dedicated method.
