  We present a new technique to determine distances to major star-forming
regions across the Perseus Molecular Cloud, using a combination of stellar
photometry, astrometric data, and $\rm ^{12} CO$ spectral-line maps.
Incorporating the Gaia DR2 parallax measurements when available, we start by
inferring the distance and reddening to stars from their Pan-STARRS1 and 2MASS
photometry, based on a technique presented in Green et al. 2014; Green et al.
2015 and implemented in their 3D "Bayestar" dust map of three-quarters of the
sky. We then refine the Green et al. technique by using the velocity slices of
a CO spectral cube as dust templates and modeling the cumulative distribution
of dust along the line of sight towards these stars as a linear combination of
the emission in the slices. Using a nested sampling algorithm, we fit these
per-star distance-reddening measurements to find the distances to the CO
velocity slices towards each star-forming region. This results in distance
estimates explicitly tied to the velocity structure of the molecular gas. We
determine distances to the B5, IC348, B1, NGC1333, L1448, and L1451
star-forming regions and find that individual clouds are located between
$\approx 275-300$ pc, with typical combined uncertainties of $\approx 5\%$. We
find that the velocity gradient across Perseus corresponds to a distance
gradient of about 25 pc, with the eastern portion of the cloud farther away
than the western portion. We determine an average distance to the complex of
$294\pm 17$ pc, about 60 pc higher than the distance derived to the western
portion of the cloud using parallax measurements of water masers associated
with young stellar objects. The method we present is not limited to the Perseus
Complex, but may be applied anywhere on the sky with adequate CO data in the
pursuit of more accurate 3D maps of molecular clouds in the solar neighborhood
and beyond.
