  We present optical depth and temperature maps of the Perseus molecular cloud,
obtained combining dust emission data from the Herschel and Planck satellites
and 2MASS/NIR dust extinction maps. The maps have a resolution of 36 arcsec in
the Herschel regions, and of 5 arcmin elsewhere. The dynamic range of the
optical depth map ranges from $1\times10^{-2}\, \mathrm{mag}$ up to $20
\,\mathrm{mag}$ in the equivalent K band extinction. We also evaluate the ratio
between the $2.2 \,\mathrm{\mu m}$ extinction coefficient and the $850
\,\mathrm{\mu m}$ opacity. The value we obtain is close to the one found in the
Orion B molecular cloud. We show that the cumulative and the differential area
function of the data (which is proportional to the probability distribution
function of the cloud column density) follow power laws with index respectively
$\simeq -2$, and $\simeq -3$. We use WISE data to improve current YSO
catalogues based mostly on \emph{Spitzer} data and we build an up-to-date
selection of Class~I/0 objects. Using this selection, we evaluate the local
Schmidt law, $\Sigma_{\mathrm{YSO}} \propto \Sigma_{\mathrm{gas}}^{\beta}$,
showing that $\beta=2.4 \pm 0.6$. Finally, we show that the area-extinction
relation is important for determining the star formation rate in the cloud,
which is in agreement with other recent works.
