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 $1times10^{-2}, mathrm{mag}$ 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.
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