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 \times 10 ^ { -2 } \mathrm { mag } up to 20 \mathrm { mag } in the equivalent K band extinction .
We also evaluate the ratio between the \SI 2.2 \um extinction coefficient and the \SI 850 \um 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 catalogs based mostly on 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 .