We present a near-infrared extinction map of a large region (approximately 2200 deg^2) covering the Orion, the Monoceros R2, the Rosette, and the Canis Major molecular clouds. We used robust and optimal methods to map the dust column density in the near-infrared (NICER and NICEST) towards ~19 million stars of the Two Micron All Sky Survey (2MASS) point source catalog. Over the relevant regions of the field, we reached a 1-sigma error of 0.03 mag in the K-band extinction with a resolution of 3 arcmin. We measured the cloud distances by comparing the observed density of foreground stars with the prediction of galactic models, thus obtaining d_{Orion A} = (371 +/- 10) pc, d_{Orion B} = (398 +/- 12) pc, $d_{Mon R2} = (905 +/- 37) pc, $d_{Rosette} = (1330 +/- 48) pc, and $d_{CMa} = (1150 +/- 64) pc, values that compare very well with independent estimates.
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