  We developed a Deep Convolutional Neural Network (CNN), used as a classifier,
to estimate photometric redshifts and associated probability distribution
functions (PDF) for galaxies in the Main Galaxy Sample of the Sloan Digital Sky
Survey at z < 0.4. Our method exploits all the information present in the
images without any feature extraction. The input data consist of 64x64 pixel
ugriz images centered on the spectroscopic targets, plus the galactic reddening
value on the line-of-sight. For training sets of 100k objects or more ($\geq$
20% of the database), we reach a dispersion $\sigma_{MAD}$<0.01, significantly
lower than the current best one obtained from another machine learning
technique on the same sample. The bias is lower than 0.0001, independent of
photometric redshift. The PDFs are shown to have very good predictive power. We
also find that the CNN redshifts are unbiased with respect to galaxy
inclination, and that $\sigma_{MAD}$ decreases with the signal-to-noise ratio
(SNR), achieving values below 0.007 for SNR >100, as in the deep stacked region
of Stripe 82. We argue that for most galaxies the precision is limited by the
SNR of SDSS images rather than by the method. The success of this experiment at
low redshift opens promising perspectives for upcoming surveys.
