  AIMS :The thermodynamic and magnetic field structure of the solar photosphere
is analyzed by means of a novel 3-dimensional spectropolarimetric inversion and
reconstruction technique. METHODS : On the basis of high-resolution,
mixed-polarity magnetoconvection simulations, we used an artificial neural
network (ANN) model to approximate the nonlinear inverse mapping between
synthesized Stokes spectra and the underlying stratification of atmospheric
parameters like temperature, line-of-sight (LOS) velocity and LOS magnetic
field. This approach not only allows us to incorporate more reliable physics
into the inversion process, it also enables the inversion on an absolute
geometrical height scale, which allows the subsequent combination of individual
line-of-sight stratifications to obtain a complete 3-dimensional reconstruction
(tomography) of the observed area. RESULTS : The magnetoconvection simulation
data, as well as the ANN inversion, have been properly processed to be
applicable to spectropolarimetric observations from the Hinode satellite. For
the first time, we show 3-dimensional tomographic reconstructions (temperature,
LOS velocity, and LOS magnetic field) of a quiet sun region observed by Hinode.
The reconstructed area covers a field of approximately 12000 by 12000 km and a
height range of 510 km in the photosphere. An enormous variety of small and
large scale structures can be identified in the 3-D reconstructions. The
low-flux region (B_{mag} = 20G) we analyzed exhibits a number of "tube-like"
magnetic structures with field strengths of several hundred Gauss. Most of
these structures rapidly loose their strength with height and only a few larger
structures can retain a higher field strength to the upper layers of the
photosphere.
